@article{boos_duan_2022, title={Pairwise comparisons using ranks in block designs}, ISSN={["1532-415X"]}, DOI={10.1080/03610926.2022.2151310}, abstractNote={Friedman’s rank test and the associated aligned rank test are the standard rank alternatives to the classical linear models F statistic for the randomized complete block design (RCBD). However, in current practice there are no good rank alternatives to the Tukey–Kramer all pairwise comparisons procedure for the normal linear model. For example, the standard rank method found in Section 7.3 of Hollander et al. [John Wiley & Sons, Inc., Hoboken, New Jersey; 2014] is based on the permutation distribution under the complete null of no differences and thus cannot strongly control the family-wise error rate (FWER). It also has low power. However, we show that the closed method introduced by Marcus et al. [Biometrika 63 (3);1976:655–60] applied to aligned ranks has strong FWER control and good power compared to the Tukey–Kramer method for long-tailed error distributions.}, journal={COMMUNICATIONS IN STATISTICS-THEORY AND METHODS}, author={Boos, Dennis and Duan, Kaiyuan}, year={2022}, month={Nov} } @article{boos_duan_2021, title={Pairwise Comparisons Using Ranks in the One-Way Model}, volume={75}, ISSN={["1537-2731"]}, DOI={10.1080/00031305.2020.1860819}, abstractNote={Abstract The Wilcoxon rank sum test for two independent samples and the Kruskal–Wallis rank test for the one-way model with k independent samples are very competitive robust alternatives to the two-sample t-test and k-sample F-test when the underlying data have tails longer than the normal distribution. However, these positives for rank methods do not extend as readily to methods for making all pairwise comparisons used to reveal where the differences in location may exist. Here, we show that the closed method of Marcus et al. applied to ranks is quite powerful for both small and large samples and better than any methods suggested in the list of applied nonparametric texts found in the recent study by Richardson. In addition, we show that the closed method applied to means is even more powerful than the classical Tukey–Kramer method applied to means, which itself is very competitive for nonnormal data with moderately long tails and small samples.}, number={4}, journal={AMERICAN STATISTICIAN}, author={Boos, Dennis D. and Duan, Siyu}, year={2021}, month={Oct}, pages={414–423} } @article{boos_duan_liu_2021, title={Pairwise comparisons for Levene-style variability parameters}, ISSN={["1532-4141"]}, DOI={10.1080/03610918.2021.1887230}, abstractNote={Abstract The simplest way to test for equality of scale in one-way data is to use the analysis of variance applied to absolute deviations from sample medians in place of the original data. This approach started by Levene (1960, using means instead of medians), appears in most statistical packages and is quite powerful for detecting heterogeneity of scale. However, researchers often want to know where the differences lie and some measure of effect for those differences. Here, the Closed Method of pairwise comparisons combined with F statistics on the absolute deviations is shown to be an excellent method for detecting differences. In addition, the Bonferroni method is combined with pairwise t-statistics to construct confidence intervals for pairwise differences in scale.}, journal={COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION}, author={Boos, Dennis D. and Duan, Kaiyuan and Liu, Xiaoni}, year={2021}, month={Feb} } @article{cowger_smith_boos_bradley_ransom_bergstrom_2020, title={Managing a Destructive, Episodic Crop Disease: A National Survey of Wheat and Barley Growers' Experience With Fusarium Head Blight}, volume={104}, ISSN={["1943-7692"]}, url={https://doi.org/10.1094/PDIS-10-18-1803-SR}, DOI={10.1094/PDIS-10-18-1803-SR}, abstractNote={ The main techniques for minimizing Fusarium head blight (FHB, or scab) and deoxynivalenol in wheat and barley are well established and generally available: planting of moderately FHB-resistant cultivars, risk monitoring, and timely use of the most effective fungicides. Yet the adoption of these techniques remains uneven across the FHB-prone portions of the U.S. cereal production area. A national survey was undertaken by the U.S. Wheat and Barley Scab Initiative in 17 states where six market classes of wheat and barley are grown. In 2014, 5,107 usable responses were obtained. The highest percentages reporting losses attributable to FHB in the previous 5 years were in North Dakota, Maryland, Kentucky, and states bordering the Great Lakes but across all states, ≥75% of respondents reported no FHB-related losses in the previous 5 years. Adoption of cultivar resistance was uneven by state and market class and was low except among hard red spring wheat growers. In 13 states, a majority of respondents had not applied an FHB-targeted fungicide in the previous 5 years. Although the primary FHB information source varied by state, crop consultants were considered to be an important source or their primary source of information on risk or management of FHB by the largest percentage of respondents. Use of an FHB risk forecasting website was about twice as high in North Dakota as the 17-state average of 6%. The most frequently cited barriers to adopting FHB management practices were weather or logistics preventing timely fungicide application, difficulty in determining flowering timing for fungicide applications, and the impracticality of FHB-reducing rotations. The results highlight the challenges of managing an episodically damaging crop disease and point to specific areas for improvement. }, number={3}, journal={PLANT DISEASE}, publisher={Scientific Societies}, author={Cowger, Christina and Smith, Joy and Boos, Dennis and Bradley, Carl A. and Ransom, Joel and Bergstrom, Gary C.}, year={2020}, month={Mar}, pages={634–648} } @article{green_brownie_boos_lu_krucoff_2016, title={Maximum likelihood estimation of time to first event in the presence of data gaps and multiple events}, volume={25}, ISSN={["1477-0334"]}, DOI={10.1177/0962280212466089}, abstractNote={ We propose a novel likelihood method for analyzing time-to-event data when multiple events and multiple missing data intervals are possible prior to the first observed event for a given subject. This research is motivated by data obtained from a heart monitor used to track the recovery process of subjects experiencing an acute myocardial infarction. The time to first recovery, T1, is defined as the time when the ST-segment deviation first falls below 50% of the previous peak level. Estimation of T1 is complicated by data gaps during monitoring and the possibility that subjects can experience more than one recovery. If gaps occur prior to the first observed event, T, the first observed recovery may not be the subject’s first recovery. We propose a parametric gap likelihood function conditional on the gap locations to estimate T1. Standard failure time methods that do not fully utilize the data are compared to the gap likelihood method by analyzing data from an actual study and by simulation. The proposed gap likelihood method is shown to be more efficient and less biased than interval censoring and more efficient than right censoring if data gaps occur early in the monitoring process or are short in duration. }, number={2}, journal={STATISTICAL METHODS IN MEDICAL RESEARCH}, author={Green, Cynthia L. and Brownie, Cavell and Boos, Dennis D. and Lu, Jye-Chyi and Krucoff, Mitchell W.}, year={2016}, month={Apr}, pages={775–792} } @article{boos_osborne_2015, title={Assessing Variability of Complex Descriptive Statistics in Monte Carlo Studies Using Resampling Methods}, volume={83}, ISSN={["1751-5823"]}, DOI={10.1111/insr.12087}, abstractNote={Summary}, number={2}, journal={INTERNATIONAL STATISTICAL REVIEW}, author={Boos, Dennis D. and Osborne, Jason A.}, year={2015}, month={Aug}, pages={228–238} } @book{boos_stefanski_2013, title={Essential statistical inference: Theory and methods}, publisher={New York: Springer}, author={Boos, D. D. and Stefanski, L. A.}, year={2013} } @article{tamura_huang_boos_2012, title={Authors' Reply}, volume={31}, ISSN={0277-6715}, url={http://dx.doi.org/10.1002/sim.5360}, DOI={10.1002/sim.5360}, abstractNote={We thank Dr. Berger for the interest in our article and for pointing out the similarity between the sequential parallel design and the three-phase design published earlier. Both designs are enriched clinical trials where the enrichment is based on the subpopulation of placebo non-responders for the sequential parallel design and on the subpopulation of drug responders for the three-phase design. Dr. Berger brings up the issue of exact tests for these enriched trials with several phases and notes the problem with deciding what to permute and what margins to fix. An alternative approach to constructing exact tests is to condition on the sufficient statistic for the nuisance parameters under the null hypothesis. For the sequential parallel design, the nuisance parameters are p1 D P (drug response in phase 1) and p2 D P (drug response in phase 2 j placebo non-response in phase 1). Under the null hypothesis, the sufficient statistic S D (total responses in phase 1, total placebo responses in phase 1, total responses in phase 2). For a test statistic T , the conditional distribution of T given S does not depend on the nuisance parameters, and therefore, exact p-values can be calculated. However, conditioning on both the total responses in phase 1 and the total placebo responses in phase 1 means that we are also conditioning on the drug responses in phase 1. Thus, all the power from the phase 1 data would be conditioned away using this approach. For example, consider a test statistic built on a linear combination of phases 1 and 2 estimated treatment differences as proposed in Huang and Tamura [1]. The conditional distribution of the test statistic would be based on outcomes with the estimated difference from phase 1 held fixed. So, for the actual test statistic to appear large relative to this conditional distribution, the estimated difference from phase 2 would have to provide all of the evidence. A second approach for exact tests for the sequential parallel design is to eliminate the nuisance parameters by taking the supremum over the nuisance parameter space. The exact p-value is then the tail probability maximized over all possible values for the nuisance parameters or restricted to a confidence set as in Berger and Boos [2]. Finally, because there are two nuisance parameters, one could use a mixed approach in which one of the nuisance parameters is eliminated by conditioning and the other eliminated by taking the supremum over the relevant parameter space. That mixed approach is quite feasible here, because conditioning on S D (total placebo responses in phase 1, total responses in phase 2) leads to a conditional distribution that depends only on p1 through the binomial distribution of the drug responses in phase 2. Although conditioning on the full sufficient statistic is unsatisfactory, it is an open question on which of the latter approaches would be preferred with regard to conservatism of level, power, and computational feasibility. We might add that the score statistics proposed by Huang and Tamura [1] and Ivanova et al. [3] had type I error probabilities close to the nominal rate even for sample sizes as low as nD 50, suggesting that exact tests may not be necessary in many settings.}, number={29}, journal={Statistics in Medicine}, publisher={Wiley}, author={Tamura, Roy N. and Huang, Xiaohong and Boos, Dennis}, year={2012}, month={Nov}, pages={4143–4144} } @misc{tamura_huang_boos_2012, title={Two-stage randomized trials: Outstanding issues Authors' Reply}, volume={31}, number={29}, journal={Statistics in Medicine}, author={Tamura, R. N. and Huang, X. H. and Boos, D.}, year={2012}, pages={4143–4144} } @article{tamura_huang_boos_2011, title={Estimation of treatment effect for the sequential parallel design}, volume={30}, ISSN={["0277-6715"]}, DOI={10.1002/sim.4412}, abstractNote={The sequential parallel clinical trial is a novel clinical trial design being used in psychiatric diseases that are known to have potentially high placebo response rates. The design consists of an initial parallel trial of placebo versus drug augmented by a second parallel trial of placebo versus drug in the placebo non‐responders from the initial trial. Statistical research on the design has focused on hypothesis tests. However, an equally important output from any clinical trial is the estimate of treatment effect and variability around that estimate. In the sequential parallel trial, the most important treatment effect is the effect in the overall population. This effect can be estimated by considering only the first phase of the trial, but this ignores useful information from the second phase of the trial. We develop estimates of treatment effect that incorporate data from both phases of the trial. Our simulations and a real data example suggest that there can be substantial gains in precision by incorporating data from both phases. The potential gains appear to be greatest in moderate‐sized trials, which would typically be the case in phase II trials. Copyright © 2011 John Wiley & Sons, Ltd.}, number={30}, journal={STATISTICS IN MEDICINE}, author={Tamura, Roy N. and Huang, Xiaohong and Boos, Dennis D.}, year={2011}, month={Dec}, pages={3496–3506} } @article{crews_boos_stefanski_2011, title={FSR methods for second-order regression models}, volume={55}, ISSN={["0167-9473"]}, DOI={10.1016/j.csda.2011.01.009}, abstractNote={Most variable selection techniques focus on first-order linear regression models. Often, interaction and quadratic terms are also of interest, but the number of candidate predictors grows very fast with the number of original predictors, making variable selection more difficult. Forward selection algorithms are thus developed that enforce natural hierarchies in second-order models to control the entry rate of uninformative effects and to equalize the false selection rates from first-order and second-order terms. Method performance is compared through Monte Carlo simulation and illustrated with data from a Cox regression and from a response surface experiment.}, number={6}, journal={COMPUTATIONAL STATISTICS & DATA ANALYSIS}, author={Crews, Hugh B. and Boos, Dennis D. and Stefanski, Leonard A.}, year={2011}, month={Jun}, pages={2026–2037} } @article{boos_stefanski_2011, title={P-Value Precision and Reproducibility}, volume={65}, ISSN={["0003-1305"]}, DOI={10.1198/tas.2011.10129}, abstractNote={P-values are useful statistical measures of evidence against a null hypothesis. In contrast to other statistical estimates, however, their sample-to-sample variability is usually not considered or estimated, and therefore not fully appreciated. Via a systematic study of log-scale p-value standard errors, bootstrap prediction bounds, and reproducibility probabilities for future replicate p-values, we show that p-values exhibit surprisingly large variability in typical data situations. In addition to providing context to discussions about the failure of statistical results to replicate, our findings shed light on the relative value of exact p-values vis-a-vis approximate p-values, and indicate that the use of *, **, and *** to denote levels 0.05, 0.01, and 0.001 of statistical significance in subject-matter journals is about the right level of precision for reporting p-values when judged by widely accepted rules for rounding statistical estimates.}, number={4}, journal={AMERICAN STATISTICIAN}, author={Boos, Dennis D. and Stefanski, Leonard A.}, year={2011}, month={Nov}, pages={213–221} } @misc{boos_hoffman_kringle_zhang_2009, title={Comment on 'New confidence bounds for QT studies' REPLY}, volume={28}, number={23}, journal={Statistics in Medicine}, author={Boos, D. D. and Hoffman, D. and Kringle, R. and Zhang, J.}, year={2009}, pages={2938–2940} } @article{boos_stefanski_wu_2009, title={Fast FSR Variable Selection with Applications to Clinical Trials}, volume={65}, ISSN={["1541-0420"]}, DOI={10.1111/j.1541-0420.2008.01127.x}, abstractNote={Summary A new version of the false selection rate variable selection method of Wu, Boos, and Stefanski (2007, Journal of the American Statistical Association 102, 235–243) is developed that requires no simulation. This version allows the tuning parameter in forward selection to be estimated simply by hand calculation from a summary table of output even for situations where the number of explanatory variables is larger than the sample size. Because of the computational simplicity, the method can be used in permutation tests and inside bagging loops for improved prediction. Illustration is provided in clinical trials for linear regression, logistic regression, and Cox proportional hazards regression.}, number={3}, journal={BIOMETRICS}, author={Boos, Dennis D. and Stefanski, Leonard A. and Wu, Yujun}, year={2009}, month={Sep}, pages={692–700} } @article{wang_stefanski_genton_boos_2009, title={Robust time series analysis via measurement error modeling}, volume={19}, number={3}, journal={Statistica Sinica}, author={Wang, Q. and Stefanski, L. A. and Genton, M. G. and Boos, D. D.}, year={2009}, pages={1263–1280} } @article{wu_boos_stefanski_2007, title={Controlling variable selection by the addition of pseudovariables}, volume={102}, ISSN={["1537-274X"]}, DOI={10.1198/016214506000000843}, abstractNote={We propose a new approach to variable selection designed to control the false selection rate (FSR), defined as the proportion of uninformative variables included in selected models. The method works by adding a known number of pseudovariables to the real dataset, running a variable selection procedure, and monitoring the proportion of pseudovariables falsely selected. Information obtained from bootstrap-like replications of this process is used to estimate the proportion of falsely selected real variables and to tune the selection procedure to control the FSR.}, number={477}, journal={JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION}, author={Wu, Yujun and Boos, Dennis D. and Stefanski, Leonard A.}, year={2007}, month={Mar}, pages={235–243} } @article{boos_hoffman_kringle_zhang_2007, title={New confidence bounds for QT studies}, volume={26}, ISSN={["0277-6715"]}, DOI={10.1002/sim.2826}, abstractNote={Abstract}, number={20}, journal={STATISTICS IN MEDICINE}, author={Boos, Dennis D. and Hoffman, David and Kringle, Robert and Zhang, Ji}, year={2007}, month={Sep}, pages={3801–3817} } @article{luo_stefanski_boos_2006, title={Tuning variable selection procedures by adding noise}, volume={48}, DOI={10.1198/004017005000000319}, abstractNote={Many variable selection methods for linear regression depend critically on tuning parameters that control the performance of the method, for example, “entry” and “stay” significance levels in forward and backward selection. However, most methods do not adapt the tuning parameters to particular datasets. We propose a general strategy for adapting variable selection tuning parameters that effectively estimates the tuning parameters so that the selection method avoids overfitting and underfitting. The strategy is based on the principle that overfitting and underfitting can be directly observed in estimates of the error variance after adding controlled amounts of additional independent noise to the response variable, then running a variable selection method. It is related to the simulation technique SIMEX found in the measurement error literature. We focus on forward selection because of its simplicity and ability to handle large numbers of explanatory variables. Monte Carlo studies show that the new method compares favorably with established methods.}, number={2}, journal={Technometrics}, author={Luo, X. H. and Stefanski, L. A. and Boos, D. D.}, year={2006}, pages={165–175} } @article{johnson_boos_2005, title={A note on the use of kernel functions in weighted estimators}, volume={72}, ISSN={["1879-2103"]}, DOI={10.1016/j.spl.2005.02.007}, abstractNote={We focus on the use of kernel-type functions in estimators for causal mean parameters in a nondynamic treatment regime setting, where treatment regime is a function of a continuous random variable. We explore the asymptotic properties of such estimators when the usual parametric modeling assumptions for the propensity score are made.}, number={4}, journal={STATISTICS & PROBABILITY LETTERS}, author={Johnson, BA and Boos, DD}, year={2005}, month={May}, pages={345–355} } @article{fuentes_boos_2005, title={Special issue - Environmental and health statistics}, volume={16}, ISSN={["1180-4009"]}, DOI={10.1002/env.711}, abstractNote={EnvironmetricsVolume 16, Issue 5 p. 421-421 Editorial Editorial Montserrat Fuentes, Montserrat Fuentes Profs. North Carolina State University, Raleigh, N.C., U.S.A.Search for more papers by this authorDennis D. Boos, Dennis D. Boos North Carolina State University, Raleigh, N.C., U.S.A.Search for more papers by this author Montserrat Fuentes, Montserrat Fuentes Profs. North Carolina State University, Raleigh, N.C., U.S.A.Search for more papers by this authorDennis D. Boos, Dennis D. Boos North Carolina State University, Raleigh, N.C., U.S.A.Search for more papers by this author First published: 27 June 2005 https://doi.org/10.1002/env.711AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL No abstract is available for this article. Volume16, Issue5Special Issue: Environmental and Health StatisticsAugust 2005Pages 421-421 RelatedInformation}, number={5}, journal={ENVIRONMETRICS}, author={Fuentes, M and Boos, DD}, year={2005}, month={Aug}, pages={421–421} } @article{isik_boos_li_2005, title={The distribution of genetic parameter estimates and confidence intervals from small disconnected diallels}, volume={110}, ISSN={["1432-2242"]}, DOI={10.1007/s00122-005-1957-0}, abstractNote={The distributions of genetic variance components and their ratios (heritability and type-B genetic correlation) from 105 pairs of six-parent disconnected half-diallels of a breeding population of loblolly pine (Pinus taeda L.) were examined. A series of simulations based on these estimates were carried out to study the coverage accuracy of confidence intervals based on the usual t-method and several other alternative methods. Genetic variance estimates fluctuated greatly from one experiment to another. Both general combining ability variance (sigma(2) (g)) and specific combining ability variance (sigma(2) (s)) had a large positive skewness. For sigma(2) (g) and sigma(2) (s), a skewness-adjusted t-method proposed by Boos and Hughes-Oliver (Am Stat 54:121-128, 2000) provided better upper endpoint confidence intervals than t-intervals, whereas they were similar for the lower endpoint. Bootstrap BCa-intervals (Efron and Tibshirani, An introduction to the bootstrap. Chapman & Hall, London 436 p, 1993) and Hall's transformation methods (Zhou and Gao, Am Stat 54:100-104, 2000) had poor coverages. Coverage accuracy of Fieller's interval endpoint(J R Stat Soc Ser B 16:175-185, 1954) and t-interval endpoint were similar for both h(2) and r(B) for sample sizes n3.3.CO;2-V}, abstractNote={Studies of biological variables such as those based on blood chemistry often have measurements taken over time at closely spaced intervals for groups of individuals. Natural scientific questions may then relate to the first time that the underlying population curve crosses a threshold (onset) and to how long it stays above the threshold (duration). In this paper we give general confidence regions for these population quantities. The regions are based on the intersection-union principle and may be applied to totally nonparametric, semiparametric, or fully parametric models where level-α tests exist pointwise at each time point. A key advantage of the approach is that no modeling of the correlation over time is required.}, number={5}, journal={BIOMETRICAL JOURNAL}, author={Berger, RL and Boos, DD}, year={1999}, pages={517–531} } @article{boos_hughes-oliver_1998, title={Applications of Basu's theorem}, volume={52}, ISSN={["0003-1305"]}, DOI={10.2307/2685927}, number={3}, journal={AMERICAN STATISTICIAN}, author={Boos, DD and Hughes-Oliver, JM}, year={1998}, month={Aug}, pages={218–221} } @article{zhang_boos_1997, title={Mantel-Haenszel test statistics for correlated binary data}, volume={53}, ISSN={["0006-341X"]}, DOI={10.2307/2533489}, abstractNote={This paper proposes two new Mantel-Haenszel test statistics for correlated binary data in 2 x 2 tables that are asymptotically valid in both sparse data (many strata) and large-strata limiting models. Monte Carlo experiments show that the statistics compare favorably to previously proposed test statistics, especially for 5-25 small to moderate-sized strata. Confidence intervals are also obtained and compared to those from the test of Liang (1985, Biometrika 72, 678-682).}, number={4}, journal={BIOMETRICS}, author={Zhang, J and Boos, DD}, year={1997}, month={Dec}, pages={1185–1198} } @article{hudson_boos_kaplan_1992, title={A statistical test for detecting geographic subdivision}, volume={9}, number={1}, journal={Molecular Biology and Evolution}, author={Hudson, R. R. and Boos, D. D. and Kaplan, N. L.}, year={1992}, pages={138–151} } @article{boos_1985, title={A CONVERSE TO SCHEFFE THEOREM}, volume={13}, ISSN={["0090-5364"]}, DOI={10.1214/aos/1176346604}, abstractNote={Convergence of densities implies convergence of their distribution functions via Scheffe's theorem. This paper is concerned with the converse: what are sufficient conditions to obtain convergence of densities from convergence of distribution functions? A general lemma is given and local limit results are obtained for translation and scale statistics.}, number={1}, journal={ANNALS OF STATISTICS}, author={BOOS, DD}, year={1985}, pages={423–427} } @article{boos_serfling_1980, title={A NOTE OF DIFFERENTIALS AND THE CLT AND LIL FOR STATISTICAL FUNCTIONS, WITH APPLICATION TO M-ESTIMATES}, volume={8}, ISSN={["0090-5364"]}, DOI={10.1214/aos/1176345012}, abstractNote={A parameter expressed as a functional $T(F)$ of a distribution function (df) $F$ may be estimated by the "statistical function" $T(F_n)$ based on the sample df $F_n$. For analysis of the estimation error $T(F_n) - T(F)$, we adapt the differential approach of von Mises (1947) to exploit stochastic properties of the Kolmogorov-Smirnov distance $\sup_x|F_n(x) - F(x)|$. This leads directly to the central limit theorem (CLT) and law of the iterated logarithm (LIL) for $T(F_n) - T(F)$. The adaptation also incorporates innovations designed to broaden the scope of statistical application of the concept of differential. Application to a wide class of robust-type $M$-estimates is carried out.}, number={3}, journal={ANNALS OF STATISTICS}, author={BOOS, DD and SERFLING, RJ}, year={1980}, pages={618–624} } @article{boos_1979, title={DIFFERENTIAL FOR L-STATISTICS}, volume={7}, ISSN={["0090-5364"]}, DOI={10.1214/aos/1176344781}, abstractNote={Abstract : The asymptotic normality result is competitive with one closely related statistic S sub n = Sum from i=(1 to n) of (c wiggle sub in)(X sub in) obtained under stronger conditions on J but a slightly milder condition on F. However, in addition to asymptotic normality of T(F sub n), the differential approach of the present paper yields characterization of the almost sure behavior of T(F sub n) and lends itself to straightforward extension to the case of dependent variables.}, number={5}, journal={ANNALS OF STATISTICS}, author={BOOS, DD}, year={1979}, pages={955–959} }