@article{chang_genton_2007, title={Extreme value distributions for the skew-symmetric family of distributions}, volume={36}, ISSN={["0361-0926"]}, DOI={10.1080/03610920601126159}, abstractNote={We derive the extreme value distribution of the skew-symmetric family, the probability density function of the latter being defined as twice the product of a symmetric density and a skewing function. We show that, under certain conditions on the skewing function, this extreme value distribution is the same as that for the symmetric density. We illustrate our results using various examples of skew-symmetric distributions as well as two data sets.}, number={9-12}, journal={COMMUNICATIONS IN STATISTICS-THEORY AND METHODS}, author={Chang, Sheng-Mao and Genton, Marc G.}, year={2007}, pages={1705–1717} }
@article{wu_genton_stefanski_2006, title={A Multivariate two-sample mean test for small sample size and missing data}, volume={62}, ISSN={["0006-341X"]}, DOI={10.1111/j.1541-0420.2006.00533.x}, abstractNote={Summary We develop a new statistic for testing the equality of two multivariate mean vectors. A scaled chi‐squared distribution is proposed as an approximating null distribution. Because the test statistic is based on componentwise statistics, it has the advantage over Hotelling's T2 test of being applicable to the case where the dimension of an observation exceeds the number of observations. An appealing feature of the new test is its ability to handle missing data by relying on only componentwise sample moments. Monte Carlo studies indicate good power compared to Hotelling's T2 and a recently proposed test by Srivastava (2004, Technical Report, University of Toronto). The test is applied to drug discovery data.}, number={3}, journal={BIOMETRICS}, author={Wu, Yujun and Genton, Marc G. and Stefanski, Leonard A.}, year={2006}, month={Sep}, pages={877–885} }
@article{wang_genton_2006, title={The multivariate skew-slash distribution}, volume={136}, ISSN={["1873-1171"]}, DOI={10.1016/j.jspi.2004.06.023}, abstractNote={The slash distribution is often used as a challenging distribution for a statistical procedure. In this article, we define a skewed version of the slash distribution in the multivariate setting and derive several of its properties. The multivariate skew-slash distribution is shown to be easy to simulate from and can therefore be used in simulation studies. We provide various examples for illustration.}, number={1}, journal={JOURNAL OF STATISTICAL PLANNING AND INFERENCE}, author={Wang, J and Genton, MG}, year={2006}, month={Jan}, pages={209–220} }
@article{naveau_genton_shen_2005, title={A skewed Kalman filter}, volume={94}, ISSN={["0047-259X"]}, DOI={10.1016/j.jmva.2004.06.002}, abstractNote={The popularity of state-space models comes from their flexibilities and the large variety of applications they have been applied to. For multivariate cases, the assumption of normality is very prevalent in the research on Kalman filters. To increase the applicability of the Kalman filter to a wider range of distributions, we propose a new way to introduce skewness to state-space models without losing the computational advantages of the Kalman filter operations. The skewness comes from the extension of the multivariate normal distribution to the closed skew-normal distribution. To illustrate the applicability of such an extension, we present two specific state-space models for which the Kalman filtering operations are carefully described.}, number={2}, journal={JOURNAL OF MULTIVARIATE ANALYSIS}, author={Naveau, P and Genton, MG and Shen, XL}, year={2005}, month={Jun}, pages={382–400} }
@article{mitchell_genton_gumpertz_2005, title={Testing for separability of space-time covariances}, volume={16}, ISSN={["1099-095X"]}, DOI={10.1002/env.737}, abstractNote={AbstractSeparable space–time covariance models are often used for modeling in environmental sciences because of their computational benefits. Unfortunately, there are few formal statistical tests for separability. We adapt a likelihood ratio test based on multivariate repeated measures to the spatio–temporal context. We apply this test to an environmental monitoring data set. Copyright © 2005 John Wiley & Sons, Ltd.}, number={8}, journal={ENVIRONMETRICS}, author={Mitchell, MW and Genton, MG and Gumpertz, ML}, year={2005}, month={Dec}, pages={819–831} }
@article{wang_boyer_genton_2004, title={A skew-symmetric representation of multivariate distributions}, volume={14}, number={4}, journal={Statistica Sinica}, author={Wang, J. Z. and Boyer, J. and Genton, M. G.}, year={2004}, pages={1259–1270} }
@inbook{eyer_genton_2004, title={An astronomical distance determination method using regression with skew-normal errors}, ISBN={1584884312}, booktitle={Skew-elliptical distibutions and their applications: A journey beyond normality}, publisher={Boca Raton, FL: Chapman & Hall/CRC}, author={Eyer, L. and Genton, M. G.}, year={2004} }
@article{ma_genton_2004, title={Flexible class of skew-symmetric distributions}, volume={31}, number={3}, journal={Scandinavian Journal of Statistics: Theory and Applications}, author={Ma, Y. Y. and Genton, M. G.}, year={2004}, pages={459–468} }
@inbook{ma_genton_davidian_2004, title={Linear mixed effects models with flexible generalized skew-elliptical random effects}, ISBN={1584884312}, booktitle={Skew-elliptical distibutions and their applications: A journey beyond normality}, publisher={Boca Raton, FL: Chapman & Hall/CRC}, author={Ma, Y. Y. and Genton, M. G. and Davidian, M.}, year={2004} }
@article{genton_perrin_2004, title={On a time deformation reducing nonstationary stochastic processes to local stationarity}, volume={41}, ISSN={["1475-6072"]}, DOI={10.1239/jap/1077134681}, abstractNote={A stochastic process is locally stationary if its covariance function can be expressed as the product of a positive function multiplied by a stationary covariance. In this paper, we characterize nonstationary stochastic processes that can be reduced to local stationarity via a bijective deformation of the time index, and we give the form of this deformation under smoothness assumptions. This is an extension of the notion of stationary reducibility. We present several examples of nonstationary covariances that can be reduced to local stationarity. We also investigate the particular situation of exponentially convex reducibility, which can always be achieved for a certain class of separable nonstationary covariances.}, number={1}, journal={JOURNAL OF APPLIED PROBABILITY}, author={Genton, MG and Perrin, O}, year={2004}, month={Mar}, pages={236–249} }
@article{gorsich_genton_2004, title={On the discretization of nonparametric isotropic covariogram estimators}, volume={14}, ISSN={["1573-1375"]}, DOI={10.1023/B:STCO.0000021408.63640.d8}, number={2}, journal={STATISTICS AND COMPUTING}, author={Gorsich, DJ and Genton, MG}, year={2004}, month={Apr}, pages={99–108} }
@inbook{baloch_krim_genton_2004, title={Shape representation with flexible skew-symmetric distributions}, ISBN={1584884312}, DOI={10.1201/9780203492000.ch17}, booktitle={Skew-elliptical distibutions and their applications: A journey beyond normality}, publisher={Boca Raton, FL: Chapman & Hall/CRC}, author={Baloch, S. H. and Krim, H. and Genton, M. G.}, year={2004} }
@book{genton_2004, title={Skew-elliptical distibutions and their applications: A journey beyond normality}, publisher={Boca Raton: Chapman & Hall/CRC}, author={Genton, M. G.}, year={2004} }
@inbook{genton_2004, title={Skew-symmetric and generalized skew-elliptical distributions}, ISBN={1584884312}, booktitle={Skew-elliptical distibutions and their applications: A journey beyond normality}, publisher={Boca Raton, FL: Chapman & Hall/CRC}, author={Genton, M. G.}, year={2004} }
@article{luna_genton_2004, title={Spatio-temporal autoregressive models for US unemployment rate}, volume={18}, ISBN={["0-7623-1148-7"]}, ISSN={["0731-9053"]}, DOI={10.1016/S0731-9053(04)18009-2}, abstractNote={We analyze spatio-temporal data on U.S. unemployment rates. For this purpose, we present a family of models designed for the analysis and time-forward prediction of spatio-temporal econometric data. Our model is aimed at applications with spatially sparse but temporally rich data, i.e. for observations collected at few spatial regions, but at many regular time intervals. The family of models utilized does not make spatial stationarity assumptions and consists in a vector autoregressive (VAR) specification, where there are as many time series as spatial regions. A model building strategy is used that takes into account the spatial dependence structure of the data. Model building may be performed either by displaying sample partial correlation functions, or automatically with an information criterion. Monthly data on unemployment rates in the nine census divisions of the U.S. are analyzed. We show with a residual analysis that our autoregressive model captures the dependence structure of the data better than with univariate time series modeling.}, journal={SPATIAL AND SPATIOTEMPORAL ECONOMETRICS}, author={Luna, X and Genton, MG}, year={2004}, pages={279–294} }
@inbook{naveau_genton_ammann_2004, title={Time series analysis with a skewed Kalman filter}, ISBN={1584884312}, booktitle={Skew-elliptical distibutions and their applications: A journey beyond normality}, publisher={Boca Raton, FL: Chapman & Hall/CRC}, author={Naveau, P. and Genton, M. G. and Ammann, C.}, year={2004} }
@article{wang_boyer_genton_2004, title={A note on an equivalence between chi-square and generalized skew-normal distributions}, volume={66}, ISSN={["0167-7152"]}, DOI={10.1016/j.spl.2003.11.006}, abstractNote={In this note, we establish an equivalence between chi-square and generalized skew-normal distributions. This result is based on a distributional invariance property of even functions in generalized skew-normal random vectors. It extends the chi-square properties related to univariate and multivariate skew-normal distributions.}, number={4}, journal={STATISTICS & PROBABILITY LETTERS}, author={Wang, JZ and Boyer, J and Genton, MG}, year={2004}, month={Mar}, pages={395–398} }
@article{genton_lucas_2003, title={Comprehensive definitions of breakdown points for independent and dependent observations}, volume={65}, number={2003}, journal={Journal of the Royal Statistical Society. Series B, Methodological}, author={Genton, M. G. and Lucas, A.}, year={2003}, pages={81–94} }
@article{genton_ronchetti_2003, title={Robust indirect inference}, volume={98}, ISSN={["0162-1459"]}, DOI={10.1198/016214503388619102}, abstractNote={In this article we develop robust indirect inference for a variety of models in a unified framework. We investigate the local robustness properties of indirect inference and derive the influence function of the indirect estimator, as well as the level and power influence functions of indirect tests. These tools are then used to design indirect inference procedures that are stable in the presence of small deviations from the assumed model. Although indirect inference was originally proposed for statistical models whose likelihood is difficult or even impossible to compute and/or to maximize, we use it here as a device to robustify the estimators and tests for models where this is not possible or is difficult with classical techniques such as M estimators. Examples from financial applications, time series, and spatial statistics are used for illustration.}, number={461}, journal={JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION}, author={Genton, MG and Ronchetti, E}, year={2003}, month={Mar}, pages={67–76} }
@article{ehm_genton_gneiting_2003, title={Stationary covariances associated with exponentially convex functions}, volume={9}, ISSN={["1350-7265"]}, DOI={10.3150/bj/1066223271}, abstractNote={We establish a bijection between exponentially convex functions and entire positive definite functions, and extend Loeve's construction of stochastic processes associated with them. As an application, we derive parametric covariance models for locally stationary random fields.}, number={4}, journal={BERNOULLI}, author={Ehm, W and Genton, MG and Gneiting, T}, year={2003}, month={Aug}, pages={607–615} }
@article{genton_gorsich_2002, title={Nonparametric variogram and covariogram estimation with Fourier-Bessel matrices}, volume={41}, ISSN={["1872-7352"]}, DOI={10.1016/S0167-9473(02)00062-2}, abstractNote={The nonparametric estimation of variograms and covariograms for isotropic stationary spatial stochastic processes is considered. It is shown that Fourier–Bessel matrices play an important role in this context because they provide an orthogonal discretization of the spectral representation of positive definite functions. Their properties are investigated and an example from a simulated two-dimensional spatial process is provided. It is shown that this approach provides a smooth and positive definite nonparametric estimator in the continuum, whereas previous methods typically suffer from spurious oscillations. A practical example from Astronomy is used for illustration.}, number={1}, journal={COMPUTATIONAL STATISTICS & DATA ANALYSIS}, author={Genton, MG and Gorsich, DJ}, year={2002}, month={Nov}, pages={47–57} }
@article{de luna_genton_2002, title={Simulation-based inference for simultaneous processes on regular lattices}, volume={12}, number={2}, journal={Statistics and Computing}, author={De Luna, X. and Genton, M. G.}, year={2002}, pages={125–134} }
@article{de luna_genton_2001, title={Robust simulation-based estimation of ARMA models}, volume={10}, ISSN={["1061-8600"]}, DOI={10.1198/10618600152628347}, abstractNote={This article proposes a new approach to the robust estimation of a mixed autoregressive and moving average (ARMA) model. It is based on the indirect inference method that originally was proposed for models with an intractable likelihood function. The estimation algorithm proposed is based on an auxiliary autoregressive representation whose parameters are first estimated on the observed time series and then on data simulated from the ARMA model. To simulate data the parameters of the ARMA model have to be set. By varying these we can minimize a distance between the simulation-based and the observation-based auxiliary estimate. The argument of the minimum yields then an estimator for the parameterization of the ARMA model. This simulation-based estimation procedure inherits the properties of the auxiliary model estimator. For instance, robustness is achieved with GM estimators. An essential feature of the introduced estimator, compared to existing robust estimators for ARMA models, is its theoretical tractability that allows us to show consistency and asymptotic normality. Moreover, it is possible to characterize the influence function and the breakdown point of the estimator. In a small sample Monte Carlo study it is found that the new estimator performs fairly well when compared with existing procedures. Furthermore, with two real examples, we also compare the proposed inferential method with two different approaches based on outliers detection.}, number={2}, journal={JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS}, author={De Luna, X and Genton, MG}, year={2001}, month={Jun}, pages={370–387} }
@article{genton_2002, title={Classes of kernels for machine learning: A statistics perspective}, volume={2}, ISSN={["1532-4435"]}, DOI={10.1162/15324430260185646}, number={2}, journal={JOURNAL OF MACHINE LEARNING RESEARCH}, author={Genton, MG}, year={2002}, pages={299–312} }