TY - JOUR
TI - ESTIMATION OF LINKAGE DISEQUILIBRIUM IN RANDOMLY MATING POPULATIONS
AU - WEIR, BS
AU - COCKERHAM, CC
T2 - HEREDITY
AB - The maximum likelihood method for estimating linkage disequilibrium from genotypic data for randomly mating populations is studied. Instead of iterative methods for finding a root of the cubic equation for one of the gametic frequencies (Hill, 1974), it is recommended that the cubic be solved completely. For data with some missing genotypic classes, it is further recommended that explicit solutions for the cubic be used.
DA - 1979///
PY - 1979///
DO - 10.1038/hdy.1979.10
VL - 42
IS - FEB
SP - 105-111
SN - 0018-067X
ER -
TY - JOUR
TI - DIFFERENTIAL FOR L-STATISTICS
AU - BOOS, DD
T2 - ANNALS OF STATISTICS
AB - The functional $T(F) = \int F^{-1}(t)J(t) dt$ associated with linear combinations of order statistics is shown to have a Frechet-type differential. As a corollary, the statistic $T(F_n)$ obtained by evaluating $T(\cdot)$ at the sample df $F_n$ is seen to be asymptotically normal and to obey a law of the iterated logarithm.
DA - 1979///
PY - 1979///
DO - 10.1214/aos/1176344781
VL - 7
IS - 5
SP - 955-959
SN - 0090-5364
ER -
TY - JOUR
TI - INFERENCES ABOUT LINKAGE DISEQUILIBRIUM
AU - WEIR, BS
T2 - BIOMETRICS
AB - Existing theory for inferences about linkage disequilibrium is restricted to a measure defined on gametic frequencies. Unless gametic frequencies are directly observable, they are inferred from genotypic frequencies under the assumption of random union of gametes. Primary emphasis in this paper is given to genotypic data, and disequilibrium coefficients are defined for all subsets of two or more of the four genes, two at each of two loci, carried by an individual. Linkage disequilibrium coefficients are defined for genes within and between gametes, and methods of estimating and testing these coefficients are given for gametic data. For genotypic data, when coupling and repulsion double heterozygotes cannot be distinguished. Burrows' composite measure of linkage disequilibrium is discussed. In particular, the estimate for this measure and hypothesis tests based on it are compared to the usual maximum likelihood estimate of gametic linkage disequilibrium, and corresponding likelihood ratio or contingency chi-square tests. General use of the composite measure, whether or not random union of gametes is an appropriate assumption, is recommended. Attention is given to small samples, where the non-normality of gene frequencies will have greatest effect on methods of inference based on normal theory. Even tools such as Fisher's z-transformation for the correlation of gene frequencies are found to perform quite satisfactorily.
DA - 1979///
PY - 1979///
DO - 10.2307/2529947
VL - 35
IS - 1
SP - 235-254
SN - 0006-341X
ER -
TY - JOUR
TI - DISTRIBUTION OF THE ESTIMATORS FOR AUTOREGRESSIVE TIME-SERIES WITH A UNIT ROOT
AU - DICKEY, DA
AU - FULLER, WA
T2 - JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
DA - 1979///
PY - 1979///
DO - 10.2307/2286348
VL - 74
IS - 366
SP - 427-431
SN - 1537-274X
ER -