The genetic distance between two loci on a chromosome is defined as
the mean number of crossovers between the loci. The parameters of the crossover
distribution are constrained by the parameters of the distribution of
chiasmata. Ott (1996) derived the maximum likelihood estimator (MLE) of the
parameters of the crossover distribution and the MLE of the mean. We
demonstrate that the MLE of the mean is pointwise less than or equal to the
empirical mean number of crossovers. It follows that the MLE is negatively
biased. For small sample sizes the bias can be nonnegligible. We recommend
reduced bias estimators.
¶ Generalizations to many other problems involving linear constraints
on parameters are made. Included in the generalizations are a variety of
problems involving simplex constraints as studied recently by Liu (2000).
Publié le : 2002-02-14
Classification:
Crossovers,
chiasma,
maximum likelihood estimation,
order-restricted inference,
nonlinear programming,
92D10,
62F10
@article{1015362190,
author = {Cohen, Arthur and Kemperman, J.H.B. and Sackrowitz, Harold},
title = {On the bias in estimating genetic length and other quantities in
simplex constrained models},
journal = {Ann. Statist.},
volume = {30},
number = {1},
year = {2002},
pages = { 202-219},
language = {en},
url = {http://dml.mathdoc.fr/item/1015362190}
}
Cohen, Arthur; Kemperman, J.H.B.; Sackrowitz, Harold. On the bias in estimating genetic length and other quantities in
simplex constrained models. Ann. Statist., Tome 30 (2002) no. 1, pp. 202-219. http://gdmltest.u-ga.fr/item/1015362190/