Open Access
February 2002 On the bias in estimating genetic length and other quantities in simplex constrained models
Arthur Cohen, J.H.B. Kemperman, Harold Sackrowitz
Ann. Statist. 30(1): 202-219 (February 2002). DOI: 10.1214/aos/1015362190


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).


Download Citation

Arthur Cohen. J.H.B. Kemperman. Harold Sackrowitz. "On the bias in estimating genetic length and other quantities in simplex constrained models." Ann. Statist. 30 (1) 202 - 219, February 2002.


Published: February 2002
First available in Project Euclid: 5 March 2002

zbMATH: 1012.62114
MathSciNet: MR1892661
Digital Object Identifier: 10.1214/aos/1015362190

Primary: 62F10 , 92D10

Keywords: chiasma , Crossovers , maximum likelihood estimation , nonlinear programming , order-restricted inference

Rights: Copyright © 2002 Institute of Mathematical Statistics

Vol.30 • No. 1 • February 2002
Back to Top