Estimation of order-restricted means from correlated data

In many applications, researchers are interested in estimating the mean of a multivariate normal random vector whose components are subject to order restrictions. Various authors have demonstrated that the likelihood-based methodology may perform poorly under certain conditions for such problems. The problem is much harder when the underlying covariance matrix is nondiagonal. In this paper a simple iterative algorithm is introduced that can be used for estimating the mean of a multivariate normal population when the components are subject to any order restriction. The proposed methodology is illustrated through an application to human reproductive hormone data. Copyright 2005, Oxford University Press.

[1]  Shyamal D. Peddada,et al.  Gene Selection and Clustering for Time-course and Dose-response Microarray Experiments Using Order-restricted Inference , 2003, Bioinform..

[2]  Shyamal D. Peddada,et al.  Confidence Interval Estimation Subject to Order Restrictions , 1994 .

[3]  Chu-in Charles Lee,et al.  The Quadratic Loss of Isotonic Regression Under Normality , 1981 .

[4]  S. Peddada,et al.  Tests for Order Restrictions in Binary Data , 2001, Biometrics.

[5]  J. Rice,et al.  Smoothing spline models for the analysis of nested and crossed samples of curves , 1998 .

[6]  Properties of Likelihood Inference for Order Restricted Models , 2000 .

[7]  Stochastic reduction of loss in estimating normal means by isotonic regression , 1989 .

[8]  J. Kalbfleisch.  Statistical Inference Under Order Restrictions , 1975 .

[9]  D D Baird,et al.  Preimplantation urinary hormone profiles and the probability of conception in healthy women. , 1999, Fertility and sterility.

[10]  Chu-in Charles Lee.  Quadratic Loss of Order Restricted Estimators for Treatment Means with a Control , 1988 .

[11]  David B Dunson,et al.  A transformation approach for incorporating monotone or unimodal constraints. , 2005, Biostatistics.

[12]  J. C. Burkill.  A First Course in Mathematical Analysis , 1962 .

[13]  A. Cohen,et al.  A discussion of some inference issues in order restricted models , 2004 .

[14]  F. T. Wright,et al.  Order restricted statistical inference , 1988 .

[15]  Shyamal D. Peddada,et al.  Parameter Estimation in Linear Models with Heteroscedastic Variances Subject to Order Restrictions , 2002 .