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Biases of the maximum likelihood and Cohen-Sackrowitz estimators for the tree-order model

Author

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  • Chaudhuri, Sanjay
  • Perlman, Michael D.

Abstract

Consider s+1 univariate normal populations with common variance [sigma]2 and means [mu]i, i=0,1,...,s, constrained by the tree-order restrictions [mu]i[greater-or-equal, slanted][mu]0, i=1,2,...,s. For certain sequences [mu]0,[mu]1,... the maximum likelihood-based estimator (MLBE) of [mu]0 diverges to -[infinity] as s-->[infinity] and its bias is unbounded. By contrast, the bias of an alternative estimator of [mu]0 proposed by Cohen and Sackrowitz (J. Statist. Plan. Infer. 107 (2002) 89-101) remains bounded. In this note the biases of the MLBEs of the other components [mu]1,[mu]2,... are studied and compared to the biases of the corresponding Cohen-Sackrowitz estimators (CSE). Unlike the MLBE of [mu]0, the MLBEs of [mu]i for i[greater-or-equal, slanted]1, are asymptotically unbiased in most cases. By contrast, the CSEs of [mu]i, i=1,2,...,s more often have nonzero asymptotic bias.

Suggested Citation

  • Chaudhuri, Sanjay & Perlman, Michael D., 2005. "Biases of the maximum likelihood and Cohen-Sackrowitz estimators for the tree-order model," Statistics & Probability Letters, Elsevier, vol. 71(3), pages 267-276, March.
  • Handle: RePEc:eee:stapro:v:71:y:2005:i:3:p:267-276
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