Directed likelihood ratio tests for ordered alternatives and inference results for the star-shaped restriction

Arthur Cohen; H. B. Sackrowitz

doi:https://doi.org/10.1016/S0378-3758(01)00220-8

Directed likelihood ratio tests for ordered alternatives and inference results for the star-shaped restriction

Arthur Cohen, H. B. Sackrowitz

School of Arts and Sciences, Statistics

Rutgers, The State University

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

To test a null hypothesis of homogeneity of parameters versus an order restricted alternative a popular method is to use a restricted likelihood ratio test. An alternative approach which oftentimes has desirable properties is a directed likelihood ratio test. In this paper, we give sufficient conditions under which these approaches coincide. We indicate cases where they do not coincide. One such case is where the parameters satisfy the lower star-shaped restriction and the underlying random variables are independent with Poisson distributions. For this model, we study and prefer the directed likelihood ratio test. We also propose estimators of the parameters which we feel are more desirable than the maximum likelihood estimators.

Original language	American English
Pages (from-to)	181-189
Number of pages	9
Journal	Journal of Statistical Planning and Inference
Volume	103
Issue number	1-2
DOIs	https://doi.org/10.1016/S0378-3758(01)00220-8
State	Published - Apr 15 2002

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

Keywords

Cone order monotonicity
Maximum likelihood estimators
Order restricted inference
Preservation of order
Projections

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https://doi.org/10.1016/S0378-3758(01)00220-8

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title = "Directed likelihood ratio tests for ordered alternatives and inference results for the star-shaped restriction",

abstract = "To test a null hypothesis of homogeneity of parameters versus an order restricted alternative a popular method is to use a restricted likelihood ratio test. An alternative approach which oftentimes has desirable properties is a directed likelihood ratio test. In this paper, we give sufficient conditions under which these approaches coincide. We indicate cases where they do not coincide. One such case is where the parameters satisfy the lower star-shaped restriction and the underlying random variables are independent with Poisson distributions. For this model, we study and prefer the directed likelihood ratio test. We also propose estimators of the parameters which we feel are more desirable than the maximum likelihood estimators.",

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AU - Cohen, Arthur

AU - Sackrowitz, H. B.

N1 - Funding Information: Research supported by the National Science Foundation, NSF Grant 9618711 and NSA Grant 904-901-0506.

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AB - To test a null hypothesis of homogeneity of parameters versus an order restricted alternative a popular method is to use a restricted likelihood ratio test. An alternative approach which oftentimes has desirable properties is a directed likelihood ratio test. In this paper, we give sufficient conditions under which these approaches coincide. We indicate cases where they do not coincide. One such case is where the parameters satisfy the lower star-shaped restriction and the underlying random variables are independent with Poisson distributions. For this model, we study and prefer the directed likelihood ratio test. We also propose estimators of the parameters which we feel are more desirable than the maximum likelihood estimators.

KW - Cone order monotonicity

KW - Maximum likelihood estimators

KW - Order restricted inference

KW - Preservation of order

KW - Projections

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Directed likelihood ratio tests for ordered alternatives and inference results for the star-shaped restriction

Abstract

ASJC Scopus subject areas

Keywords

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