Sieve likelihood ratio inference on general parameter space

Xiaotong Shen; Jian Shi

doi:10.1360/03ys0202

Sieve likelihood ratio inference on general parameter space

Xiaotong Shen, Jian Shi

Statistics (Twin Cities)

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

13 Scopus citations

Abstract

In this paper, a theory on sieve likelihood ratio inference on general parameter spaces (including infinite dimensional) is studied. Under fairly general regularity conditions, the sieve log-likelihood ratio statistic is proved to be asymptotically χ² distributed, which can be viewed as a generalization of the well-known Wilks' theorem. As an example, a semiparametric partial linear model is investigated.

Original language	English (US)
Pages (from-to)	67-78
Number of pages	12
Journal	Science in China, Series A: Mathematics
Volume	48
Issue number	1
DOIs	https://doi.org/10.1360/03ys0202
State	Published - Jan 2005

Bibliographical note

Funding Information:
Acknowledgements This work was supported in part by National Science Foundation of the USA (Grant IIS-0328802, Grant DMS-0072635) and the National Natural Science Foundation of China (Grant. No. 10071090 and 10231030).

Keywords

Likelihood ratio sieves
Nonparametric and semiparametric models
Wavelets

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10.1360/03ys0202

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author = "Xiaotong Shen and Jian Shi",

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AB - In this paper, a theory on sieve likelihood ratio inference on general parameter spaces (including infinite dimensional) is studied. Under fairly general regularity conditions, the sieve log-likelihood ratio statistic is proved to be asymptotically χ2 distributed, which can be viewed as a generalization of the well-known Wilks' theorem. As an example, a semiparametric partial linear model is investigated.

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KW - Nonparametric and semiparametric models

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Sieve likelihood ratio inference on general parameter space

Abstract

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