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Sieve likelihood ratio inference on general parameter space

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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.

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Authors and Affiliations

  1. School of Statistics, University of Minnesota, 55455, Minneapolis, MN, USA

    Xiaotong Shen

  2. Academy of Mathematics and Systems Science, 100080, Beijing, China

    Jian Shi

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  1. Xiaotong Shen
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  2. Jian Shi
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Correspondence to Jian Shi.

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Shen, X., Shi, J. Sieve likelihood ratio inference on general parameter space. Sci. China Ser. A-Math. 48, 67–78 (2005). https://doi.org/10.1360/03ys0202

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  • DOI: https://doi.org/10.1360/03ys0202

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