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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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).
- Likelihood ratio sieves
- Nonparametric and semiparametric models