 On posterior consistency in nonparametric regression problemsTaeryon Choi and Mark J. Schervish Journal of Multivariate Analysis, 2007, vol. 98, issue 10, 1969-1987 Abstract: We provide sufficient conditions to establish posterior consistency in nonparametric regression problems with Gaussian errors when suitable prior distributions are used for the unknown regression function and the noise variance. When the prior under consideration satisfies certain properties, the crucial condition for posterior consistency is to construct tests that separate from the outside of the suitable neighborhoods of the parameter. Under appropriate conditions on the regression function, we show there exist tests, of which the type I error and the type II error probabilities are exponentially small for distinguishing the true parameter from the complements of the suitable neighborhoods of the parameter. These sufficient conditions enable us to establish almost sure consistency based on the appropriate metrics with multi-dimensional covariate values fixed in advance or sampled from a probability distribution. We consider several examples of nonparametric regression problems. Keywords: Almost; sure; consistency; Differentiable; functions; Empirical; probability; measure; Hellinger; metric; In; probability; metric; Sieve (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:98:y:2007:i:10:p:1969-1987 Ordering information: This journal article can be ordered from Access Statistics for this article Journal of Multivariate Analysis is currently edited by de Leeuw, J. More articles in Journal of Multivariate Analysis from Elsevier |
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