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»Smooth test» for goodness of fit
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In this article, Pearson's test for goodness of fit is dedicated to the memory of Karl Pearson (27 March 1857-27 April 1936) who originated the problem of a test for fit and was first to advance its solution.Abstract:
Dedicated to the memory of Karl Pearson (27 March 1857—27 April 1936) who originated the problem of a test for goodness of fit and was first to advance its solution.read more
Citations
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Posterior predictive assessment of model fitness via realized discrepancies
TL;DR: In this article, the authors consider Bayesian counterparts of the classical tests for good-ness of fit and their use in judging the fit of a single Bayesian model to the observed data.
Book
Elements of large-sample theory
TL;DR: The most useful parts of large-sample theory are accessible to scientists outside statistics and certainly to master's-level statistics students who ignore most of measure theory as discussed by the authors, which constitutes a coherent body of concepts and results that are central to both theoretical and applied statistics.
Journal ArticleDOI
Generalized likelihood ratio statistics and Wilks phenomenon
TL;DR: The generalized likelihood ratio statistics are shown to be general and powerful for nonparametric testing problems based on function estimation and can even be adaptively optimal in the sense of Spokoiny by using a simple choice of adaptive smoothing parameter.
Journal ArticleDOI
Nonparametric model checks for regression
TL;DR: In this article, a marked empirical process based on residuals is studied, and results on its large-sample behavior may be used to provide nonparametric full-model checks for regression, and their decomposition into principal components gives new insight into the question: which kind of departure from a hypothetical model may be well detected by residual-based goodness-offit methods?
Book ChapterDOI
Asymptotically Optimal Tests for Multinomial Distributions
TL;DR: In this paper, it was shown that chi-square tests of simple and composite hypotheses are inferior to the corresponding likelihood ratio tests, provided that α → 0 at a suitable rate.
References
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Free functions and the ≫student≫-fisher theorem
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