Nonparametric Goodness-of-fit
نویسنده
چکیده
This paper develops an approach to testing the adequacy of both classical and Bayesian models given sample data. An important feature of the approach is that we are able to test the practical scientiic hypothesis of whether the true underlying model is close to some hypothesized model. The notion of closeness is based on measurement precision and requires the introduction of a metric for which we consider the Kolmogorov distance. The approach is nonparametric in the sense that the model under the alternative hypothesis is a Dirichlet process.
منابع مشابه
A New Goodness-of-Fit Test for a Distribution by the Empirical Characteristic Function
Extended Abstract. Suppose n i.i.d. observations, X1, …, Xn, are available from the unknown distribution F(.), goodness-of-fit tests refer to tests such as H0 : F(x) = F0(x) against H1 : F(x) $neq$ F0(x). Some nonparametric tests such as the Kolmogorov--Smirnov test, the Cramer-Von Mises test, the Anderson-Darling test and the Watson test have been suggested by comparing empirical ...
متن کاملBayesian Nonparametric Goodness of Fit Tests
We survey in some detail the rather small literature on Bayes nonparametric Testing. We mostly concentrate on Bayesian testing of goodness of fit to a parametric null with nonparametric alternatives. We also survey briefly some related unpublished material. We discuss both methodology and posterior consistency.
متن کاملThree Papers by Peter Bickel on Nonparametric Curve Estimation
The following is a brief review of three landmark papers of Peter Bickel on theoretical and methodological aspects of nonparametric density and regression estimation and the related topic of goodness-of-fit testing, including a class of semiparametric goodness-of-fit tests. We consider the context of these papers, their contribution and their impact. Bickel’s first work on density estimation wa...
متن کاملAn empirical likelihood goodness-of-fit test for time series
Standard goodness-of-fit tests for a parametric regression model against a series of nonparametric alternatives are based on residuals arising from a fitted model.When a parametric regression model is compared with a nonparametric model, goodness-of-fit testing can be naturally approached by evaluating the likelihood of the parametric model within a nonparametric framework. We employ the empiri...
متن کاملNonparametric Goodness-of-Fit Tests for Discrete Null Distributions
Methodology extending nonparametric goodness-of-fit tests to discrete null distributions has existed for several decades. However, modern statistical software has generally failed to provide this methodology to users. We offer a revision of R’s ks.test() function and a new cvm.test() function that fill this need in the R language for two of the most popular nonparametric goodness-of-fit tests. ...
متن کاملBayesian Goodness-of-Fit Testing with Mixtures of Triangular Distributions
We consider the consistency of the Bayes factor in goodness of fit testing for a parametric family of densities against a nonparametric alternative. Sufficient conditions for consistency of the Bayes factor are determined and demonstrated with priors using certain mixtures of triangular densities. Running headline: Bayesian Goodness of Fit Testing
متن کامل