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Full-Text Articles in Physical Sciences and Mathematics
Plenary: Nonparametric Hypothesis Testing For A Spatial Signal, Noel A. Cressie
Plenary: Nonparametric Hypothesis Testing For A Spatial Signal, Noel A. Cressie
Professor Noel Cressie
Summary form only given. Nonparametric hypothesis testing for a spatial signal can involve a large number of hypotheses. For instance, two satellite images of the same scene, taken before and after an event, could be used to test a hypothesis that the event has no environmental impact. This is equivalent to testing that the mean difference of "after-before" is zero at each of the (typically thousands of) pixels that make up the scene. In such a situation, conventional testing procedures that control the overall Type I error deteriorate as the number of hypotheses increase. Powerful testing procedures are needed for …
The Vprt - A Sequential Testing Procedure Dominating The Sprt, Noel A. Cressie, Peter Morgan
The Vprt - A Sequential Testing Procedure Dominating The Sprt, Noel A. Cressie, Peter Morgan
Professor Noel Cressie
Under more general assumptions than those usually made in the sequential analysis literature, a variable-sample-size-sequential probability ratio test (VPRT) of two simple hypotheses is found that maximizes the expected net gain over all sequential decision procedures. In contrast, Wald and Wolfowitz [25] developed the sequential probability ratio test (SPRT) to minimize expected sample size, but their assumptions on the parameters of the decision problem were restrictive. In this article we show that the expected net-gain-maximizing VPRT also minimizes the expected (with respect to both data and prior) total sampling cost and that, under slightly more general conditions than those imposed …
Size And Power Considerations For Testing Loglinear Models Using Divergence Test Statistics, Noel A. Cressie, L Pardo, M Del Carmen Pardo
Size And Power Considerations For Testing Loglinear Models Using Divergence Test Statistics, Noel A. Cressie, L Pardo, M Del Carmen Pardo
Professor Noel Cressie
In this article, we assume that categorical data are distributed according to a multinomial distribution whose probabilities follow a loglinear model. The inference problem we consider is that of hypothesis testing in a loglinear-model setting. The null hypothesis is a composite hypothesis nested within the alternative. Test statistics are chosen from the general class of divergence statistics. This article collects together the operating characteristics of the hypothesis test based on both asymptotic (using large-sample theory) and finite-sample (using a designed simulation study) results. Members of the class of power divergence statistics are compared, and it is found that the Cressie-Read …
Minimum Phi Divergence Estimator And Hierarchical Testing In Loglinear Models, Noel A. Cressie, Leandro Pardo
Minimum Phi Divergence Estimator And Hierarchical Testing In Loglinear Models, Noel A. Cressie, Leandro Pardo
Professor Noel Cressie
In this paper we consider inference based on very general divergence measures, under assumptions of multinomial sampling and loglinear models. We define the minimum phi divergence estimator, which is seen to be a generalization of the maximum likelihood estimator. This estimator is then used in a phi divergence goodness-of-fit statistic, which is the basis of two new statistics for solving the problem of testing a nested sequence of loglinear models.