Kernels, degrees of freedom and power properties of quadratic distance goodness of fit tests

Lindsay, B. G., Markatou, M. and Ray, S. (2014) Kernels, degrees of freedom and power properties of quadratic distance goodness of fit tests. Journal of the American Statistical Association, 109(505), pp. 395-410. (doi: 10.1080/01621459.2013.836972)

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Publisher's URL: http://dx.doi.org/10.1080/01621459.2013.836972

Abstract

In this paper we study the power properties of quadratic distance based goodness of fit tests. First, we introduce the concept of a root kerneland discuss the considerations that enter the selection of this kernel. We derive an easy to use normal approximation to the power of quadratic distance goodness of fit tests and base the construction of a noncentrality index,an analogue of the traditional noncentrality parameter, on it. This leads to a method akin to the Neyman-Pearson lemma for constructing optimal kernels for specific alternatives. We then introduce a midpower analysis as a device for choosing optimal degrees of freedom for a family of alternatives of interest. Finally, we introduce a new diffusion kernel, called the Pearson-normal kernel and study the extend to which the normal approximation to the power of tests based on this kernel is valid.

Item Type:Articles
Keywords:Midpower analysis, high dimensional testing, optimal kernel construction, Pearson-normal kernel, power lemma, big data
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Ray, Professor Surajit and Lindsay, Professor Bruce
Authors: Lindsay, B. G., Markatou, M., and Ray, S.
Subjects:H Social Sciences > HA Statistics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Statistics
Journal Name:Journal of the American Statistical Association
Publisher:Taylor & Francis
ISSN:0162-1459
ISSN (Online):1537-274X
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