Saddlepoint approximations to P-values for comparison of density estimates |
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Authors: | Hoi-Jeong Lim |
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Institution: | (1) Department of Preventive Medicine, Seoul National University College of Medicine, 28 Yongon-dong, 110-799 Chongno-gu, Seoul, Korea |
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Abstract: | Summary This article is concerned with computing approximate p-values for the maximum of the absolute difference between kernel density
estimates. The approximations are based on treating the process of local extrema of the differences as a nonhomogeneous Poisson
Process and estimating the corresponding local intensity function. The process of local extrema is characterized by the intensity
function, which determines the rate of local extrema above a given threshold. A key idea of this article is to provide methods
for more accurate estimation of the intensity function by using saddlepoint approximations for the joint density of the difference
between kernel density estimates and using the first and second derivative of the difference. In this article, saddlepoint
approximations are compared to gaussian approximations. Simulation results from saddlepoint approximations show consistently
better agreement between empirical p-value and predetermined value with various bandwidths of kernel density estimates. |
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Keywords: | saddlepoint approximations Poisson Process local extrema boundary crossing probability |
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