Kernels, Degrees of Freedom, and Power Properties of Quadratic Distance Goodness-of-Fit Tests.
In this article, we study the power properties of quadratic-distance-based goodness-of-fit tests. First, we introduce the concept of aroot 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 anoncentrality 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 amidpower analysisas a device for choosing optimal degrees of freedom for a family of alternatives of interest. Finally, we introduce a new diffusion kernel, called thePearson-normal kernel, and study the extent to which the normal approximation to the power of tests based on this kernel is valid. Supplementary materials for this article are available online.
Professor, Department of Statistics, Pennsylvania State University, University Park, PA 16802 (E-mail: bgl@psu.edu ).
Bruce G
BG
Lindsay
Professor at the Departments of Biostatistics and Biomedical Informatics, SUNY at Buffalo, 3435 Main Street, 726 Kimball Hall ; School of Public Health and Health Professions, and School of Medicine, Buffalo, NY 14260 (E-mail: markatou@buffalo.edu ).
Marianthi
M
Markatou
Professor, Department of Statistics, Pennsylvania State University, University Park, PA 16802 (E-mail: bgl@psu.edu ).
Surajit
S
Ray
Big data; High-dimensional testing; Midpower analysis; Optimal kernel construction; Pearson-normal kernel; Power lemma