Minimax Tests for Nonparametric Alternatives with Applications to High Frequency Data

• Other Authors: Yu, Han (authoraut)
• Format: Others
• Language: English; English
• Published: Florida State University
• Subjects: Statistics
• Online Access: http://purl.flvc.org/fsu/fd/FSU_migr_etd-0796

We present a general methodology for developing an asymptotically distribution-free, asymptotic minimax tests. The tests are constructed via a nonparametric density-quantile function and the limiting distribution is derived by a martingale approach. The procedure can be viewed as a novel parametric extension of the classical parametric likelihood ratio test. The proposed tests are shown to be omnibus within an extremely large class of nonparametric global alternatives characterized by simple conditions. Furthermore, we establish that the proposed tests provide better minimax distinguishability. The tests have much greater power for detecting high-frequency nonparametric alternatives than the existing classical tests such as Kolmogorov-Smirnov and Cramer-von Mises tests. The good performance of the proposed tests is demonstrated by Monte Carlo simulations and applications in High Energy Physics. === A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. === Degree Awarded: Summer Semester, 2006. === Date of Defense: April 24, 2006. === Nonparametric Alternatives, Nonparametric Likelihood Ratio, Minimaxity, Kullback-Leibler === Includes bibliographical references. === Kai-Sheng Song, Professor Directing Dissertation; Jack Quine Professor, Outside Committee Member; Fred Huffer Professor, Committee Member; Dan McGee Professor, Committee Member.