ESTIMATION OF THE DISTRIBUTION FUNCTIONS OF THE STANDARDIZED STATISTICS USING MONTE CARLO APPROXIMATION TO EDGEWORTH EXPANSIONS

ACKNOWLEDGMENTS I sincerely appreciate my advisor. Dr. Shan Sun, for giving me the opportunity to work with her, for inspiring me, guiding me throughout this thesis work, and spending considerable,time in clearing my doubts. This thesis would,not have been possible without,her guidance,and patience. I would like to thank Dr.Benjamin Duran, for his valuable advice. I want to thank Dr. Robert Byerly, for his great help in the program work on this thesis. I would also like to thank the professors, administrative staff, and other graduate students in the Department,of Mathematics and Statistics. They have been supporting,me since I came here two years ago. Special appreciation goes to my family for their constant support, love and en­ couragement through my life. A very special appreciation goes to Yunyun, for her great love. 11 CONTENTS