Berry-Esseen bounds for nonlinear statistics, and asymptotic relative efficiency between correlation statistics

Four papers, written in collaboration with the author’s graduate school advisor, are presented. In the first paper, uniform and non-uniform Berry-Esseen (BE) bounds on the convergence to normality of a general class of nonlinear statistics are provided; novel applications to specific statistics, including the non-central Student’s, Pearson’s, and the non-central Hotelling’s, are also stated. In the second paper, a BE bound on the rate of convergence of the F-statistic used in testing hypotheses from a general linear model is given. The third paper considers the asymptotic relative efficiency (ARE) between the Pearson, Spearman, and Kendall correlation statistics; conditions sufficient to ensure that the Spearman and Kendall statistics are equally (asymptotically) efficient are provided, and several models are considered which illustrate the use of such conditions. Lastly, the fourth paper proves that, in the bivariate normal model, the ARE between any of these correlation statistics possesses certain monotonicity properties; quadratic lower and upper bounds on the ARE are stated as direct applications of such monotonicity patterns.

Skin Lesion Extraction And Its Application

In this thesis, I study skin lesion detection and its applications to skin cancer diagnosis. A skin lesion detection algorithm is proposed. The proposed algorithm is based color information and threshold. For the proposed algorithm, several color spaces are studied and the detection results are compared. Experimental results show that YUV color space can achieve the best performance. Besides, I develop a distance histogram based threshold selection method and the method is proven to be better than other adaptive threshold selection methods for color detection. Besides the detection algorithms, I also investigate GPU speed-up techniques for skin lesion extraction and the results show that GPU has potential applications in speeding-up skin lesion extraction. Based on the skin lesion detection algorithms proposed, I developed a mobile-based skin cancer diagnosis application. In this application, the user with an iPhone installed with the proposed application can use the iPhone as a diagnosis tool to find the potential skin lesions in a persons' skin and compare the skin lesions detected by the iPhone with the skin lesions stored in a database in a remote server.