This dissertation includes two essays. In the first essay, I proposed an alternative estimator for multivariate densities. This estimator can be characterized as a transformation based estimator. The first stage estimates each marginal density separately. In the second stage, the joint density of estimated marginal cumulative distribution functions (CDF) are approximated by the exponential series estimator. The final estimate is then obtained as the product of the marginal densities and the joint density estimated in the second stage. Extensive Monte Carlo studies show the proposed estimator outperforms kernel estimators in joint density and tail distribution estimation. An illustrative example on estimating the conditional copula density between S & P 500 and FTSE 100 given Hangseng and Nikkei 225 is also discussed. In the second essay, I extended the semiparametric model by Chen and Fan [X. Chen, Y. Fan, Estimation of copula-based semiparametric time series models, Journal of Econometrics 130 (2006) 307-335], and studied a class of univariate copula-based nonparametric stationary Markov models in which the copulas and the marginal distributions are estimated nonparametrically. In particular, I focused on the stationary Markov process of order 1 with continuous state space because it has the beta-mixing property for the analysis of weakly dependent processes. The copula density functions for time series models are approximated by the series estimate on sieve spaces. In this study, a finite dimensional linear space spanned by a sequence of power functions is treated as the sieve space where the estimation space of the copula density function is based. This sieve series estimator can be characterized as the exponential series estimator under mild smoothness conditions. By using the beta-mixing properties, I showed that the copula density function approximated by the exponential series estimator for stationary first-order Markov processes has the same convergence rate as the i.i.d. data. The Monte Carlo simulations show that the proposed estimator outperforms the kernel estimator in the conditional density estimation, except for the Frank copula-based Markov model. In addition, the proposed estimator considerably dominates the the kernel estimator when used in the one-step-ahead forecast.

Thesis, M.Phil., University of Hong Kong, 1982. / Also available in print.

Thesis (Ph.D.)--University of Texas at Arlington, 2009.

Thesis supervisor: Kung-Sik Chan. Includes bibliographic references (p. 108-110).

Thesis (Ph.D.)--University of Southern California, 2008. / Adviser: Ronald C. Henry. Includes bibliographical references.

Thesis (Ph. D.)--Carleton University, 1988. / Also available in electronic format on the Internet.

Thesis (Ph. D.)--University of Hong Kong, 2010. / Includes bibliographical references (leaves 169-173). Also available in print.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1984. / Typescript. Vita. Includes bibliographical references (leaves 92-98).

Thesis (M. Phil.)--University of Hong Kong, 2005. / Title proper from title frame. Also available in printed format.

Thesis (Ph. D.)--Florida State University, 2006. / Advisor: Florentina Bunea, Florida State University, College of Arts and Sciences, Dept. of Statistics. Title and description from dissertation home page (viewed Sept.18, 2006). Document formatted into pages; contains xi, 89 pages. Includes bibliographical references.