Grant: Discovery Grants Program - Individual

The objectives of this research are to develop novel and efficient methods in two areas: 1. Nonparametric Distribution, Quantle and Regression Inference Existing inference methods for nonparametric distribution, quantile and regression estimation lack good efficiency on tails of the distribution or have other difficulties. This project will develop novel inference methods, by studying a family of weighted empirical distribution functions and explore the optimal weights that minimize the estimation errors. It will develop non-kernel density, quantile and regression estimation methods by using orthogonal series and L-statistics (noting that the kernel estimation methods have problems of the selection of bandwidth and kernel). The work will compare the new methods with existing methods, and study theoretical efficiency, consistency, rate of convergence, and robustness properties of the resulting methods. It will develop computational methods to compute the exact efficiency and error, and study Monte Carlo simulations to confirm theoretical results. The new methods will be applied to practical problems. 2. Inference Methods for Heavy Tailed Distributions In recent years, heavy tailed distributions have been applied widely to extreme values, risk analysis and survival analysis, with applications in actuarial science, medical research and network analysis. There are some difficult problems in the inference of heavy tailed distributions. This project will explore innovative nonparametric or semi-parametric inference methods for heavy tailed distributions, and compare them with existing methods. It will study the theoretical and simulation efficiencies, consistency and robustness properties. Also it will apply the above new methods to real world problems, to estimate value-at-risk, survival functions and hazard functions, and waiting time distributions in queueing networks. The work will provide an alternative efficient approach to overcome difficulties in the field, and suggest new ideas for future research. This work will solve real world problems with more accurate solutions.