This article reviews the literature on sparse high-dimensional models and discusses some applications in economics and finance. Recent developments in theory, methods, and implementations in penalized least-squares and penalized likelihood methods are highlighted. These variable selection methods are effective in sparse high-dimensional modeling. The limits of dimensionality that regularization methods can handle, the role of penalty functions, and their statistical properties are detailed. Some recent advances in sparse ultra-high-dimensional modeling are also briefly discussed.
The varying coefficient models are very important tool to explore the dynamic pattern in many scientific areas, such as economics, finance, politics, epidemiology, medical science, ecology and so on. They are natural extensions of classical parametric models with good interpretability and are becoming more and more popular in data analysis. Thanks to their flexibility and interpretability, in the past ten years, the varying coefficient models have experienced deep and exciting developments on methodological, theoretical and applied sides. This paper gives a selective overview on the major methodological and theoretical developments on the varying coefficient models.
This volume presents selections of Peter J. Bickels major papers, along with comments on their novelty and impact on the subsequent development of statistics as a discipline. Each of the eight parts concerns a particular area of research and provides new commentary by experts in the area. The parts range from Rank-Based Nonparametrics to Function Estimation and Bootstrap Resampling. Peters amazing career encompasses the majority of statistical developments in the last half-century or about about half of the entire history of the systematic development of statistics. This volume shares insights on these exciting statistical developments with future generations of statisticians. The compilation of supporting material about Peters life and work help readers understand the environment under which his research was conducted. The material will also inspire readers in their own research-based pursuits. This volume includes new photos of Peter Bickel, his biography, publication list, and a list of his students. These give the reader a more complete picture of Peter Bickel as a teacher, a friend, a colleague, and a family man.
This paper gives a brief overview of the nonparametric techniques that are useful for financial econometric problems. The problems include estimation and inference for instantaneous returns and volatility functions of time-homogeneous and time-dependent diffusion processes, and estimation of transition densities and state price densities. We first briefly describe the problems and then outline the main techniques and main results. Some useful probabilistic aspects of diffusion processes are also briefly summarized to facilitate our presentation and applications.
It is a great honor for me to be invited by Tsinghua University to talk today. Tsinghua has, in its history, made many contributions to mathematics. The two most famous mathematicians in modern Chinese history have both been closely related to Tsinghua University. One is Professor Hua Lo-Keng, the other is Prof essor Chern Shiing-Sheng. Especially since Professor Chern is my teacher, I feel proud to be able to say some words in the opening ceremony for the Center for Advanced Study. I chose the title of my talk also for this reason. Due to my critical comments, I have decided to spend most of my time in giving a general talk in English. The remainder of the talk will be in Chinese.