Yuhong Yang

Bio: Yuhong Yang is an academic researcher from University of Minnesota. The author has contributed to research in topics: Model selection & Estimator. The author has an hindex of 31, co-authored 108 publications receiving 5212 citations. Previous affiliations of Yuhong Yang include Ford Motor Company & Iowa State University.

Information-theoretic determination of minimax rates of convergence

Abstract: We present some general results determining minimax bounds on statistical risk for density estimation based on certain information-theoretic considerations. These bounds depend only on metric entropy conditions and are used to identify the minimax rates of convergence.

Can the Strengths of AIC and BIC Be Shared

Abstract: It is well known that AIC and BIC have dierent properties in model selection. BIC is consistent in the sense that if the true model is among the candidates, the probability of selecting the true model approaches 1. On the other hand, AIC is minimax-rate optimal for both parametric and nonparametric cases for estimating the regression function. There are several successful results on constructing new model selection criteria to share some strengths of AIC and BIC. However, we show that in a rigorous sense, even in the setting that the true model is included in the candidates, the above mentioned main strengths of AIC and BIC cannot be shared. That is, for any model selection criterion to be consistent, it must behave sup-optimally compared to AIC in terms of mean average squared error.

Can the strengths of AIC and BIC be shared? A conflict between model indentification and regression estimation

Abstract: A traditional approach to statistical inference is to identify the true or best model first with little or no consideration of the specific goal of inference in the model identification stage. Can the pursuit of the true model also lead to optimal regression estimation? In model selection, it is well known that BIC is consistent in selecting the true model, and AIC is minimax-rate optimal for estimating the regression function. A recent promising direction is adaptive model selection, in which, in contrast to AIC and BIC, the penalty term is data-dependent. Some theoretical and empirical results have been obtained in support of adaptive model selection, but it is still not clear if it can really share the strengths of AIC and BIC. Model combining or averaging has attracted increasing attention as a means to overcome the model selection uncertainty. Can Bayesian model averaging be optimal for estimating the regression function in a minimax sense? We show that the answers to these questions are basically in the negative: for any model selection criterion to be consistent, it must behave suboptimally for estimating the regression function in terms of minimax rate of covergence; and Bayesian model averaging cannot be minimax-rate optimal for regression estimation.

Adaptive Regression by Mixing

Abstract: Adaptation over different procedures is of practical importance. Different procedures perform well under different conditions. In many practical situations, it is rather hard to assess which conditions are (approximately) satisfied so as to identify the best procedure for the data at hand. Thus automatic adaptation over various scenarios is desirable. A practically feasible method, named adaptive regression by mixing (ARM), is proposed to convexly combine general candidate regression procedures. Under mild conditions, the resulting estimator is theoretically shown to perform optimally in rates of convergence without knowing which of the original procedures work the best. Simulations are conducted in several settings, including comparing a parametric model with nonparametric alternatives, comparing a neural network with a projection pursuit in multidimensional regression, and combining bandwidths in kernel regression. The results clearly support the theoretical property of ARM. The ARM algorithm assigns we...

Nonparametric Regression with Correlated Errors

Abstract: Nonparametric regression techniques are often sensitive to the presence of correlation in the errors. The practical consequences of this sensitivityare explained, including the breakdown of several popu- lar data-driven smoothing parameter selection methods. We review the existing literature in kernel regression, smoothing splines and wavelet regression under correlation, both for short-range and long-range depen- dence. Extensions to random design, higher dimensional models and adaptive estimation are discussed. some of the difficulties associated with the presence of correlation in nonparametric regression, (2) to provide an overview of the nonparameteric regres- sion literature that deals with the correlated errors case and (3) to discuss some new developments in this area. Much of the literature in nonparametric regression relies on asymptotic arguments to clarify the probabilistic behavior of the proposed meth- ods. The same approach will be used here, but we attempt to provide intuition into the results as well. In this article, we will be looking at the following statistical model:

The Design and Analysis of Experiments

Abstract: THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

Regression Diagnostics: Identifying Influential Data and Sources of Collinearity

Abstract: 1. Introduction and Overview. 2. Detecting Influential Observations and Outliers. 3. Detecting and Assessing Collinearity. 4. Applications and Remedies. 5. Research Issues and Directions for Extensions. Bibliography. Author Index. Subject Index.

A survey of cross-validation procedures for model selection

Abstract: Used to estimate the risk of an estimator or to perform model selection, cross-validation is a widespread strategy because of its simplicity and its apparent universality. Many results exist on the model selection performances of cross-validation procedures. This survey intends to relate these results to the most recent advances of model selection theory, with a particular emphasis on distinguishing empirical statements from rigorous theoretical results. As a conclusion, guidelines are provided for choosing the best cross-validation procedure according to the particular features of the problem in hand.

A survey of cross-validation procedures for model selection

Abstract: Used to estimate the risk of an estimator or to perform model selection, cross-validation is a widespread strategy because of its simplicity and its apparent universality. Many results exist on the model selection performances of cross-validation procedures. This survey intends to relate these results to the most recent advances of model selection theory, with a particular emphasis on distinguishing empirical statements from rigorous theoretical results. As a conclusion, guidelines are provided for choosing the best cross-validation procedure according to the particular features of the problem in hand.