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A SIMPLE VARIANCE ESTIMATOR IN NONPARAMETRIC REGRESSION MODELS WITH MULTIVARIATE PREDICTORS
YOUNG KYUNG LEE,TAE YOON KIM,BYEONG U. PARK 한국통계학회 2006 Journal of the Korean Statistical Society Vol.35 No.1
In this paper we propose a simple and computationally attractive diere-nce-based variance estimator in nonparametric regression models with mul-tivariate predictors. We show that the estimator achievesn1=2 rate ofconvergence for regression functions with only a rst derivative whend, thedimension of the predictor, is less than or equal to 4. Whend > 4, the rateturns out to ben4=(d+4) under the rst derivative condition for the regres-sion functions. A numerical study suggests that the proposed estimator hasa good nite sample performance.AMS 2000 subject classications.Primary 62G08; Secondary 62G20.Keywords.Variance estimation, multivariate regression, rate of convergence.1. IntroductionA homoscedastic regression problem of the formYi = m(Xi) + i (1 i n) (1.1)is considered wherem is an unknown regression function, the errors are indepen-dent and identically distributed random variables with mean zero and variance, and the random design pointsXi are assumed to arise from independent re-alizations of a distribution having a densityf on IRd. Recently, estimation ofReceived January 2006; accepted March 2006.yYoung Kyung Lee was supported by the Brain Korea 21 Project in 2004. Tae Yoon Kimwas supported by KOSEF R01-2003-000-10589-0. Byeong U. Park was supported by KOSEFthrough Statistical Research Center for Complex Systems at Seoul National University.
Advances in Data-Driven Bandwidth Selection
Park, Byeong U. The Korean Statistical Society 1991 Journal of the Korean Statistical Society Vol.20 No.1
Considerable progress on the problem of data-driven bandwidth selection in kernel density estimation has been made recently. The goal of this paper is to provide an introduction to the methods currently available, with discussion at both a practical and a nontechnical theoretical level. The main setting considered here is global bandwidth kernel estimation, but some recent results on variable bandwidth kernel estimation are also included.
Asymptotically Optimal Estimators of the Differences of Two Regression Parameters
Park, Byeong U.,Kim, Woo C.,Song, Moon S. The Korean Statistical Society 1989 Journal of the Korean Statistical Society Vol.18 No.2
We consider two semiparametric regression lines where the density of the error terms are unknown. We give simultaneous estimatros of the differences of intercepts and slopes which turn out to be asymptotically minimax as well as efficient in semiparametric sense.
Park, Byeong U.,Jeon, Jong W.,Song, Moon S.,Kim, Woo C. The Korean Statistical Society 1991 Journal of the Korean Statistical Society Vol.20 No.1
A set of conditions ensuring local asymptotic normality for independent but not necessarily identically distributed observations in semiparametric models is presented here. The conditions are turned out to be more direct and easier to verify than those of Oosterhoff and van Zwet(1979) in semiparametric models. Examples considered include the simple linear regression model and Cox's proportional hazards model without censoring where the covariates are not random.
On Nonparametric Estimation of Data Edges
Park, Byeong U. The Korean Statistical Society 2001 Journal of the Korean Statistical Society Vol.30 No.2
Estimation of the edge of a distribution has many important applications. It is related to classification, cluster analysis, neural network, and statistical image recovering. The problem also arises in measuring production efficiency in economic systems. Three most promising nonparametric estimators in the existing literature are introduced. Their statistical properties are provided, some of which are new. Themes of future study are also discussed.
A Simple Estimator of Error Correlation in Non-parametric Regression Models
PARK, BYEONG U.,LEE, YOUNG KYUNG,KIM, TAE YOON,PARK, CHEOLYONG Almqvist & Wiksell Periodical Co 2006 Scandinavian journal of statistics, theory and app Vol.33 No.3
<P>Abstract. </P><P>It is well known that major strength of non-parametric regression function estimation breaks down when correlated errors exist in the data. Positively (negatively) correlated errors tend to produce undersmoothing (oversmoothing). Several remedies have been proposed in the context of bandwidth selection problem, but they are hard to implement without prior knowledge of error correlations. In this paper we propose a simple estimator of error correlation which is ready to implement and reports a reasonably good performance.</P>