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UNIFORM CONFIDENCE BOUNDS FOR NONPARAMETRIC REGRESSION

Steinar Bjerve, Kjell A. Doksum, Brian S. Yandell

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Abstract

Let (X, Y) be a bivariate random variable and let m(x) = E(YIX = x) be the regression function of Y on X. Suppose that v 1 , .••,Yn are independent observations of Y at X= x 1 , .••,xn.We consider nearest neighbor estimates, m(x), and employ well-known inequalities to obtain exact and asymptotic uniform confidence bounds for Em(x) and m(x) based on m(x).Finally we discuss bias-properties of m(x).

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Let (X, Y) be a bivariate random variable and let m(x) = E(YIX = x) be the regression function of Y on X. Suppose that v 1 , .••,Yn are independent observations of Y at X= x 1 , .••,xn.We consider nearest neighbor estimates, m(x), and employ well-known inequalities to obtain exact and asymptotic uniform confidence bounds for Em(x) and m(x) based on m(x).Finally we discuss bias-properties of m(x).

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Available abstract

Let (X, Y) be a bivariate random variable and let m(x) = E(YIX = x) be the regression function of Y on X. Suppose that v 1 , .••,Yn are independent observations of Y at X= x 1 , .••,xn.We consider nearest neighbor estimates, m(x), and employ well-known inequalities to obtain exact and asymptotic uniform confidence bounds for Em(x) and m(x) based on m(x).Finally we discuss bias-properties of m(x).

Key concepts: Nonparametric statistics, Statistics, Regression, Nonparametric regression, Confidence interval, Regression analysis, Econometrics, Mathematics

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