# Coverage Accuracy of Confidence Intervals in Nonparametric Regression

Coverage Accuracy of Confidence Intervals in Nonparametric Regression Point-wise confidence intervals for a nonparametric regression function with random design points are considered. The confidence intervals are those based on the traditional normal approximation and the empirical likelihood. Their coverage accuracy is assessed by developing the Edgeworth expansions for the coverage probabilities. It is shown that the empirical likelihood confidence intervals are Bartlett correctable. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

# Coverage Accuracy of Confidence Intervals in Nonparametric Regression

, Volume 19 (3) – Mar 3, 2017

## Coverage Accuracy of Confidence Intervals in Nonparametric Regression

Acta Mathematicae Applicatae Sinica, English Series Vol. 19, No. 3 (2003) 387–396 Coverage Accuracy of Conﬁdence Intervals in Nonparametric Regression 1 2 Song-xi Chen , Yong-song Qin Department of Statistics and Applied Probability, National University of Singapore, Singapore 117543, Singapore (Email: stacsx@nus.edu.sg) Department of Mathematics, Guangxi Normal University, Guilin 541004, China (Email: ysqin@eyou.com) Abstract Point-wise conﬁdence intervals for a nonparametric regression function with random design points are considered. The conﬁdence intervals are those based on the traditional normal approximation and the empirical likelihood. Their coverage accuracy is assessed by developing the Edgeworth expansions for the coverage probabilities. It is shown that the empirical likelihood conﬁdence intervals are Bartlett correctable. Keywords Conﬁdence interval, empirical likelihood, Nadaraya-Watson estimator, normal approximation 2000 MR Subject Classiﬁcation 62G05, 62E20 1 Introduction d+1 d Let (X ,Y ),··· , (X ,Y ) be independent copies of R random vectors (X, Y )where X ∈ R 1 1 n n with density f.Let m(x)= E(Y |X = x) be the conditional mean function and σ (x)= Var(Y |X = x) be the conditional variance function of Y given X = x.For any x, u ∈ R ,let 2 2 2 V (u|x)= E[{Y − m(x)} |X = u]. Clearly, V (u|x)= σ (u)+ {m(u) − m(x)} . The Nadaraya-Watson estimator for m(x)at any given x is K (x − X )Y h i i m  (x)= , (1.1) K (x − X ) h i where K (t)= K(t/h), K is a kernel function and h is the smoothing bandwidth. This paper is concerned with the construction of point-wise conﬁdence intervals for m(x) at any ﬁxed x in conjunction with the Nadaraya-Watson estimator when the design points are random. Conﬁdence intervals based on the asymptotic normality of the Nadaraya-Watson [8] estimator and the percentile bootstrap are reviewed in [11]. Hall considers coverage accuracy of...

/lp/springer_journal/coverage-accuracy-of-confidence-intervals-in-nonparametric-regression-3z0HzIL15s
Publisher
Springer Journals
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
D.O.I.
10.1007/s10255-003-0113-3
Publisher site
See Article on Publisher Site

### Abstract

Point-wise confidence intervals for a nonparametric regression function with random design points are considered. The confidence intervals are those based on the traditional normal approximation and the empirical likelihood. Their coverage accuracy is assessed by developing the Edgeworth expansions for the coverage probabilities. It is shown that the empirical likelihood confidence intervals are Bartlett correctable.

### Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Mar 3, 2017

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