Consistent nonparametric multiple regression: the fixed design case
TLDR
In this paper, the authors studied the behavior of the general nonparametric estimate for the unknown regression function g, where the weight function wni is of the form wni(x) = wni (x; xi(n), …, xn(n)).About:
This article is published in Journal of Multivariate Analysis.The article was published on 1988-04-01 and is currently open access. It has received 89 citations till now. The article focuses on the topics: Nonparametric regression.read more
Citations
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Fixed design regression for time series: asymptotic normality
TL;DR: In this paper, the asymptotic normality of the Gasser-Muller estimator is established under weak conditions, and the applicability of the results obtained is demonstrated by means of a concrete example from the class of autoregressive processes.
Journal ArticleDOI
Asymptotic properties for estimates of nonparametric regression models based on negatively associated sequences
Han-Ying Liang,Bing-Yi Jing +1 more
TL;DR: In this article, the pointwise and uniform convergence of nonparametric estimator g"n(x) of g(x"n"i) is studied and its asymptotic normality is investigated.
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Consistent regression estimation with fixed design points under dependence conditions
TL;DR: In this paper, the authors considered the problem of estimating a continuous real-valued function on R p, subject to errors eni and showed that the estimate is asymptotically unbiased.
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Complete convergence for arrays of rowwise negatively superadditive-dependent random variables and its applications
TL;DR: In this paper, the complete convergence of arrays of negatively superadditive-dependent (NSD) random variables was studied using the Rosenthal-type maximal inequalities and Kolmogorov-type exponential inequality.
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Complete consistency for the estimator of nonparametric regression models based on extended negatively dependent errors
TL;DR: In this article, the authors provide some exponential inequalities for extended negatively dependent (END) random variables and investigate the complete consistency for the estimator of nonparametric regression model based on end errors.
References
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Journal ArticleDOI
Consistent Nonparametric Regression
TL;DR: In this article, a sequence of probability weight functions defined in terms of nearest neighbors is constructed and sufficient conditions for consistency are obtained, which are applied to verify the consistency of the estimators of the various quantities discussed above and the consistency in Bayes risk of the approximate Bayes rules.
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Smoothing noisy data with spline functions
TL;DR: In this article, a generalized cross-validation estimate for smoothing polynomial splines is proposed, where the tradeoff between the "roughness" of the solution, as measured by the average square error of the smoothing spline, is defined.
Journal ArticleDOI
Bootstrapping Regression Models
TL;DR: In this article, it is shown that the bootstrap approximation to the distribution of the least squares estimates is valid and some error bounds are given, and the regression and correlation models are considered.
Journal ArticleDOI
Complete Convergence and the Law of Large Numbers
P. L. Hsu,Herbert Robbins +1 more
TL;DR: The set of all ω to such that the relation within the braces holds, is the distribution function of X, and the random variables of a sequence X1, X2 ... are independent if, for every sequence x1, x2, … of real numbers, the sets are independent.
Book ChapterDOI
Kernel estimation of regression functions
Theo Gasser,Hans-Georg Müller +1 more
TL;DR: For the nonparametric estimation of regression functions with a one-dimensional design parameter, a new kernel estimate is defined and shown to be superior to the one introduced by Priestley and Chao (1972) as discussed by the authors.