Journal ArticleDOI
Estimating the error distribution function in semiparametric additive regression models
TLDR
In this paper, the authors consider semiparametric additive regression models with a linear parametric part and a nonparametric part, both involving multivariate covariates, and prove a functional central limit theorem for the residual-based empirical distribution function, up to a uniformly negligible remainder term.About:
This article is published in Journal of Statistical Planning and Inference.The article was published on 2012-02-01. It has received 32 citations till now. The article focuses on the topics: Semiparametric regression & Variance function.read more
Citations
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Journal ArticleDOI
Nonparametric independence testing via mutual information
TL;DR: This work proposes a test of independence of two multivariate random vectors, given a sample from the underlying population, based on the estimation of mutual information, whose decomposition into joint and marginal entropies facilitates the use of recently-developed efficient entropy estimators derived from nearest neighbour distances.
Posted Content
A comparison of different nonparametric methods for inference on additive models
TL;DR: In this paper, the authors highlight the main differences of available methods for the analysis of regression functions that are probably additive separable and compare the tests in a brief discussion, focusing on the (non-) reliability of the methods when the covariates are strongly correlated among themselves.
Journal ArticleDOI
The transfer principle: A tool for complete case analysis
TL;DR: In this article, a general method for deriving limiting distributions of complete case statistics for missing data models from corresponding results for the model where all data are observed is presented, which provides a convenient tool for obtaining the asymptotic behavior of established full data methods without lengthy proofs.
Journal ArticleDOI
The transfer principle: A tool for complete case analysis
TL;DR: In this paper, a general method for deriving limiting distributions of complete case statistics for missing data models from corresponding results for the model where all data are observed is presented, which provides a convenient tool for obtaining the asymptotic behavior of established full data methods without lengthy proofs.
Journal ArticleDOI
Oracally efficient estimation of autoregressive error distribution with simultaneous confidence band
TL;DR: In this paper, the authors proposed a kernel estimator for the distribution function of unobserved errors in autoregressive time series, based on residuals computed by estimating the auto-gressive coefficients with the Yule-Walker method.
References
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Book ChapterDOI
Probability Inequalities for sums of Bounded Random Variables
TL;DR: In this article, upper bounds for the probability that the sum S of n independent random variables exceeds its mean ES by a positive number nt are derived for certain sums of dependent random variables such as U statistics.
Book
Empirical processes with applications to statistics
Galen R. Shorack,Jon A. Wellner +1 more
TL;DR: In this paper, a broad cross-section of the literature available on one-dimensional empirical processes is summarized, with emphasis on real random variable processes as well as a wide-ranging selection of applications in statistics.
Journal ArticleDOI
Estimating Optimal Transformations for Multiple Regression and Correlation.
Leo Breiman,Jerome H. Friedman +1 more
TL;DR: In this article, a procedure for estimating functions θ and O 1, O 1, O p that minimize e 2 = E{[θ(Y) − Σ O j (Xj )]2}/var[ θ(X)], given only a sample {(yk, xk1, k 1, xkp ), 1 ⊽ k ⩽ N} and making minimal assumptions concerning the data distribution or the solution functions.
Journal ArticleDOI
Optimal Global Rates of Convergence for Nonparametric Regression
TL;DR: In this article, it was shown that the optimal rate of convergence for an estimator of an unknown regression function (i.e., a regression function of order 2p + d) with respect to a training sample of size n = (p - m)/(2p + 2p+d) is O(n−1/n−r) under appropriate regularity conditions, where n−1 is the optimal convergence rate if q < q < \infty.
Journal ArticleDOI
Additive Regression and Other Nonparametric Models
TL;DR: In this article, a variety of parametric and nonparametric models for the joint distribution of a pair of random variables are discussed in relation to flexibility, dimensionality, and interpretability.