EXPONENTIAL INEQUALITIES FOR SPATIAL PROCESSES AND UNIFORM CONVERGENCE RATES FOR DENSITY ESTIMATION

This paper studies the uniform convergence rates of Li and Vuong’s (1998, Journal of Multivariate Analysis 65, 139–165; hereafter LV) nonparametric deconvolution estimator and its regularized version by Comte and Kappus (2015, Journal of Multivariate Analysis 140, 31–46) for the classical measurement error model, where repeated noisy measurements on the error-free variable of interest are available. In contrast to LV, our assumptions allow unbounded supports for the error-free variable and measurement errors. Compared to Bonhomme and Robin (2010, Review of Economic Studies 77, 491–533) specialized to the measurement error model, our assumptions do not require existence of the moment generating functions of the square and product of repeated measurements. Furthermore, by utilizing a maximal inequality for the multivariate normalized empirical characteristic function process, we derive uniform convergence rates that are faster than the ones derived in these papers under such weaker conditions.

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Uniform convergence rates for wavelet curve estimation in sup-norm loss

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2021.113752 ◽

2021 ◽

pp. 113752

Author(s):

Xingcai Zhou

Keyword(s):

Uniform Convergence ◽

Convergence Rates ◽

Curve Estimation

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Optimal Uniform Convergence Rates for Sieve Nonparametric Instrumental Variables Regression

SSRN Electronic Journal ◽

10.2139/ssrn.2349684 ◽

2013 ◽

Author(s):

Xiaohong Chen ◽

Timothy Christensen

Keyword(s):

Uniform Convergence ◽

Instrumental Variables ◽

Convergence Rates

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Strong uniform convergence rates in robust nonparametric time series analysis and prediction: Kernel regression estimation from dependent observations

Stochastic Processes and their Applications ◽

10.1016/0304-4149(86)90017-7 ◽

1986 ◽

Vol 23 (1) ◽

pp. 77-89 ◽

Cited By ~ 123

Author(s):

Gérard Collomb ◽

Wolfgang Härdle

Keyword(s):

Time Series ◽

Time Series Analysis ◽

Uniform Convergence ◽

Convergence Rates ◽

Kernel Regression ◽

Regression Estimation ◽

Dependent Observations ◽

Series Analysis ◽

Strong Uniform Convergence ◽

Kernel Regression Estimation

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Strong Uniform Convergence Rates for Some Robust Equivariant Nonparametric Regression Estimates for Mixing Processes

International Statistical Review ◽

10.2307/1403692 ◽

1991 ◽

Vol 59 (3) ◽

pp. 355 ◽

Cited By ~ 20

Author(s):

Graciela Boente ◽

Ricardo Fraiman

Keyword(s):

Uniform Convergence ◽

Nonparametric Regression ◽

Convergence Rates ◽

Mixing Processes ◽

Strong Uniform Convergence

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Sup-norm convergence rates for Lévy density estimation

Extremes ◽

10.1007/s10687-016-0246-4 ◽

2016 ◽

Vol 19 (3) ◽

pp. 371-403 ◽

Cited By ~ 1

Author(s):

Valentin Konakov ◽

Vladimir Panov

Keyword(s):

Density Estimation ◽

Convergence Rates ◽

Norm Convergence ◽

Lévy Density

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Uniform convergence rates for nonparametric regression and principal component analysis in functional/longitudinal data

The Annals of Statistics ◽

10.1214/10-aos813 ◽

2010 ◽

Vol 38 (6) ◽

pp. 3321-3351 ◽

Cited By ~ 81

Author(s):

Yehua Li ◽

Tailen Hsing

Keyword(s):

Principal Component Analysis ◽

Longitudinal Data ◽

Uniform Convergence ◽

Nonparametric Regression ◽

Convergence Rates ◽

Principal Component ◽

Component Analysis

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Convergence rates for Bayesian density estimation of infinite-dimensional exponential families

The Annals of Statistics ◽

10.1214/009053606000000911 ◽

2006 ◽

Vol 34 (6) ◽

pp. 2897-2920 ◽

Cited By ~ 14

Author(s):

Catia Scricciolo

Keyword(s):

Density Estimation ◽

Convergence Rates ◽

Exponential Families ◽

Infinite Dimensional ◽

Bayesian Density Estimation

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UNIFORM CONVERGENCE RATES OVER MAXIMAL DOMAINS IN STRUCTURAL NONPARAMETRIC COINTEGRATING REGRESSION

Econometric Theory ◽

10.1017/s0266466616000451 ◽

2017 ◽

Vol 33 (6) ◽

pp. 1387-1417 ◽

Cited By ~ 4

Author(s):

James A. Duffy

Keyword(s):

Regression Model ◽

Uniform Convergence ◽

Lower Order ◽

Unit Root ◽

Autoregressive Model ◽

Convergence Rates ◽

Kernel Regression ◽

Infinite Variance ◽

Standard Unit ◽

Regression Estimators

This paper presents uniform convergence rates for kernel regression estimators, in the setting of a structural nonlinear cointegrating regression model. We generalise the existing literature in three ways. First, the domain to which these rates apply is much wider than the domains that have been considered in the existing literature, and can be chosen so as to contain as large a fraction of the sample as desired in the limit. Second, our results allow the regression disturbance to be serially correlated, and cross-correlated with the regressor; previous work on this problem (of obtaining uniform rates) having been confined entirely to the setting of an exogenous regressor. Third, we permit the bandwidth to be data-dependent, requiring it to satisfy only certain weak asymptotic shrinkage conditions. Our assumptions on the regressor process are consistent with a very broad range of departures from the standard unit root autoregressive model, allowing the regressor to be fractionally integrated, and to have an infinite variance (and even infinite lower-order moments).

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The Lower Bound of Density Estimation for Biased Data in Sobolev Spaces

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.765-767.744 ◽

2013 ◽

Vol 765-767 ◽

pp. 744-748

Author(s):

Jin Ru Wang ◽

Yuan Zhou

Keyword(s):

Lower Bound ◽

Density Estimation ◽

Sobolev Spaces ◽

Convergence Rates ◽

Estimation Problem ◽

Independent And Identically Distributed

In this paper, we consider the density estimation problem from independent and identically distributed (i.i.d.) biased observations. We study the lower bound of convergence rates of density estimation over Sobolev spaces WrN(NN+) under the Lp risk by using Fanos lemma.

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