In this article, nonparametric estimators of the regression function, and its derivatives, obtained by means of weighted local polynomial fitting are studied. Consider the fixed regression model where the error random...
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In this article, nonparametric estimators of the regression function, and its derivatives, obtained by means of weighted local polynomial fitting are studied. Consider the fixed regression model where the error random variables are coming from a stationary stochastic process satisfying a mixing condition. Uniform strong consistency, along with rates, are established for these estimators. Furthermore, when the errors follow an AR(l) correlation structure, strong consistency properties are also derived for a modified version of the local polynomial estimators proposed by Vilar-Fernandez and Francisco-Fernandez (Vilar-Fernandez, J. M., Francisco-Fern ndez, M. (2002). Local polynomial regression smoothers with AR-error structure. TEST 11(2):439-464).
This paper presents relative stability properties of various nonparametric density estimators (histogram, kernel estimates) and of regression estimators (partitioning, kernel, and nearest neighbor estimates). In densi...
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This paper presents relative stability properties of various nonparametric density estimators (histogram, kernel estimates) and of regression estimators (partitioning, kernel, and nearest neighbor estimates). In density estimation, let E-n denote the L-1 error of an estimate calculated from n data, whereas in regressionestimation, the L-2 error of the estimate is used. Sufficient conditions for E-n/E{E-n} --> 1 in probability are provided. If this limit holds, the asymptotic behavior of the random error E-n can be characterized by its expectation E{E-n}, and one may apply, for example, the established rate-of-convergence results for E{E-n}.
For semi-recursive and recursive kernel estimates of a regression of Y on X (d-dimensional random vector X, integrable real random variable Y), introduced by Devroye and Wagner and by Revesz, respectively, strong univ...
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For semi-recursive and recursive kernel estimates of a regression of Y on X (d-dimensional random vector X, integrable real random variable Y), introduced by Devroye and Wagner and by Revesz, respectively, strong universal pointwise consistency is shown, i.e. strong consistency Px-almost everywhere for general distribution of (X, Y). Similar results are shown for the corresponding partitioning estimates.
This paper considers estimation of the function g in the model Y-t = g(X-t) + epsilon (t) when E(epsilon (t)\X-t) not equal 0 with nonzero probability. We assume the existence of an instrumental variable Z(t) that is ...
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This paper considers estimation of the function g in the model Y-t = g(X-t) + epsilon (t) when E(epsilon (t)\X-t) not equal 0 with nonzero probability. We assume the existence of an instrumental variable Z(t) that is independent of epsilon (t), and of an innovation eta (t) = X-t - E(X-t\Z(t)). We use a nonparametricregression of X-t on Z(t) to obtain residuals <()over cap>(t), which in turn are used to obtain a consistent estimator of g. The estimator was first analyzed by Newey, Powell & Vella (1999) under the assumption that the observations are independent and identically distributed. Here we derive a sample mean-squared-error convergence result for independent identically distributed observations as well as a uniform-convergence result under time-series dependence.
The strong universal pointwise consistency of some modified versions of the standard regression function estimates of partitioning, kernel, and nearest neighbor type is shown. (C) 1999 Academic Press.
The strong universal pointwise consistency of some modified versions of the standard regression function estimates of partitioning, kernel, and nearest neighbor type is shown. (C) 1999 Academic Press.
For different classes of deterministic and random sampling (t(k)), we establish the asymptotic expressions for the bias and the variance of the estimate r(n)(x) based on sampled data (X-tk, Y-tk)k=1,...,n for the regr...
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For different classes of deterministic and random sampling (t(k)), we establish the asymptotic expressions for the bias and the variance of the estimate r(n)(x) based on sampled data (X-tk, Y-tk)k=1,...,n for the regression function r(x) = E(Y-t/X-t = x) of unbounded continuous-time processes (X-t, Y-t)(t is an element of R) (not necessarily stationary). Under mild mixing conditions, we show that r(n)(x) has exactly the same asymptotic quadratic error as in the i.i.d. case. In order to prove this result, we use some large deviations inequalities for mixing processes.
The L-2-error of the partitioning regression estimator of a regression function m(x) = E(Y/X = x) using a cubic partition is shown to be asymptotically normal under the condition that X has a continuous density f of b...
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The L-2-error of the partitioning regression estimator of a regression function m(x) = E(Y/X = x) using a cubic partition is shown to be asymptotically normal under the condition that X has a continuous density f of bounded support and Y satisfies some moment condition. (C) 1998 Elsevier Science B.V. All rights reserved.
Common wavelet-based methods for nonparametric regression estimation are difficult to apply when the design is random. This paper proposes a modification of the linear wavelet estimator, called the binned wavelet esti...
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Common wavelet-based methods for nonparametric regression estimation are difficult to apply when the design is random. This paper proposes a modification of the linear wavelet estimator, called the binned wavelet estimator leading to a fast O(n) method with asymptotic properties identical with those of linear wavelet estimators under a fixed equidistant design. (C) 1997 Elsevier Science B.V.
In this paper we propose a Bernstein type estimate of the regression function m(x) = E[Y\X = x]. Various local and global asymptotic properties of this estimate are studied.
In this paper we propose a Bernstein type estimate of the regression function m(x) = E[Y\X = x]. Various local and global asymptotic properties of this estimate are studied.
Given the model Y i =m(χ i )+e{open}i,where E(e{open} i) =0, X i ≠Ci=1, ..., n, and C is a p-dimensional compact set, we have designed a new method for testing the hypothesis that the regression function follows a g...
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