Titlebook: Nonparametric Estimation of Probability Densities and Regression Curves; E. A. Nadaraya Book 1989 Kluwer Academic Publishers 1989 Maxima.c

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Introduction,ric estimation. A nonparametric procedure is usually defined as a procedure which is valid independently of the distribution of the sampled observations. The problem of estimating the functional characteristics of a distribution law of observations belongs to problems of nonparametric estimation. In

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Asymptotic Properties of Certain Measures of Deviation for Kernel-Type Nonparametric Estimators of e assume that the required density f(x) belongs to the space L. (− ∞, ∞) of functions which are square integrable with respect to the Lebesgue measure and consider the methods of empirical approximations to this density — when the errors are measured in the L(− ∞, ∞) metric — of the form . Here K(x)

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Strongly Consistent in Functional Metrics Estimators of Probability Density,tribution function F(x) be absolutely continuous and f(x) be the corresponding density function. As an estimator of the density f(x) we consider a non-parametric estimator f.(x) of the form (cf. 1.1.1) .where K(x) is a probability density and {a.} is a sequence of positive numbers approaching infini

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Limiting Distributions of Deviations of Kernel-Type Density Estimators,orems proved therein were basically of a qualitative nature. The problem of accuracy and reliability of approximations for large samples was not addressed in these theorems. In this section the limiting behavior of the distribution of the maximal deviation of an empirical density f.(x) of the type (

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Nonparametric Estimation of Regression Curves and Components of a Convolution, In particular in this and in the succeeding three sections we shall investigate properties of the non parametric estimators r.(x) of the regression curve r(x) which was introduced and studied by the author in [21]. Interest in this estimator has been constantly growing and many interesting results

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Limiting Distribution of Quadratic Deviation for a Wide Class of Probability Density Estimators,of the density f(x) constructed by means of ‘kernels’ was studied by P. Bickel and M. Rosenblatt [49]. An analogous problem for estimators constructed by means of systems of orthonormal functions (‘projection estimators’) was investigated by E. A. Nadaraya [91]. The basic method utilized in these in

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