A note on orthogonal series regression function estimators

Waldemar Popiński

Displaying similar documents to “A note on orthogonal series regression function estimators”

Convergence rates of orthogonal series regression estimators

Waldemar Popiński (2000)

Applicationes Mathematicae

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General conditions for convergence rates of nonparametric orthogonal series estimators of the regression function f(x)=E(Y | X = x) are considered. The estimators are obtained by the least squares method on the basis of a random observation sample (Yi,Xi), i=1,...,n, where $X_{i} \in A \subset ℝ^{d}$ have marginal distribution with density $ϱ \in L^{1} (A)$ and Var( Y | X = x) is bounded on A. Convergence rates of the errors $E_{X} {(f (X) - {\hat{f}}_{N} (X))}^{2}$ and $∥ f - {\hat{f}}_{N} ∥_{\infty}$ for the estimator ${\hat{f}}_{N} (x) = \sum_{k = 1}^{N} {\hat{c}}_{k} e_{k} (x)$ , constructed using an orthonormal system $e_{k}$ , k=1,2,..., in $L^{2} (A)$ are obtained. ...

Least-squares trigonometric regression estimation

Waldemar Popiński (1999)

Applicationes Mathematicae

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The problem of nonparametric function fitting using the complete orthogonal system of trigonometric functions $e_{k}$ , k=0,1,2,..., for the observation model $y_{i} = f (x_{i n}) + η_{i}$ , i=1,...,n, is considered, where $η_{i}$ are uncorrelated random variables with zero mean value and finite variance, and the observation points $x_{i n} \in [0, 2 π]$ , i=1,...,n, are equidistant. Conditions for convergence of the mean-square prediction error $(1 / n) \sum_{i = 1}^{n} E {(f (x_{i n}) - {\hat{f}}_{N (n)} (x_{i n}))}^{2}$ , the integrated mean-square error $E ‖ f - {\hat{f}}_{N (n)} ‖^{2}$ and the pointwise mean-square error $E {(f (x) -_{N (n)} (x))}^{2}$ of the estimator ${\hat{f}}_{N (n)} (x) = \sum_{k = 0}^{N (n)} {\hat{c}}_{k} e_{k} (x)$ for f ∈...

On least squares estimation of Fourier coefficients and of the regression function

Waldemar Popiński (1993)

Applicationes Mathematicae

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Orthogonal series regression estimators for an irregularly spaced design

Waldemar Popiński (2000)

Applicationes Mathematicae

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Nonparametric orthogonal series regression function estimation is investigated in the case of a fixed point design where the observation points are irregularly spaced in a finite interval [a,b]i ⊂ ℝ. Convergence rates for the integrated mean-square error and pointwise mean-square error are obtained in the case of estimators constructed using the Legendre polynomials and Haar functions for regression functions satisfying the Lipschitz condition.

Regression quantiles and trimmed least squares estimator under a general design

Jana Jurečková (1984)

Kybernetika

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Robust estimation and forecasting for beta-mixed hierarchical models of grouped binary data.

Maxim A. Pashkevich, Yurij S. Kharin (2004)

SORT

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The paper focuses on robust estimation and forecasting techniques for grouped binary data with misclassified responses. It is assumed that the data are described by the beta-mixed hierarchical model (the beta-binomial or the beta-logistic), while the misclassifications are caused by the stochastic additive distorsions of binary observations. For these models, the effect of ignoring the misclassifications is evaluated and expressions for the biases of the method-of-moments estimators...

Estimators in the location model with gradual changes

Marie Hušková (1998)

Commentationes Mathematicae Universitatis Carolinae

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A number of papers has been published on the estimation problem in location models with abrupt changes (e.g., Cs" orgő and Horváth (1996)). In the present paper we focus on estimators in location models with gradual changes. Estimators of the parameters are proposed and studied. It appears that the limit behavior (both the rate of consistency and limit distribution) of the estimators of the change point in location models with abrupt changes and gradual changes differ substantially. ...

Minimax mutual prediction

Stanisław Trybuła (2000)

Applicationes Mathematicae

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The problems of minimax mutual prediction are considered for binomial and multinomial random variables and for sums of limited random variables with unknown distribution. For the loss function being a linear combination of quadratic losses minimax mutual predictors are determined where the parameters of predictors are obtained by numerical solution of some equations.