Displaying similar documents to “Regression quantiles and trimmed least squares estimator under a general design”

Exponential regression

Lubomír Kubáček, Ludmila Kubáčková, Eva Tesaříková (2001)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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Combining forecasts using the least trimmed squares

Jan Ámos Víšek (2001)

Kybernetika

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Employing recently derived asymptotic representation of the least trimmed squares estimator, the combinations of the forecasts with constraints are studied. Under assumption of unbiasedness of individual forecasts it is shown that the combination without intercept and with constraint imposed on the estimate of regression coefficients that they sum to one, is better than others. A numerical example is included to support theoretical conclusions.

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 ∈ A ⊂ ℝ d have marginal distribution with density ϱ ∈ L 1 ( A ) and Var( Y | X = x) is bounded on A. Convergence rates of the errors E X ( f ( X ) - f ^ N ( X ) ) 2 and ∥ f - f ^ N ∥ ∞ for the estimator f ^ N ( x ) = ∑ k = 1 N c ^ k e k ( x ) , constructed using an orthonormal system e k , k=1,2,..., in L 2 ( A ) are obtained. ...

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.