Displaying similar documents to “Bootstrapping the shorth for regression”

Goodness of fit test for isotonic regression

Cécile Durot, Anne-Sophie Tocquet (2001)

ESAIM: Probability and Statistics

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We consider the problem of hypothesis testing within a monotone regression model. We propose a new test of the hypothesis H 0 : “ f = f 0 ” against the composite alternative H a : “ f ≠ f 0 ” under the assumption that the true regression function f is decreasing. The test statistic is based on the 𝕃 1 -distance between the isotonic estimator of f and the function f 0 , since it is known that a properly centered and normalized version of this distance is asymptotically standard normally distributed under H 0 . We study...

Change-point estimator in continuous quadratic regression

Daniela Jarušková (2001)

Commentationes Mathematicae Universitatis Carolinae

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The paper deals with the asymptotic distribution of the least squares estimator of a change point in a regression model where the regression function has two phases --- the first linear and the second quadratic. In the case when the linear coefficient after change is non-zero the limit distribution of the change point estimator is normal whereas it is non-normal if the linear coefficient is zero.

Exact adaptive pointwise estimation on Sobolev classes of densities

Cristina Butucea (2001)

ESAIM: Probability and Statistics

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The subject of this paper is to estimate adaptively the common probability density of n independent, identically distributed random variables. The estimation is done at a fixed point x 0 ∈ ℝ , over the density functions that belong to the Sobolev class W n ( β , L ) . We consider the adaptive problem setup, where the regularity parameter β is unknown and varies in a given set B n . A sharp adaptive estimator is obtained, and the explicit asymptotical constant, associated to its rate of convergence is found. ...