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A note on almost sure convergence and convergence in measure

P. Kříž, Josef Štěpán (2014)

Commentationes Mathematicae Universitatis Carolinae

The present article studies the conditions under which the almost everywhere convergence and the convergence in measure coincide. An application in the statistical estimation theory is outlined as well.

A note on the strong consistency of least squares estimates

Joǎo Lita da Silva (2009)

Discussiones Mathematicae Probability and Statistics

The strong consistency of least squares estimates in multiples regression models with i.i.d. errors is obtained under assumptions on the design matrix and moment restrictions on the errors.

Adaptive goodness-of-fit testing from indirect observations

Cristina Butucea, Catherine Matias, Christophe Pouet (2009)

Annales de l'I.H.P. Probabilités et statistiques

In a convolution model, we observe random variables whose distribution is the convolution of some unknown density f and some known noise density g. We assume that g is polynomially smooth. We provide goodness-of-fit testing procedures for the test H0: f=f0, where the alternative H1is expressed with respect to 𝕃 2 -norm (i.e. has the form ψ n - 2 f - f 0 2 2 𝒞 ). Our procedure is adaptive with respect to the unknown smoothness parameterτ of f. Different testing rates (ψn) are obtained according to whether f0 is polynomially...

Adaptive trimmed likelihood estimation in regression

Tadeusz Bednarski, Brenton R. Clarke, Daniel Schubert (2010)

Discussiones Mathematicae Probability and Statistics

In this paper we derive an asymptotic normality result for an adaptive trimmed likelihood estimator of regression starting from initial high breakdownpoint robust regression estimates. The approach leads to quickly and easily computed robust and efficient estimates for regression. A highlight of the method is that it tends automatically in one algorithm to expose the outliers and give least squares estimates with the outliers removed. The idea is to begin with a rapidly computed consistent robust...

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