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Normalizing constants for a statistic based on logarithms of disjoint m-spacings

100%
Czekała F.
Applicationes Mathematicae
|
1995-1996
|
tom 23
|
nr 4
405-416
EN
The paper is concerned with the asymptotic normality of a certain statistic based on the logarithms of disjoint m-spacings. The exact and asymptotic mean and variance are computed in the case of uniform distribution on the interval [0,1]. This result is generalized to the case when the sample is drawn from a distribution with positive step density on [0,1].
2

Asymptotic normality and efficiency of variance components estimators with high breakdown points

100%
Müller C.
Discussiones Mathematicae Probability and Statistics
|
2000
|
tom 20
|
nr 1
85-95
EN
For estimating the variance components of a one-way random effect model recently Uhlig (1995, 1997) and Lischer (1996) proposed non-iterative estimators with high breakdown points. These estimators base on the high breakdown point scale estimators of Rousseeuw and Croux (1992, 1993), which they called Q-estimators. In this paper the asymptotic normal distribution of the new variance components estimators is derived so that the asymptotic efficiency of these estimators can be compared with that of the maximum likelihood estimators.
3
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Robust estimation in the multivariate normal model

88%
Kulawik A., Zontek S.
Discussiones Mathematicae Probability and Statistics
|
2016
|
tom 36
|
nr 1-2
53-66
EN
Robust estimation presented in the following paper is based on Fisher consistent and Fréchet differentiable statistical functionals. The method has been used in the multivariate normal model with variance components [5]. To transfer the method to estimate vector of expectations and positive definite covariance matrix of the multivariate normal model it is required to express the covariance matrix as a linear combination of basic elements of the vector space of real, square and symmetric matrices. The theoretical results have been completed with computer simulation studies. The robust estimator has been investigated both for model and contaminated data. Comparison with the maximum likelihood estimator has also been included.
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