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Asymptotic distribution of the conditional regret risk for selecting good exponential populations

Shanti S. Gupta, Friedrich Liese (2000)

Kybernetika

In this paper empirical Bayes methods are applied to construct selection rules for the selection of all good exponential distributions. We modify the selection rule introduced and studied by Gupta and Liang [10] who proved that the regret risk converges to zero with rate O ( n - λ / 2 ) , 0 < λ 2 . The aim of this paper is to study the asymptotic behavior of the conditional regret risk n . It is shown that n n tends in distribution to a linear combination of independent χ 2 -distributed random variables. As an application we...

Asymptotic distribution of the estimated parameters of an ARMA(p,q) process in the presence of explosive roots

Sugata Sen Roy, Sankha Bhattacharya (2012)

Applicationes Mathematicae

We consider an autoregressive moving average process of order (p,q)(ARMA(p,q)) with stationary, white noise error variables having uniformly bounded fourth order moments. The characteristic polynomials of both the autoregressive and moving average components involve stable and explosive roots. The autoregressive parameters are estimated by using the instrumental variable technique while the moving average parameters are estimated through a derived autoregressive process using the same sample. The...

Asymptotic distributions οf linear combinations of order statistics

Małgorzata Bogdan (1994)

Applicationes Mathematicae

We study the asymptotic distributions of linear combinations of order statistics (L-statistics) which can be expressed as differentiable statistical functionals and we obtain Berry-Esseen type bounds and the Edgeworth series for the distribution functions of L-statistics. We also analyze certain saddlepoint approximations for the distribution functions of L-statistics.

Asymptotic normality and efficiency of two Sobol index estimators

Alexandre Janon, Thierry Klein, Agnès Lagnoux, Maëlle Nodet, Clémentine Prieur (2014)

ESAIM: Probability and Statistics

Many mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the variability of a quantity of interest (output of the model). One of the statistical tools used to quantify the influence of each input variable on the output is the Sobol sensitivity index. We consider the statistical estimation of this index from a finite sample of model outputs: we present two estimators and...

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

Christine H. Müller (2000)

Discussiones Mathematicae Probability and Statistics

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...

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