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Asymptotic behaviour of the probability-weighted moments and penultimate approximation

Jean Diebolt, Armelle Guillou, Rym Worms (2003)

ESAIM: Probability and Statistics

The P.O.T. (Peaks-Over-Threshold) approach consists of using the Generalized Pareto Distribution (GPD) to approximate the distribution of excesses over a threshold. We use the probability-weighted moments to estimate the parameters of the approximating distribution. We study the asymptotic behaviour of these estimators (in particular their asymptotic bias) and also the functional bias of the GPD as an estimate of the distribution function of the excesses. We adapt penultimate approximation results...

Asymptotic behaviour of the probability-weighted moments and penultimate approximation

Jean Diebolt, Armelle Guillou, Rym Worms (2010)

ESAIM: Probability and Statistics

The P.O.T. (Peaks-Over-Threshold) approach consists of using the Generalized Pareto Distribution (GPD) to approximate the distribution of excesses over a threshold. We use the probability-weighted moments to estimate the parameters of the approximating distribution. We study the asymptotic behaviour of these estimators (in particular their asymptotic bias) and also the functional bias of the GPD as an estimate of the distribution function of the excesses. We adapt penultimate approximation results...

Asymptotic covariances for the generalized gamma distribution

Christopher S. Withers, Saralees Nadarajah (2011)

Applicationes Mathematicae

The five-parameter generalized gamma distribution is one of the most flexible distributions in statistics. In this note, for the first time, we provide asymptotic covariances for the parameters using both the method of maximum likelihood and the method of moments.

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 ℛ n . It is shown that n ℛ 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.

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