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Some applications of probability generating function based methods to statistical estimation

100%

Esquível M.

Discussiones Mathematicae Probability and Statistics

2009

tom 29

nr 2

131-153

After recalling previous work on probability generating functions for real valued random variables we extend to these random variables uniform laws of large numbers and functional limit theorem for the empirical probability generating function. We present an application to the study of continuous laws, namely, estimation of parameters of Gaussian, gamma and uniform laws by means of a minimum contrast estimator that uses the empirical probability generating function of the sample. We test the procedure by simulation and we prove the consistency of the estimator.

Small perturbations with large effects on value-at-risk

51%

Esquível M., Dimas L., Mexia J., Didier P.

Discussiones Mathematicae Probability and Statistics

2013

tom 33

nr 1-2

151-169

We show that in the delta-normal model there exist perturbations of the Gaussian multivariate distribution of the returns of a portfolio such that the initial marginal distributions of the returns are statistically undistinguishable from the perturbed ones and such that the perturbed V@R is close to the worst possible V@R which, under some reasonable assumptions, is the sum of the V@Rs of each of the portfolio assets.

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2 Discussiones Mathematicae Probability and Statistics

2 Esquível M.

1 Didier P.

1 Dimas L.

1 Mexia J.

1 2013

1 2009

Wyniki wyszukiwania

Some applications of probability generating function based methods to statistical estimation

Small perturbations with large effects on value-at-risk