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Extremal (in)dependence of a maximum autoregressive process

100%

Ferreira M.

Discussiones Mathematicae Probability and Statistics

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2013

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tom 33

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nr 1-2

47-64

EN

Maximum autoregressive processes like MARMA (Davis and Resnick, [5] 1989) or power MARMA (Ferreira and Canto e Castro, [12] 2008) have singular joint distributions, an unrealistic feature in most applications. To overcome this pitfall, absolute continuous versions were presented in Alpuim and Athayde [2] (1990) and Ferreira and Canto e Castro [14] (2010b), respectively. We consider an extended version of absolute continuous maximum autoregressive processes that accommodates both asymptotic tail dependence and independence. A full characterization of the bivariate lag-m tail dependence is presented. This will be useful in an adjustment procedure of the model to real data. An illustration with financial data is presented at the end.

2

On the tail index estimation of an autoregressive Pareto process

100%

Ferreira M.

Discussiones Mathematicae Probability and Statistics

|

2013

|

tom 33

|

nr 1-2

65-77

EN

In this paper we consider an autoregressive Pareto process which can be used as an alternative to heavy tailed MARMA. We focus on the tail behavior and prove that the tail empirical quantile function can be approximated by a Gaussian process. This result allows to derive a class of consistent and asymptotically normal estimators for the shape parameter. We will see through simulation that the usual estimation procedure based on an i.i.d. setting may fall short of the desired precision.

3

Estimating the extremal index through the tail dependence concept

100%

Ferreira M.

Discussiones Mathematicae Probability and Statistics

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2015

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tom 35

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nr 1-2

61-74

EN

The extremal index Θ is an important parameter in extreme value analysis when extending results from independent and identically distributed sequences to stationary ones. A connection between the extremal index and the tail dependence coefficient allows the introduction of new estimators. The proposed ones are easy to compute and we analyze their performance through a simulation study. Comparisons with other existing methods are also presented. Case studies within environment are considered in the end.

4

The extreme value Birnbaum-Saunders model, its moments and an application in biometry

51%

Gomes M. I., Ferreira M., Leiva V.

Biometrical Letters

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2012

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tom 49

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nr 2

81-94

EN

The Birnbaum-Saunders (BS) model is a life distribution that has been widely studied and applied. Recently, a new version of the BS distribution based on extreme value theory has been introduced, named the extreme value Birnbaum-Saunders (EVBS) distribution. In this article we provide some further details on the EVBS models that can be useful as a supplement to the existing results. We use these models to analyse real survival time data for patients treated with alkylating agents for multiple myeloma. This analysis allow us to show the adequacy of these new statistical distributions and identify them as models useful for medical practitioners in order to predict survival times for such patients and evaluate changes in their treatment dose.

Ograniczanie wyników

3 Discussiones Mathematicae Probability and Statistics

1 Biometrical Letters

4 Ferreira M.

1 Gomes M. I.

1 Leiva V.

1 2015

2 2013

1 2012

Extremal (in)dependence of a maximum autoregressive process

On the tail index estimation of an autoregressive Pareto process

Estimating the extremal index through the tail dependence concept

The extreme value Birnbaum-Saunders model, its moments and an application in biometry