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Applications of regime-switching models based on aggregation operators

Jozef Komorník, Magda Komorníková (2007)

Kybernetika

A synthesis of recent development of regime-switching models based on aggregation operators is presented. It comprises procedures for model specification and identification, parameter estimation and model adequacy testing. Constructions of models for real life data from hydrology and finance are presented.

Approximate bias for first-order autoregressive model with uniform innovations. Small sample case

Karima Nouali, Hocine Fellag (2002)

Discussiones Mathematicae Probability and Statistics

The first-order autoregressive model with uniform innovations is considered. The approximate bias of the maximum likelihood estimator (MLE) of the parameter is obtained. Also, a formula for the approximate bias is given when a single outlier occurs at a specified time with a known amplitude. Simulation procedures confirm that our formulas are suitable. A small sample case is considered only.

Approximate maximum likelihood estimation for a spatial point pattern.

Jorge Mateu, Francisco Montes (2000)

Qüestiió

Several authors have proposed stochastic and non-stochastic approximations to the maximum likelihood estimate for a spatial point pattern. This approximation is necessary because of the difficulty of evaluating the normalizing constant. However, it appears to be neither a general theory which provides grounds for preferring a particular method, nor any extensive empirical comparisons. In this paper, we review five general methods based on approximations to the maximum likelihood estimate which have...

Approximate polynomial expansion for joint density

D. Pommeret (2005)

Applicationes Mathematicae

Let (X,Y) be a random vector with joint probability measure σ and with margins μ and ν. Let ( P ) n and ( Q ) n be two bases of complete orthonormal polynomials with respect to μ and ν, respectively. Under integrability conditions we have the following polynomial expansion: σ ( d x , d y ) = n , k ϱ n , k P ( x ) Q k ( y ) μ ( d x ) ν ( d y ) . In this paper we consider the problem of changing the margin μ into μ̃ in this expansion. That is the case when μ is the true (or estimated) margin and μ̃ is its approximation. It is shown that a new joint probability with new margins...

Approximated maximum likelihood estimation of parameters of discrete stable family

Lenka Slámová, Lev B. Klebanov (2014)

Kybernetika

In this article we propose a method of parameters estimation for the class of discrete stable laws. Discrete stable distributions form a discrete analogy to classical stable distributions and share many interesting properties with them such as heavy tails and skewness. Similarly as stable laws discrete stable distributions are defined through characteristic function and do not posses a probability mass function in closed form. This inhibits the use of classical estimation methods such as maximum...

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