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On Fourier coefficient estimators consistent in the mean-square sense

Waldemar Popiński (1994)

Applicationes Mathematicae

The properties of two recursive estimators of the Fourier coefficients of a regression function f L 2 [ a , b ] with respect to a complete orthonormal system of bounded functions (ek) , k=1,2,..., are considered in the case of the observation model y i = f ( x i ) + η i , i=1,...,n , where η i are independent random variables with zero mean and finite variance, x i [ a , b ] R 1 , i=1,...,n, form a random sample from a distribution with density ϱ =1/(b-a) (uniform distribution) and are independent of the errors η i , i=1,...,n . Unbiasedness and mean-square...

On inconsistency of Hellwig's variable choice method in regression models

Tadeusz Bednarski, Filip Borowicz (2009)

Discussiones Mathematicae Probability and Statistics

It is shown that a popular variable choice method of Hellwig, which is recommended in the Polish econometric textbooks does not enjoy a very basic consistency property. It means in particular that the method may lead to rejection of significant variables in econometric modeling. A simulation study and a real data analysis case are given to support theoretical results.

On maximum likelihood estimation in mixed normal models with two variance components

Mariusz Grządziel (2014)

Discussiones Mathematicae Probability and Statistics

In the paper we deal with the problem of parameter estimation in the linear normal mixed model with two variance components. We present solutions to the problem of finding the global maximizer of the likelihood function and to the problem of finding the global maximizer of the REML likelihood function in this model.

On minimax sequential procedures for exponential families of stochastic processes

Ryszard Magiera (1998)

Applicationes Mathematicae

The problem of finding minimax sequential estimation procedures for stochastic processes is considered. It is assumed that in addition to the loss associated with the error of estimation a cost of observing the process is incurred. A class of minimax sequential procedures is derived explicitly for a one-parameter exponential family of stochastic processes. The minimax sequential procedures are presented in some special models, in particular, for estimating a parameter of exponential families of...

On multiple periodic autoregression

Jiří Anděl (1987)

Aplikace matematiky

The model of periodic autoregression is generalized to the multivariate case. The autoregressive matrices are periodic functions of time. The mean value of the process can be a non-vanishing periodic sequence of vectors. Estimators of parameters and tests of statistical hypotheses are based on the Bayes approach. Two main versions of the model are investigated, one with constant variance matrices and the other with periodic variance matrices of the innovation process.

On non-nested regression models

Jiří Anděl (1993)

Commentationes Mathematicae Universitatis Carolinae

A generalization of a test for non-nested models in linear regression is derived for the case when there are several regression models with more regressors.

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