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On a linearization of regression models

Lubomír Kubáček (1995)

Applications of Mathematics

An approximate value of a parameter in a nonlinear regression model is known in many cases. In such situation a linearization of the model is possible however it is important to recognize, whether the difference between the actual value of the parameter and the approximate value does not cause significant changes, e.g., in the bias of the estimator or in its variance, etc. Some rules suitable for a solution of this problem are given in the paper.

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 parameter-effects arrays in non-linear regression models

Rastislav Potocký, Van Ban To (1993)

Applications of Mathematics

Formulas for a new three- and four-dimensional parameter-effects arrays corresponding to transformations of parameters in non-linear regression models are given. These formulae make the construction of the confidence regions for parameters easier. An example is presented which shows that some care is necessary when a new array is computed.

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