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This paper gives an analytical expression for the best linear unbiased estimator (BLUE) of the unknown parameters in the linear Haar-wavelet model. From the analytical expression, we solve for the eigenvalues of the covariance matrix of the BLUE in analytical form. Further, we use these eigenvalues to construct some conventional discrete optimal designs for the model. The equivalences among these...
The asymptotic behavior of S-estimators in a random design linear model with long-range-dependent Gaussian errors is considered. It turns out that the S-estimators of regression parameter and error variance are strongly consistent under mild conditions. Furthermore, the asymptotic distribution of the S-estimator of regression parameter is normal if the design vectors are i.i.d. and is non-normal if...
In the paper the problem of simultaneous linear estimation of fixed and random effects in the mixed linear model is considered. A necessary and sufficient conditions for a linear estimator of a linear function of fixed and random effects in balanced nested and crossed classification models to be admissible are given.
In this paper we introduce a new regression model in which the response variable is bounded by two unknown parameters. A special case is a bounded alternative to the four parameter logistic model. The four parameter model which has unbounded responses is widely used, for instance, in bioassays, nutrition, genetics, calibration and agriculture. In reality, the responses are often bounded although the...
This paper considers predictions of vectors of parameters under a general linear model $$\mathbf{y}= \mathbf{X}{\pmb {\beta }}+ {\pmb {\varepsilon }}$$ y = X β + ε with the random coefficients $${\pmb {\beta }}$$ β satisfying $${\pmb {\beta }}=\mathbf{A}{\pmb {\alpha }}+ {\pmb {\gamma }}$$ β = A α + γ . It utilizes a standard method of solving constrained...
We improve a known result on the strong consistency of M-estimates of the regression parameters in a linear model for independent and identically distributed random errors under some mild conditions.
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