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Generalized linear and nonlinear mixed-effects models are used extensively in biomedical, social, and agricultural sciences. The statistical analysis of these models is based on the asymptotic properties of the maximum likelihood estimator. However, it is usually assumed that the maximum likelihood estimator is consistent, without providing a proof. A rigorous proof of the consistency by verifying...
In this paper, varying coefficient proportional hazard regression models are considered. The model is an important extension of the Cox model, and arises naturally if the coefficients change over different groups characterized by certain covariates in practice. Under random censorship, weighted partial likelihood estimators are defined for the varying coefficients by maximizing weighted partial likelihoods...
The strong consistency of the least squares estimator in multiple regression models is established assuming the randomness of the regressors and errors with infinite variance. Only moderately restrictive conditions are imposed on the stochastic model matrix and the errors will be random variables having moment of order $$r,\,1 \leqslant r \leqslant 2$$ . In our treatment, we use Etemadi’s strong...
This paper presents a new random weighting method to estimation of the stable exponent. Assume that $$X_1, X_2, \ldots ,X_n$$ X 1 , X 2 , ... , X n is a sequence of independent and identically distributed random variables with $$\alpha $$ α -stable distribution G, where $$\alpha \in (0,2]$$ α ∈ ( 0 , 2 ] is the stable exponent. Denote the empirical distribution...
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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