In small area estimation, linear mixed models are frequently used. Variable selection methods for linear mixed models are available. However, in many applications such as small area estimation data users often apply variable selection methods that ignore the random effects. In this paper, we first evaluate the accuracy of such variable selection method for the Fay-Herriot model, a regression model when dependent variable is subject to sampling error variability. We show that the approximation error, that is, the difference between the standard variable selection criterion and the corresponding ideal variable selection criterion without any sampling error variability, does not converge to zero in probability even for a large sample size. In our simulation, we notice that standard variable selection criterion could severely underestimate the ideal adjusted R 2 and BIC variable selection criteria in presence of high sampling error variability. We propose a simple adjustment to the standard variable selection method for the Fay-Herriot model that reduces the approximation errors. In particular, we show that the approximation error for our new variable selection criteria converge to zero in probability for large sample size. Using a Monte Carlo simulation, we demonstrate that our proposed variable selection criterion tracks the corresponding ideal variable selection criterion very well compared to the standard variable selection method.
After a brief historical survey of parametric survival models, from actuarial, biomedical, demographical and engineering sources, this paper discusses the persistent reasons why parametric models still play an important role in exploratory statistical research. The phase-type models are advanced as a flexible family of latent-class models with interpretable components. These models are now supported by computational statistical methods that make numerical calculation of likelihoods and statistical estimation of parameters feasible in theory for quite complicated settings. However, consideration of Fisher Information and likelihood-ratio type tests to discriminate between model families indicates that only the simplest phase-type model topologies can be stably estimated in practice, even on rather large datasets. An example of a parametric model with features of mixtures, multiple stages or 'hits', and a trapping-state is given to illustrate simple computational tools in R, both on simulated data and on a large SEER 1992-2002 breast-cancer dataset.
We apply Stein's method to obtain a non-uniform exponential bound for normal approximations for certain types of random variables. In particular, we establish the bound for a random variable such that its exchangeable pair coupling exists and the distance between the pair is bounded. Using our result, we obtain better bounds for a wide range of applications, such as sums of bounded independent random variables, the combinatorial central limit theorem, and the numbers of descents and inversions of a permutation.
In this paper, we obtain a nonuniform Berry–Esseen bound for a normal approximation via the Stein method and the exchangeable-pair coupling technique where the boundedness condition of the difference between the exchangeable pair is not required. As applications of the result, we obtain nonuniform bounds for the normal approximations in two well-known applications that are the independence test and the quadratic form. Our results suggest that the obtained bounds for the two applications are sharper than other existing bounds.
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