Communication in Statistics- Theory and Methods

Demidenko, Eugene; Sargent, James; Onega, Tracy

doi: 10.1080/03610926.2010.535631pmid: 23750070

The key feature of a mixed model is the presence of random effects. We have developed a coefficient, called the random effects coefficient of determination, , that estimates the proportion of the conditional variance of the dependent variable explained by random effects. This coefficient takes values from 0 to 1 and indicates how strong the random effects are. The difference from the earlier suggested fixed effects coefficient of determination is emphasized. If is close to 0, there is weak support for random effects in the model because the reduction of the variance of the dependent variable due to random effects is small; consequently, random effects may be ignored and the model simplifies to standard linear regression. The value of apart from 0 indicates the evidence of the variance reduction in support of the mixed model. If random effects coefficient of determination is close to 1 the variance of random effects is very large and random effects turn into free fixed effects—the model can be estimated using the dummy variable approach. We derive explicit formulas for in three special cases: the random intercept model, growth curve model, and meta-analysis model. Theoretical results are illustrated with three mixed model examples: (1) travel time to the nearest cancer center for women with breast cancer in the U.S.; (2) cumulative time watching alcohol related scenes in movies among young U.S. teens, as a risk factor for early drinking onset; and (3) the classic example of the meta-analysis model for combination of 13 studies on tuberculosis vaccine.

Chen, Yanhong; Song, Lixin; Feng, Jinghai

doi: 10.1080/03610926.2010.535627pmid: N/A

This article develops empirical likelihood for threshold autoregressive models. We propose general estimating equations based on moment constraint. Under some suitable conditions, we show the empirical likelihood estimators for parameter are asymptotically normally distributed, and the proposed log empirical likelihood ratio statistic asymptotically follows a standard chi-squared distribution.

Zardasht, V.; Zeephongsekul, P.; Asadi, M.

doi: 10.1080/03610926.2010.535629pmid: N/A

This article considers the properties of a nonparametric estimator developed for a reliability function which is used in many reliability problems. Properties such as asymptotic unbiasedness and consistency are proven for the estimator and using U-statistics, weak convergence of the estimator to a normal distribution is shown. Finally, numerical examples based on an extensive simulation study are presented to illustrate the theory and compare the estimator developed in this article with another based directly on the ratio of two empirical distributions studied in Zardasht and Asadi (2010).

Olivares-Pacheco, Juan F.; Salas, Estrella; Gómez, Héctor W.; Bolfarine, Heleno

doi: 10.1080/03610926.2010.533229pmid: N/A

In this article, we introduce an asymmetric extension to the univariate slash-elliptical family of distributions studied in Gómez et al. (2007a). This new family results from a scale mixture between the epsilon-skew-symmetric family of distributions and the uniform distribution. A general expression is presented for the density with special cases such as the normal, Cauchy, Student-t, and Pearson type II distributions. Some special properties and moments are also investigated. Results of two real data sets applications are also reported, illustrating the fact that the family introduced can be useful in practice.

Fu, Ying-Zi

doi: 10.1080/03610926.2010.535633pmid: N/A

Count data with extra zeros are common in many biomedical applications and the zero-inflated generalized power series (ZIGPS) distribution may be appropriate, in which the baseline discrete distribution is a generalized power series distribution, which is a natural extension of power series distribution. In this article, a Monte Carlo EM (MCEM) algorithm is proposed to obtain maximum likelihood estimates and standard errors for ZIGPS distribution with missing responses. A Monte Carlo approximation method combining the Gibbs sampler and M-H algorithm is used to implement E-step, whereas the M-step is completed via the method of conditional maximization. As classical model selection procedure such as Akaike's information criterion (AIC) becomes problematic for our considered ZIGPS distribution with incomplete data, some variations on AIC are presented under two different missingness mechanisms, namely, missing at random (MAR) and missing not at random (MNAR), respectively. The most attractive point is that our methods cannot only be used to select distributions and variables, but also can be used to find out whether there exists zero-inflation or not, which is conducted via score test or Bayesian test in previous literature. Finally, a simulation study and a real example are used to illustrate the proposed methodology.

Gökpinar, Fikri; Arzu Özdemir, Yaprak

doi: 10.1080/03610926.2010.533235pmid: N/A

In this study, we define the Horvitz-Thompson estimator of the population mean using the inclusion probabilities of a ranked set sample in a finite population setting. The second-order inclusion probabilities that are required to calculate the variance of the Horvitz-Thompson estimator were obtained. The Horvitz-Thompson estimator, using the inclusion probabilities of ranked set sample, tends to be more efficient than the classical ranked set sampling estimator especially in a positively skewed population with small sizes. Also, we present a real data example with the volatility of gasoline to illustrate the Horvitz-Thompson estimator based on ranked set sampling.

Qomi, M. Naghizadeh; Nematollahi, N.; Parsian, A.

doi: 10.1080/03610926.2010.535630pmid: N/A

Let X 1 and X 2 be two independent random variables from normal populations Π1, Π2 with different unknown location parameters θ1 and θ2, respectively and common known scale parameter σ. Let X (2) = max (X 1, X 2) and X (1) = min (X 1, X 2). We consider the problem of estimating the location parameter θ M (or θ J ) of the selected population under the reflected normal loss function. We obtain minimax estimators of θ M and θ J . Also, we provide sufficient conditions for the inadmissibility of invariant estimators of θ M and θ J .

Martins-Filho, Carlos; Saraiva, Paulo

doi: 10.1080/03610926.2010.535632pmid: N/A

Nonparametric density and regression estimators commonly depend on a bandwidth. The asymptotic properties of these estimators have been widely studied when bandwidths are non stochastic. In practice, however, in order to improve finite sample performance of these estimators, bandwidths are selected by data driven methods, such as cross-validation or plug-in procedures. As a result, nonparametric estimators are usually constructed using stochastic bandwidths. In this article, we establish the asymptotic equivalence in probability of local polynomial regression estimators under stochastic and nonstochastic bandwidths. Our result extends previous work by Boente and Fraiman (1995) and Ziegler (2004).

Vilar, Juan M.; Vilar, José A.

doi: 10.1080/03610926.2010.535634pmid: N/A

A bootstrap procedure for testing the equality of several regression curves under dependence conditions is proposed. The errors are assumed to follow different ARMA structures. A test statistic based on the functional distances between nonparametric estimators of the regression functions is considered. The critical test values are obtained using a resampling method that takes into account the correlation structure. The consistency of the bootstrap procedure is established and its finite sample performance is investigated in a Monte Carlo study. Simulations show that our bootstrap-based test outperforms the asymptotic test. Applications are illustrated with a real data example.

Xia, Qiang; Liu, Jinshan; Pan, Jiazhu; Liang, Rubing

doi: 10.1080/03610926.2010.538792pmid: N/A

We consider Bayesian analysis of threshold autoregressive moving average model with exogenous inputs (TARMAX). In order to obtain the desired marginal posterior distributions of all parameters including the threshold value of the two-regime TARMAX model, we use two different Markov chain Monte Carlo (MCMC) methods to apply Gibbs sampler with Metropolis-Hastings algorithm. The first one is used to obtain iterative least squares estimates of the parameters. The second one includes two MCMC stages for estimate the desired marginal posterior distributions and the parameters. Simulation experiments and a real data example show support to our approaches.