Statistical Methodology最新文献

The extended growth curve model is discussed in this paper. There are two versions of the model studied in the literature, which differ in the way how the column spaces of the design matrices are nested. The nesting is applied either to the between-individual or to the within-individual design matrices. Although both versions are equivalent via reparametrization, the properties of estimators cannot be transferred directly because of non-linearity of estimators. Since in many applications the between-individual matrices are one-way ANOVA matrices, it is reasonable to assume orthogonality of the column spaces of between-individual design matrices along with nestedness of the column spaces of within-individual design matrices. We present the maximum likelihood estimators and their basic moments for the model with such orthogonality condition.

Univariate Birnbaum–Saunders distribution has received a considerable amount of attention during the last few years. Recently, Kundu et al. (2010) introduced a bivariate Birnbaum–Saunders distribution. It is observed that the bivariate Birnbaum–Saunders distributions can be written as the weighted mixture of bivariate inverse Gaussian distribution and its reciprocals. In this paper further we introduce a mixture of two bivariate Birnbaum–Saunders distributions and discuss its different properties. The mixture model has eleven parameters, hence it is a very flexible model. The maximum likelihood estimators cannot be obtained in explicit forms. We propose to use the EM algorithm to compute the maximum likelihood estimators. It is observed that it saves computational time significantly. We performed some simulation experiments, and one data analysis has been performed to illustrate the EM algorithm. It is observed that the performance of the EM algorithm is quite satisfactory.

Sequential methods are developed for conducting a large number of simultaneous tests while controlling the Type I and Type II generalized familywise error rates. Namely, for the chosen values of $\alpha$, $\beta$, $k$, and $m$, we derive simultaneous tests of $d$ individual hypotheses, based on sequentially collected data, that keep the probability of at least $k$ Type I errors not exceeding level $\alpha$ and the probability of at least $m$ Type II errors not greater than $\beta$. This generalization of the classical notions of familywise error rates allows substantial reduction of the expected sample size of the multiple testing procedure.

Data from a surveillance system can be used to estimate the size of a disease population. For certain surveillance systems, a binomial mixture model arises as a natural choice. The Chao estimator estimates a lower bound of the population size. The Zelterman estimator estimates a parameter that is neither a lower bound nor an upper bound. By comparing the Chao estimator and the Zelterman estimator both theoretically and numerically, we conclude that the Chao estimator is better.

In this paper, a lemma is presented and then it is used to construct simultaneous confidence intervals (SCIs) for the differences of location parameters of successive exponential distributions in the unbalanced case under heteroscedasticity. A simulation study based comparison of our SCIs with two recently proposed procedures in terms of coverage probability and average volume revealed that the proposed method can be recommended for small and moderate sample sizes.

With evolving genomic technologies, it is possible to get different measures of the same underlying biological phenomenon using different technologies. The goal of this paper is to build a prediction model for an outcome variable $Y$ from covariates $X$. Besides $X$, we have surrogate covariates $W$ which are related to $X$. We want to utilize the information in $W$ to boost the prediction for $Y$ using $X$. In this paper, we propose a kernel machine-based method to improve prediction of $Y$ by $X$ by incorporating auxiliary information $W$. By combining single kernel machines, we also propose a hybrid kernel machine predictor, which can yield a smaller prediction error than its constituents. The prediction error of our kernel machine predictors is evaluated using simulations. We also apply our method to a lung cancer dataset and an Alzheimer’s disease dataset.

In this paper, we apply the maximum entropy test designed for a goodness of fit in iid samples (cf. Lee et al. (2011)) to GARCH(1,1) models. Its approximate asymptotic distribution is derived under the null hypothesis. A bootstrap version of the test is also discussed and its performance is evaluated through Monte Carlo simulations. A real data analysis is conducted for illustration.

A review is provided of the concept confidence distributions. Material covered include: fundamentals, extensions, applications of confidence distributions and available computer software. We expect that this review could serve as a source of reference and encourage further research with respect to confidence distributions.

Instead of using sample information only to do variable selection, in this article we also take priori information — linear constraints of regression coefficients — into account. The penalized likelihood estimation method is adopted. However under constraints, it is not guaranteed that information criteria like AIC and BIC are minimized at an oracle solution using the lasso or SCAD penalty. To overcome such difficulties, a modified SCAD penalty is proposed. The definitions of information criteria GCV, AIC and BIC for constrained variable selection problems are also proposed. Statistically, we show that if the tuning parameter is appropriately chosen, the proposed estimators enjoy the oracle properties and satisfy the linear constraints. Additionally, they also possess the robust property to outliers if the linear model with M-estimation is used.

The present paper is mainly concerned with the statistical tests of the independence problem between random vectors. We develop an approach based on general empirical processes indexed by a particular class of functions. We prove two abstract approximation theorems that include some existing results as particular cases. Finally, we characterize the limiting behavior of the Möbius transformation of empirical processes indexed by functions under contiguous sequences of alternatives.