Small area estimation under a multivariate linear model for repeated measures data

In this article, small area estimation under a multivariate linear model for repeated measures data is considered. The proposed model aims to get a model which borrows strength both across small areas and over time. The model accounts for repeated surveys, grouped response units, and random effects variations. Estimation of model parameters is discussed within a likelihood based approach. Prediction of random effects, small area means across time points, and per group units are derived. A parametric bootstrap method is proposed for estimating the mean squared error of the predicted small area means. Results are supported by a simulation study.     

Estimating Spatial Autocorrelation With Sampled Network Data

Spatial autocorrelation is a parameter of importance for network data analysis. To estimate spatial autocorrelation, maximum likelihood has been popularly used. However, its rigorous implementation requires the whole network to be observed. This is practically infeasible if network size is huge (e.g., Facebook, Twitter, Weibo, WeChat, etc.). In that case, one has to rely on sampled network data to infer about spatial autocorrelation. By doing so, network relationships (i.e., edges) involving unsampled nodes are overlooked. This leads to distorted network structure and underestimated spatial autocorrelation. To solve the problem, we propose here a novel solution. By temporarily assuming that the spatial autocorrelation is small, we are able to approximate the likelihood function by its first-order Taylor’s expansion. This leads to the method of approximate maximum likelihood estimator (AMLE), which further inspires the development of paired maximum likelihood estimator (PMLE). Compared with AMLE, PMLE is computationally superior and thus is particularly useful for large-scale network data analysis. Under appropriate regularity conditions (without assuming a small spatial autocorrelation), we show theoretically that PMLE is consistent and asymptotically normal. Numerical studies based on both simulated and real datasets are presented for illustration purpose.     

Dimension-reduced empirical likelihood inference for response mean with data missing at random

To make efficient inference for mean of a response variable when the data are missing at random and the dimension of covariate is not low, we construct three bias-corrected empirical likelihood (EL) methods in conjunction with dimension-reduced kernel estimation of propensity or/and conditional mean response function. Consistency and asymptotic normality of the maximum dimension-reduced EL estimators are established. We further study the asymptotic properties of the resulting dimension-reduced EL ratio functions and the corresponding EL confidence intervals for the response mean are constructed. The finite-sample performance of the proposed estimators is studied through simulation, and an application to HIV-CD4 data set is also presented.     

Likelihood inference for Type I bivariate Pólya–Aeppli distribution

This article discusses likelihood inference for the Type I bivariate Pólya–Aeppli distribution. The Type I bivariate Pólya–Aeppli distribution was derived by Minkova and Balakrishnan by using compounding with geometric random variables and the trivariate reduction method. They also discussed the moment estimation of the parameters of the Type I bivariate Pólya–Aeppli distribution. Here, we carry out a simulation study to compare the performance of the developed Maximum Likelihood Estimation (MLE) method with the moment estimation. The obtained results show that, through the MLEs require more computational time compared to the moment estimates (MoM), the MLEs perform better, in most of the settings, than the MoM. Finally, we apply the Type I bivariate Pólya–Aeppli model to a real dataset containing the frequencies of railway accidents in two subsequent six-year periods for the purpose of illustration. We also carry out some hypothesis tests using the Wald test statistic. From these results, we conclude that the two variables belong to the same univariate Pólya–Aeppli distribution, but are correlated.     

A simulation comparison on spatial Poisson mixed models

The statistical methods for analyzing spatial count data have often been based on random fields so that a latent variable can be used to specify the spatial dependence. In this article, we introduce two frequentist approaches for estimating the parameters of model-based spatial count variables. The comparison has been carried out by a simulation study. The performance is also evaluated using a real dataset and also by the simulation study. The simulation results show that the maximum likelihood estimator appears to be with the better sampling properties.     

The Marshall–Olkin extended generalized Lindley distribution: Properties and applications

In this article, we define and study a new three-parameter model called the Marshall–Olkin extended generalized Lindley distribution. We derive various structural properties of the proposed model including expansions for the density function, ordinary moments, moment generating function, quantile function, mean deviations, Bonferroni and Lorenz curves, order statistics and their moments, Rényi entropy and reliability. We estimate the model parameters using the maximum likelihood technique of estimation. We assess the performance of the maximum likelihood estimators in a simulation study. Finally, by means of two real datasets, we illustrate the usefulness of the new model.     

Exact inference for exponential distribution with multiply Type-I censored data

In this paper, we focus on exact inference for exponential distribution under multiple Type-I censoring, which is a general form of Type-I censoring and represents that the units are terminated at different times. The maximum likelihood estimate of mean parameter is calculated. Further, the distribution of maximum likelihood estimate is derived and it yields an exact lower confidence limit for the mean parameter. Based on a simulation study, we conclude that the exact limit outperforms the bootstrap limit in terms of the coverage probability and average limit. Finally, a real dataset is analyzed for illustration.     

Lifetime performance index based on ranked set sampling

In this article, we assume that the lifetimes of products follow a one-parameter exponential distribution and use both conjugate and Jeffreys prior distributions for finding a Bayes estimator based on the RSS scheme for lifetime performance index CL. We also obtained maximum likelihood and adhac estimators for CL. Monte Carlo simulation study is done for comparing the obtained estimators in two sampling schemes SRS and RSS. Fisher information has been utilized to obtain lower confidence bound of CL for both schemes in asymptotically state and use this bounds for hypothesis testing of CL.     

On hypothesis tests for disk-type intensities of spatial poisson processes

We consider the problem of testing whether realizations of a spatial Poisson process come from a circular intensity model or from an elliptical intensity model. We describe the behavior of the Generalized Likelihood Ratio and Wald tests, in the asymptotics of large samples. The power functions are studied under local alternatives and results of numerical simulations comparing them to the Neyman–Pearson envelope are presented.     

On a multivariate Lindley distribution

This article proposes a multivariate extension of the generalized Lindley distribution introduced by Abouammoh et al. (2015 Abouammoh, A.M., Alshangiti Arwa, M., Ragab, I.E. (2015). Reliability estimation of the generalized Lindley distributions. J. Stat. Comput. Simul. 85(17):3662–3678.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]). The proposed model is based on a probabilistic construction in which several Lindley random variables are connected by a common shock. Many statistical properties of this new distribution are explored. In particular, explicit forms of product moments, moment-generating function, and conditional moments are derived. Explicit expressions of moment-based estimators of the underlying parameters of the proposed model are established. Estimation using the maximum likelihood procedure is also investigated. Simulations attesting to the quality of the proposed estimators are presented. Application of the proposed model in reliability is also discussed.