Approximate composite marginal likelihood inference in spatial generalized linear mixed models

Non-Gaussian spatial responses are usually modeled using spatial generalized linear mixed model with spatial random effects. The likelihood function of this model cannot usually be given in a closed form, thus the maximum likelihood approach is very challenging. There are numerical ways to maximize the likelihood function, such as Monte Carlo Expectation Maximization and Quadrature Pairwise Expectation Maximization algorithms. They can be applied but may in such cases be computationally very slow or even prohibitive. Gauss–Hermite quadrature approximation only suitable for low-dimensional latent variables and its accuracy depends on the number of quadrature points. Here, we propose a new approximate pairwise maximum likelihood method to the inference of the spatial generalized linear mixed model. This approximate method is fast and deterministic, using no sampling-based strategies. The performance of the proposed method is illustrated through two simulation examples and practical aspects are investigated through a case study on a rainfall data set.     

Diagnostics of multiple group influential observations for logistic regression models

In this paper, two new multiple influential observation detection methods, GCD.GSPR and mCD*, are introduced for logistic regression. The proposed diagnostic measures are compared with the generalized difference in fits (GDFFITS) and the generalized squared difference in beta (GSDFBETA), which are multiple influential diagnostics. The simulation study is conducted with one, two and five independent variable logistic regression models. The performance of the diagnostic measures is examined for a single contaminated independent variable for each model and in the case where all the independent variables are contaminated with certain contamination rates and intensity. In addition, the performance of the diagnostic measures is compared in terms of the correct identification rate and swamping rate via a frequently referred to data set in the literature.     

Inference and optimal design of multiple constant-stress testing for generalized half-normal distribution under type-II progressive censoring

The generalized half-normal (GHN) distribution and progressive type-II censoring are considered in this article for studying some statistical inferences of constant-stress accelerated life testing. The EM algorithm is considered to calculate the maximum likelihood estimates. Fisher information matrix is formed depending on the missing information law and it is utilized for structuring the asymptomatic confidence intervals. Further, interval estimation is discussed through bootstrap intervals. The Tierney and Kadane method, importance sampling procedure and Metropolis-Hastings algorithm are utilized to compute Bayesian estimates. Furthermore, predictive estimates for censored data and the related prediction intervals are obtained. We consider three optimality criteria to find out the optimal stress level. A real data set is used to illustrate the importance of GHN distribution as an alternative lifetime model for well-known distributions. Finally, a simulation study is provided with discussion.     

Communication in Statistics-Theory and methods improved GQL estimation method for the generalised BINMA(1) model

In a recent research, the quasi-likelihood estimation methodology was developed to estimate the regression effects in the Generalized BINMA(1) (GBINMA(1)) process. The method provides consistent parameter estimates but, in the intermediate computations, moment estimating equations were used to estimate the serial- and cross-correlation parameters. This procedure may not result optimal parameter estimates, in particular, for the regression effects. This paper provides an alternative simpler GBINMA(1) process based on multivariate thinning properties where the main effects are estimated via a robust generalized quasi-likelihood (GQL) estimation approach. The two techniques are compared through some simulation experiments. A real-life data application is studied.     

Modeling spatial overdispersion via the generalized Waring point process

Modeling spatial overdispersion requires point process models with finite‐dimensional distributions that are overdisperse relative to the Poisson distribution. Fitting such models usually heavily relies on the properties of stationarity, ergodicity, and orderliness. In addition, although processes based on negative binomial finite‐dimensional distributions have been widely considered, they typically fail to simultaneously satisfy the three required properties for fitting. Indeed, it has been conjectured by Diggle and Milne that no negative binomial model can satisfy all three properties. In light of this, we change perspective and construct a new process based on a different overdisperse count model, namely, the generalized Waring (GW) distribution. While comparably tractable and flexible to negative binomial processes, the GW process is shown to possess all required properties and additionally span the negative binomial and Poisson processes as limiting cases. In this sense, the GW process provides an approximate resolution to the conundrum highlighted by Diggle and Milne.     

A comparative study of confidence intervals to assess biosimilarity from analytical data

Assessment of analytical similarity of tier 1 quality attributes is based on a set of hypotheses that tests the mean difference of reference and test products against a margin adjusted for standard deviation of the reference product. Thus, proper assessment of the biosimilarity hypothesis requires statistical tests that account for the uncertainty associated with the estimations of the mean differences and the standard deviation of the reference product. Recently, a linear reformulation of the biosimilarity hypothesis has been proposed, which facilitates development and implementation of statistical tests. These statistical tests account for the uncertainty in the estimation process of all the unknown parameters. In this paper, we survey methods for constructing confidence intervals for testing the linearized reformulation of the biosimilarity hypothesis and also compare the performance of the methods. We discuss test procedures using confidence intervals to make possible comparison among recently developed methods as well as other previously developed methods that have not been applied for demonstrating analytical similarity. A computer simulation study was conducted to compare the performance of the methods based on the ability to maintain the test size and power, as well as computational complexity. We demonstrate the methods using two example applications. At the end, we make recommendations concerning the use of the methods.     

Variable selection and estimation for high-dimensional spatial autoregressive models

Spatial regression models are important tools for many scientific disciplines including economics, business, and social science. In this article, we investigate postmodel selection estimators that apply least squares estimation to the model selected by penalized estimation in high-dimensional regression models with spatial autoregressive errors. We show that by separating the model selection and estimation process, the postmodel selection estimator performs at least as well as the simultaneous variable selection and estimation method in terms of the rate of convergence. Moreover, under perfect model selection, the ℓ₂ rate of convergence is the oracle rate of $\sqrt{s/n}$, compared with the convergence rate of $\text{◂√▸}\sqrt{s\log p/n}$ in the general case. Here, n is the sample size and p, s are the model dimension and number of significant covariates, respectively. We further provide the convergence rate of the estimation error in the form of $\sup$ norm, and ideally the rate can reach as fast as $\text{◂√▸}\sqrt{\log s/n}$.     

Rényi entropy of m-generalized order statistics

Abstract

Characterizing relations via Rényi entropy of m-generalized order statistics are considered along with examples and related stochastic orderings. Previous results for common order statistics are included.     

Interval estimation for conformance proportions of multiple quality characteristics

A conformance proportion is an important and useful index to assess industrial quality improvement. Statistical confidence limits for a conformance proportion are usually required not only to perform statistical significance tests, but also to provide useful information for determining practical significance. In this article, we propose approaches for constructing statistical confidence limits for a conformance proportion of multiple quality characteristics. Under the assumption that the variables of interest are distributed with a multivariate normal distribution, we develop an approach based on the concept of a fiducial generalized pivotal quantity (FGPQ). Without any distribution assumption on the variables, we apply some confidence interval construction methods for the conformance proportion by treating it as the probability of a success in a binomial distribution. The performance of the proposed methods is evaluated through detailed simulation studies. The results reveal that the simulated coverage probability (cp) for the FGPQ-based method is generally larger than the claimed value. On the other hand, one of the binomial distribution-based methods, that is, the standard method suggested in classical textbooks, appears to have smaller simulated cps than the nominal level. Two alternatives to the standard method are found to maintain their simulated cps sufficiently close to the claimed level, and hence their performances are judged to be satisfactory. In addition, three examples are given to illustrate the application of the proposed methods.     

Joint modelling of longitudinal binary data and survival data

The medical costs in an ageing society substantially increase when the incidences of chronic diseases, disabilities and inability to live independently are high. Healthy lifestyles not only affect elderly individuals but also influence the entire community. When assessing treatment efficacy, survival and quality of life should be considered simultaneously. This paper proposes the joint likelihood approach for modelling survival and longitudinal binary covariates simultaneously. Because some unobservable information is present in the model, the Monte Carlo EM algorithm and Metropolis-Hastings algorithm are used to find the estimators. Monte Carlo simulations are performed to evaluate the performance of the proposed model based on the accuracy and precision of the estimates. Real data are used to demonstrate the feasibility of the proposed model.