ABSTRACT When product quality follows the Gamma distribution and is related to one or more covariate(s), then Gamma regression model (GRM) profiling will be used. The Gamma profiling is generally based on a maximum likelihood estimator (MLE). In GRM profiling, when two or more covariates are linearly related, the MLE-based GRM profiling is unsuitable. In this situation, an alternative to MLE-based profiling is required. So, this study develops the Gamma ridge regression profiling based on Pearson and deviance residuals. The performance of the proposed profiling is evaluated with the help of a simulation study under different conditions, where average run length is considered as the performance evaluation criterion. The simulation findings show that the Pearson residual based profiling with ridge estimator is better than the deviance residuals-based profiling with MLE as well as ridge estimator. Furthermore, we consider an application to evaluate the performance of the proposed methods.

Often arises in counting data analysis that both violation of distributional assumption and large-scale over-dispersion substantially impair the validity of the methods for multiple comparisons. For over-dispersed data fitting to the generalized linear models, we describe the simultaneous inference method in assessing a sequence of estimable functions based on the root using the quasi-likelihood estimation of the regression coefficients. A new method for deriving the limiting distributions of the score function and the root under a list of mild regularity conditions is presented. This approach has a close connection to the asymptotic normality of the root in general linear models that it provides a heuristic analogy for classroom presentation. Hence, researchers can routinely estimate quantiles based on the limiting distribution of the root for simultaneous inference. We apply the percentile bootstrap method to estimate the quantiles as a resampling-based alternative. As will be shown, the simultaneous test based on both the approximation methods above is anti-conservative in designs with small sample sizes. We propose the simultaneous testing method using Efron's bias-corrected percentile bootstrapping procedure as an improvement. In small-sample designs, we demonstrate through the simulation study that the proposed method provides a viable alternative to the large-sample and the percentile bootstrap approximation methods. Moreover, the proposed method persists in controlling the familywise error rate in simultaneous testing for highly over-dispersed data from substantially small-sample designs, where the percentile-t bootstrap method provides a liberal test.

This paper proves that in mixed linear model, the analysis of variance estimation (ANOVAE), the minimum norm quadratic unbiased estimation (MINQUE), the spectral decomposition estimation (SDE) and the restricted maximum likelihood estimation (RMLE) of variance components are the same under some conditions. Based on this result, we construct a linear Bayes estimation (LBE) for the parameter vector consisting of variance components and establish its superiorities. Numerical computations and an illustration show that the LBE is comparable to Lindley's approximation, Tierney and Kadane's approximation and the usual Bayes estimation (UBE) obtained by the MCMC method and easy to use as well.

In competing risks model, subjects are exposed to failure due to more than one cause. In this study, we develop a model for recall-based competing risks data when the causes associated with time to event are assumed to follow different distributions respectively. The chances of an individual recalling an event will be high if elapsed time between monitoring time and time to event is less. This information is utilized by taking non-recall probability as a function of this elapsed time. For point estimation, an expectation-maximization based algorithm is developed. For interval estimation, we construct the observed Fisher information matrix by using the missing information principle. The study is further extended to the Bayesian paradigm under suitable choices of prior distributions. The samples from full conditionals are drawn using a Gibbs sampling-based algorithm. To assess the performance of proposed estimators, an extensive simulation study is carried out for different proportions of non-recall and censored data with varying sample sizes under uniform and exponential monitoring patterns. Finally, the median duration of breastfeeding cessation for US women is estimated.

This paper establishes a new estimator for simple linear measurement error models with correlated errors. Under a small-noise asymptotic regime and using perturbation theory, an unbiased estimator has been developed. The consistency and the asymptotic normality of the new estimator have been established and then validated by using synthetic data. Moreover, the confidence intervals of the slope have been revisited. Simulation results show that our estimator is certainly the most stable of existing methods and its performance exceeds that of other existing methods in terms of coverage and interval length.

Of interest in this paper is the development of a model that uses fixed, then inverse sampling of binary data that is subject to false-positive misclassification in an effort to estimate a proportion. From this model, both the proportion of success and false-positive misclassification rate may be estimated. Also, three first-order likelihood-based confidence intervals for the proportion of success are mathematically derived and studied via a Monte Carlo simulation. The simulation results indicate that the likelihood ratio interval is generally preferable over the Wald and score interval. Lastly, the model is applied to two different real-world medical data sets.

We consider the problem of simultaneous variable selection and parameter estimation in an ultra-high dimensional linear regression model. The adaptive penalty functions are used in this regard to achieve the oracle variable selection property with simpler assumptions and lesser computational burden. Noting the non-robust nature of the usual adaptive procedures (e.g. adaptive LASSO) based on the squared error loss function against data contamination, quite frequent with modern large-scale data sets (e.g. noisy gene expression data, spectra and spectral data), in this paper, we present a new adaptive regularization procedure using a robust loss function based on the density power divergence (DPD) measure under a general class of error distributions. We theoretically prove that the proposed adaptive DPD-LASSO estimator of the regression coefficients is highly robust, consistent, asymptotically normal and leads to robust oracle-consistent variable selection under easily verifiable assumptions. Numerical illustrations are provided for the mostly used normal and heavy-tailed error densities. Finally, the proposal is applied to analyse an interesting spectral dataset, in the field of chemometrics, regarding the electron-probe X-ray microanalysis (EPXMA) of archaeological glass vessels from the 16th and 17th centuries.

In this communication, various statistical inferential procedures for estimating unknown model parameters are investigated via utilizing partially observed dependent competing risks data under the unified hybrid censoring scheme when the latent failure times follow Marshall–Olkin bivariate Kumaraswamy distribution. The existence and uniqueness of the maximum likelihood estimators (MLEs) have been established. By using asymptotic normality property of MLE, the approximate confidence intervals have been constructed via observed Fisher information matrix. Moreover, Bayes estimates and the highest posterior density credible intervals have been computed under a highly flexible gamma-Dirichlet prior distribution by using Markov chain Monte Carlo technique. In addition, to compare the performance of proposed methods, a Monte Carlo simulation has been carried out. Finally, a real-life data set has been analysed to illustrate the operability and applicability of the methods considered.

Sparse quantile regression is a useful tool for variable selection, robust estimation and heteroscedasticity treatment in high-dimensional data analysis. Due to the non-smooth of quantile loss, the computation is heavier than the least square models. In the literature, there are various numerical methods for linear quantile regression, such as ADMM developed in Gu et al. [Technometrics. 2017;60(3):319–331]. However, the computation of multivariate quantile regression has not yet been fully resolved, especially when the dimension is high. Motivated by this, we will focus on the design of fast numerical algorithms for row-sparse multivariate quantile regression model. By virtue of proximal operator and Majorize–Minimization, four smoothed algorithms are designed. For all the obtained algorithms, we analyse their convergence and the parameter selection. We conduct plenty of simulations and four real data sets analysis. Finally, we conclude that the smoothed method is faster than the non-smooth method, especially when the number of predictors is large.

In this paper, the asymptotic normality and strong consistency for M estimators of the unknown regression coefficients in classical linear models are established under the assumptions that the errors are identically distributed φ-mixing random variables. The results obtained in this paper generalize the corresponding ones of Chen and Zhao [M-methods in linear model. Shanghai: Scientific and Technical Publishers; 1996] and Zhao [Strong consistency of M-estimates in linear model. Sci China Ser A. 2002;45:1420–1427] for independent errors. Finally, the simulation study is provided to verify the finite sample performance of the theoretical results and a real example is analysed for illustration.