Feasible algorithm for linear mixed model for massive data

This article studies computation problem in the context of estimating parameters of linear mixed model for massive data. Our algorithms combine the factored spectrally transformed linear mixed model method with a sequential singular value decomposition calculation algorithm. This combination solves the operation limitation of the method and also makes this algorithm feasible to big dataset, especially when the data has a tall and thin design matrix. Our simulation studies show that our algorithms make the calculation of linear mixed model feasible for massive data on ordinary desktop and have same estimating accuracy with the method based on the whole data.     

Estimation for the censored partially linear quantile regression models

In this article, we develop estimation procedures for partially linear quantile regression models, where some of the responses are censored by another random variable. The nonparametric function is estimated by basis function approximations. The estimation procedure is easy to implement through existing weighted quantile regression, and it requires no specification of the error distributions. We show the large-sample properties of the resulting estimates, the proposed estimator of the regression parameter is root-n consistent and asymptotically normal and the estimator of the functional component achieves the optimal convergence rate of the nonparametric function. The proposed method is studied via simulations and illustrated with the analysis of a primary biliary cirrhosis (BPC) data.     

Determination of a new mixed variable lot-size multiple dependent state sampling plan based on the process capability index

This article proposes a new mixed variable lot-size multiple dependent state sampling plan in which the attribute sampling plan can be used in the first stage and the variables multiple dependent state sampling plan based on the process capability index will be used in the second stage for the inspection of measurable quality characteristics. The proposed mixed plan is developed for both symmetric and asymmetric fraction non conforming. The optimal plan parameters can be determined by considering the satisfaction levels of the producer and the consumer simultaneously at an acceptable quality level and a limiting quality level, respectively. The performance of the proposed plan over the mixed single sampling plan based on C_pk and the mixed variable lot size plan based on C_pk with respect to the average sample number is also investigated. Tables are constructed for easy selection of plan parameters for both symmetric and asymmetric fraction non conforming and real world examples are also given for the illustration and practical implementation of the proposed mixed variable lot-size plan.     

Allocation strategies of standby redundancies in series/parallel system

This article deals with the topic of optimal allocation of two standby redundancies in a two-component series/parallel system. There are two original components C₁ and C₂ which can be used to construct a series/parallel system, and two spares R₁ (same as C₁) and R₂ (different from both C₁ and C₂) at hand with them being standby redundancies so as to enhance the reliability level of the system. The goal for an engineer is to seek after the optimal allocation policy in this framework. It is shown that, for the series structure, the engineer should allocate R₂ to C₁ and R₁ to C₂ provided that C₁ (or R₁) performs either the best or worst among all the units; otherwise, the allocation policy should be reversed. For the parallel structure, the optimal allocation strategy is just opposed to that of series case. We also provide some numerical examples for illustrating the theoretical results.     

Asymptotic distributions in affiliation networks with an increasing sequence

A central limit theorem for a linear combination of all the maximum likelihood estimators with an increasing dimension for affiliation networks has been established. Simulation studies are provided to illustrate the asymptotic results.     

Performance of the stein-type two-parameter estimator in multiple linear regression model

In this article, we consider the Stein-type approach to the estimation of the regression parameter in a multiple regression model under a multicollinearity situation. The Stein-type two-parameter estimator is proposed when it is suspected that the regression parameter may be restricted to a subspace. The bias and the quadratic risk of the proposed estimator are derived and compared with the two-parameter estimator (TPE), the restricted TPE and the preliminary test TPE. The conditions of superiority of the proposed estimator are obtained. Finally, a real data example is provided to illustrate some of the theoretical results.     

Asymptotic normality of the local linear estimation of the conditional density for functional time-series data

This article focuses on the conditional density of a scalar response variable given a random variable taking values in a semimetric space. The local linear estimators of the conditional density and its derivative are considered. It is assumed that the observations form a stationary α-mixing sequence. Under some regularity conditions, the joint asymptotic normality of the estimators of the conditional density and its derivative is established. The result confirms the prospect in Rachdi et al. (2014 Rachdi, M., A. Laksaci, J. Demongeot, A. Abdali, and F. Madani. 2014. Theoretical and practical aspects of the quadratic error in the local linear estimation of the conditional density for functional data. Computational Statistics and Data Analysis 73 :53–68.[Crossref], [Web of Science ®] , [Google Scholar]) and can be applied in time-series analysis to make predictions and build confidence intervals. The finite-sample behavior of the estimator is investigated by simulations as well.     

Performance of the difference-based Liu-type estimator in partially linear model

This paper discusses the parameter estimation in a partially linear model. We proposed a difference-based Liu-type estimator of the unknown parameters in the partially linear model. The asymptotically properties of the proposed estimator are discussed. We propose a iterative method to choose the biasing parameters. Finally, a simulation study and a numerical example are presented to explain the performance of the estimators.     

A simple,doubly robust,efficient estimator for survival functions using pseudo observations

Survival functions are often estimated by nonparametric estimators such as the Kaplan‐Meier estimator. For valid estimation, proper adjustment for confounding factors is needed when treatment assignment may depend on confounding factors. Inverse probability weighting is a commonly used approach, especially when there is a large number of potential confounders to adjust for. Direct adjustment may also be used if the relationship between the time‐to‐event and all confounders can be modeled. However, either approach requires a correctly specified model for the relationship between confounders and treatment allocation or between confounders and the time‐to‐event. We propose a pseudo‐observation–based doubly robust estimator, which is valid when either the treatment allocation model or the time‐to‐event model is correctly specified and is generally more efficient than the inverse probability weighting approach. The approach can be easily implemented using standard software. A simulation study was conducted to evaluate this approach under a number of scenarios, and the results are presented and discussed. The results confirm robustness and efficiency of the proposed approach. A real data example is also provided for illustration.