Bayesian Tobit quantile regression using g-prior distribution with ridge parameter

A Bayesian approach is proposed for coefficient estimation in the Tobit quantile regression model. The proposed approach is based on placing a g-prior distribution depends on the quantile level on the regression coefficients. The prior is generalized by introducing a ridge parameter to address important challenges that may arise with censored data, such as multicollinearity and overfitting problems. Then, a stochastic search variable selection approach is proposed for Tobit quantile regression model based on g-prior. An expression for the hyperparameter g is proposed to calibrate the modified g-prior with a ridge parameter to the corresponding g-prior. Some possible extensions of the proposed approach are discussed, including the continuous and binary responses in quantile regression. The methods are illustrated using several simulation studies and a microarray study. The simulation studies and the microarray study indicate that the proposed approach performs well.     

General class of estimators in multi-character surveys

In this paper, a general class of estimators for the estimation of a finite population total in multi-character surveys is proposed. It is shown that the estimators proposed by Arnab (2002), Amahiaet al. (1989) and Bansal and Singh (1985) are the special cases of the proposed class of estimators. The proposed class of estimators is always more efficient than the estimator proposed by Rao (1966).     

On a Multiple Three-Decision Problem for Comparing Several Treatments with the Best Control

In this article, a multiple three-decision procedure is proposed to classify p (≥2) treatments as better or worse than the best of q (≥2) control treatments in one way layout. Critical constants required for the implementation of the proposed procedure are tabulated for some pre-specified values of probability of no misclassification. Power function of the proposed procedure is defined and a common sample size necessary to guarantee various pre-specified power levels are tabulated under two optimal allocation schemes. Finally the implementation of the proposed methodology is demonstrated through numerical examples based on real life data.     

A note on successive comparisons between several ordered variances

ABSTRACT

In this article, a procedure for comparisons between k (k ? 3) successive populations with respect to the variance is proposed when it is reasonable to assume that variances satisfy simple ordering. Critical constants required for the implementation of the proposed procedure are computed numerically and selected values of the computed critical constants are tabulated. The proposed procedure for normal distribution is extended for making comparisons between successive exponential populations with respect to scale parameter. A comparison between the proposed procedure and its existing competitor procedures is carried out, using Monte Carlo simulation. Finally, a numerical example is given to illustrate the proposed procedure.     

Higher order inference for stress–strength reliability with independent Burr-type X distributions

In this paper, a small-sample asymptotic method is proposed for higher order inference in the stress–strength reliability model, R=P(Y<X), where X and Y are distributed independently as Burr-type X distributions. In a departure from the current literature, we allow the scale parameters of the two distributions to differ, and the likelihood-based third-order inference procedure is applied to obtain inference for R. The difficulty of the implementation of the method is in obtaining the the constrained maximum likelihood estimates (MLE). A penalized likelihood method is proposed to handle the numerical complications of maximizing the constrained likelihood model. The proposed procedures are illustrated using a sample of carbon fibre strength data. Our results from simulation studies comparing the coverage probabilities of the proposed small-sample asymptotic method with some existing large-sample asymptotic methods show that the proposed method is very accurate even when the sample sizes are small.     

Design of a sign chart using a new EWMA statistic

Abstract

In this article, a new non parametric control chart based on the modified or controlled exponentially weighted moving average (EWMA) statistic is developed to monitor the process deviation from the target value. The proposed control chart is evaluated for different values of design parameters using the average run length as a performance criterion under various sample sizes. The proposed chart is compared with the existing non parametric EWMA sign control chart. It is observed that the proposed chart is better than the existing EWMA sign control chart in terms of run length characteristics. An empirical example is provided for the practical implementation of the proposed chart.     

Monitoring simple linear profiles using variable sample size schemes

ABSTRACT

Profile monitoring is one of the new research areas in statistical process control. Most of the control charts in this area are designed with fixed sampling rate which makes the control chart slow in detecting small to moderate shifts. In order to improve the performance of the conventional fixed control charts, adaptive features are proposed in which, one or more design parameters vary during the process. In this paper the variable sample size feature of EWMA₃ and MEWMA schemes are proposed for monitoring simple linear profiles. The EWMA₃ method is based on the combination of three exponentially weighted moving average (EWMA) charts for monitoring three parameters of a simple linear profile separately and the Multivariate EWMA (MEWMA) chart is based on the using a single chart to monitor the coefficients and variance of a general linear profile. Also a two-sided control chart is proposed for monitoring the standard deviation in the EWMA₃ method. The performance of the proposed charts is compared in terms of the average time to signal. Numerical examples show that using adaptive features increase the power of control charts in detecting the parameter shifts. Finally, the performance of the proposed variable sample size schemes is illustrated through a real case in the leather industry.     

Performance of the almost unbiased ridge-type principal component estimator in logistic regression model

ABSTRACT

This article considers some different parameter estimation methods in logistic regression model. In order to overcome multicollinearity, the almost unbiased ridge-type principal component estimator is proposed. The scalar mean squared error of the proposed estimator is derived and its properties are investigated. Finally, a numerical example and a simulation study are presented to show the performance of the proposed estimator.     

Design of acceptance sampling plan using a modified EWMA statistic

In this paper, a modified exponentially weighted moving average (EWMA) statistic is proposed. The approximate distribution of the proposed modified EWMA statistic is derived. A variable acceptance sampling plan is designed using the proposed EWMA statistic. The plan parameters of the proposed sampling plan are determined such that the given producer's risk and consumer's risk are satisfied. The efficiency of the proposed plan based on the new EWMA statistic is compared with the existing EWMA plan in terms of the sample size required. The application of the proposed plan is given with the help of an example.     

A prior-valued estimator applied to multinomial classification

A multinomial classification rule is proposed based on a prior-valued smoothing for the state probabilities. Asymptotically, the proposed rule has an error rate that converges uniformly and strongly to that of the Bayes rule. For a fixed sample size the prior-valued smoothing is effective in obtaining reason¬able classifications to the situations such as missing data. Empirically, the proposed rule is compared favorably with other commonly used multinomial classification rules via Monte Carlo sampling experiments     

An entropy test for the Rayleigh distribution and power comparison

In this paper, a goodness-of-fit test is proposed for the Rayleigh distribution. This test is based on the Kullback–Leibler discrimination methodology proposed by Song [2002, Goodness of fit tests based on Kullback–Leibler discrimination, IEEE Trans. Inf. Theory 48(5), pp. 1103–1117]. The critical values and powers for some alternatives are obtained by simulation. The proposed test is compared with other tests, namely Kolmogorov–Smirnov, Kuiper, Cramer–von Mises, Watson and Anderson–Darling. The use of the proposed test is shown in a real example.     

Bias Reduction in Logistic Regression with Missing Responses When the Missing Data Mechanism is Nonignorable

ABSTRACT

In logistic regression with nonignorable missing responses, Ibrahim and Lipsitz proposed a method for estimating regression parameters. It is known that the regression estimates obtained by using this method are biased when the sample size is small. Also, another complexity arises when the iterative estimation process encounters separation in estimating regression coefficients. In this article, we propose a method to improve the estimation of regression coefficients. In our likelihood-based method, we penalize the likelihood by multiplying it by a noninformative Jeffreys prior as a penalty term. The proposed method reduces bias and is able to handle the issue of separation. Simulation results show substantial bias reduction for the proposed method as compared to the existing method. Analyses using real world data also support the simulation findings. An R package called brlrmr is developed implementing the proposed method and the Ibrahim and Lipsitz method.     

A mixed double sampling plan based on Cpk

Abstract

Acceptance sampling plans are quality tools for the manufacturer and the customer. The ultimate result of reduction of nonconforming items will increase the profit of the manufacturer and enhance the satisfaction of the consumer. In this article, a mixed double sampling plan is proposed in which the attribute double sampling inspection is used in the first stage and a variables sampling plan based on the process capability index C_pk is used in the second stage. The optimal parameters are determined so that the producer’s and the consumer’s risks are to be satisfied with minimum average sample number. The optimal parameters of the proposed plan are estimated using different plan settings using two points on the operating characteristic curve approach. In designing the proposed mixed double sampling plan, we consider the symmetric and asymmetric nonconforming cases under variables inspection. The efficiency of the proposed plan is discussed and compared with the existing sampling plans. Tables are constructed for easy selection of the optimal plan parameters and an industrial example is also included for implementation of the proposed plan.     

Efficient regression modeling for correlated and overdispersed count data

Abstract

The objective of this paper is to propose an efficient estimation procedure in a marginal mean regression model for longitudinal count data and to develop a hypothesis test for detecting the presence of overdispersion. We extend the matrix expansion idea of quadratic inference functions to the negative binomial regression framework that entails accommodating both the within-subject correlation and overdispersion issue. Theoretical and numerical results show that the proposed procedure yields a more efficient estimator asymptotically than the one ignoring either the within-subject correlation or overdispersion. When the overdispersion is absent in data, the proposed method might hinder the estimation efficiency in practice, yet the Poisson regression based regression model is fitted to the data sufficiently well. Therefore, we construct the hypothesis test that recommends an appropriate model for the analysis of the correlated count data. Extensive simulation studies indicate that the proposed test can identify the effective model consistently. The proposed procedure is also applied to a transportation safety study and recommends the proposed negative binomial regression model.     

A Multivariate Adaptive Exponentially Weighted Moving Average Control Chart

A multivariate extension of the adaptive exponentially weighted moving average (AEWMA) control chart is proposed. The new multivariate scheme can detect small and large shifts in the process mean vector effectively. The proposed scheme can be viewed as a smooth combination of a multivariate exponentially weighted moving average (MEWMA) chart and a Shewhart χ²-chart. The optimal design of the proposed chart is given according to a pre-specified in-control average run length and two shift sizes; a small and large shift each measured in terms of the non centrality parameter. The signal resistance of the newly proposed multivariate chart is also given. Comparisons among the new chart, the MEWMA chart, and the combined Shewhart-MEWMA (S-MEWMA) chart in terms of the standard and worst-case average run length profiles are presented. In addition, the three charts are compared with respect to their worst-case signal resistance values. The proposed chart gives somewhat better worst-case ARL and signal resistance values than the competing charts. It also gives better standard ARL performance especially for moderate and large shifts. The effectiveness of our proposed chart is illustrated through an example with simulated data set.     

A Novel Estimation Approach for Mixture Transition Distribution Model in High-Order Markov Chains

A transformation is proposed to convert the nonlinear constraints of the parameters in the mixture transition distribution (MTD) model into box-constraints. The proposed transformation removes the difficulties associated with the maximum likelihood estimation (MLE) process in the MTD modeling so that the MLEs of the parameters can be easily obtained via a hybrid algorithm from the evolutionary algorithms and/or quasi-Newton algorithms for global optimization. Simulation studies are conducted to demonstrate MTD modeling by the proposed novel approach through a global search algorithm in R environment. Finally, the proposed approach is used for the MTD modelings of three real data sets.     

An exact test for comparing two predictive values in small‐size clinical trials

Positive and negative predictive values describe the performance of a diagnostic test. There are several methods to test the equality of predictive values in paired designs. However, these methods were premised on large sample theory, and they may not be suitable for small‐size clinical trials because of inflation of the type 1 error rate. In this study, we propose an exact test to control the type 1 error rate strictly for conducting a small‐size clinical trial that investigates the equality of predictive values in paired designs. In addition, we execute simulation studies to evaluate the performance of the proposed exact test and existing methods in small‐size clinical trials. The proposed test can calculate the exact P value, and as a result of simulations, the empirical type 1 error rate for the proposed test did not exceed the significance level regardless of the setting, and the empirical power for the proposed test is not much different from the other methods based on large‐sample theory. Therefore, it is considered that the proposed exact test is useful when the type 1 error rate needs to be controlled strictly.     

Semiparametric methods for center effect measures based on the ratio of survival functions

The survival function is often of chief interest in epidemiologic studies of time to an event. We develop methods for evaluating center-specific survival outcomes through a ratio of survival functions. The proposed method assumes a center-stratified additive hazards model, which provides a convenient framework for our purposes. Under the proposed methods, the center effects measure is cast as the ratio of subject-specific survival functions under two scenarios: the scenario in which the subject is treated at center \(j\) ; and that wherein the subject is treated at a hypothetical center with survival function equal to the population average. The proposed measure reduces to the ratio of baseline survival functions, but is invariant to the choice of baseline covariate level. We derive the asymptotic properties of the proposed estimators, and assess finite-sample characteristics through simulation. The proposed methods are applied to national kidney transplant data.     

A Class of Two-Stage Selection Procedures Using L-Statistics

Summary: A class of selection procedures for selecting the least dispersive distribution from k available distributions has been proposed. This problem finds applications in reliability and engineering. In engineering, for example, the goal of the experimenter is to select a firm whose components have least dispersive distribution from the available set of competing firms manufacturing the components of the desired specifications meant for the same purpose. The proposed procedures can be used even when the underlying distributions belong to different families. Applications of the proposed selection procedures are discussed by taking exponential, gamma and Lehmann type distributions. Performance of the proposed selection procedures is assessed through simulation study. Implementation of the proposed selection procedure is illustrated through an example. * The authors are very grateful to the editor and referees for their valuable comments.     

A competing risks model for correlated data based on the subdistribution hazard

Family-based follow-up study designs are important in epidemiology as they enable investigations of disease aggregation within families. Such studies are subject to methodological complications since data may include multiple endpoints as well as intra-family correlation. The methods herein are developed for the analysis of age of onset with multiple disease types for family-based follow-up studies. The proposed model expresses the marginalized frailty model in terms of the subdistribution hazards (SDH). As with Pipper and Martinussen’s (Scand J Stat 30:509–521, 2003) model, the proposed multivariate SDH model yields marginal interpretations of the regression coefficients while allowing the correlation structure to be specified by a frailty term. Further, the proposed model allows for a direct investigation of the covariate effects on the cumulative incidence function since the SDH is modeled rather than the cause specific hazard. A simulation study suggests that the proposed model generally offers improved performance in terms of bias and efficiency when a sufficient number of events is observed. The proposed model also offers type I error rates close to nominal. The method is applied to a family-based study of breast cancer when death in absence of breast cancer is considered a competing risk.