SIMPLE LM TESTS FOR THE UNBALANCED NESTED ERROR COMPONENT REGRESSION MODEL

This paper derives several Lagrange Multiplier tests for the unbalanced nested error component model. Economic data with a natural nested grouping include firms grouped by industry; or students grouped by schools. The LM tests derived include the joint test for both effects as well as the test for one effect conditional on the presence of the other. The paper also derives the standardized versions of these tests, their asymptotic locally mean most powerful version as well as their robust to local misspecification version. Monte Carlo experiments are conducted to study the performance of these LM tests.     

Optimum group limits for estimation in scaled log-logistic distribution from a grouped data

The well known logistic distribution is considered. A transformation of the logistic variate in terms of exponential function results in a new distribution called log-logistic distribution suggested by Balakrishnanet al (1987). Estimation of its scale parameter from a grouped data is presented. Optimal group limits in the case of equispaced as well as unequispaced groupings so as to have a maximum asymptotic relative efficiency are worked out. The grouping correction in the case of equispaced grouped data with a mid point type estimator is also suggested. The results are expalined by an example.     

A Unified Approach to Estimating and Testing Income Distributions With Grouped Data

We propose a unified approach that is flexibly applicable to various types of grouped data for estimating and testing parametric income distributions. To simplify the use of our approach, we also provide a parametric bootstrap method and show its asymptotic validity. We also compare this approach with existing methods for grouped income data, and assess their finite-sample performance by a Monte Carlo simulation. For empirical demonstrations, we apply our approach to recovering China's income/consumption distributions from a sequence of income/consumption share tables and the U.S. income distributions from a combination of income shares and sample quantiles. Supplementary materials for this article are available online.     

Estimation of weibull parameters for grouped data with competing risks

We consider the problem of estimating Weibull parameters for grouped data when competing risks are present. We propose two simple methods of estimation and derive their asymptotic properties. A Monte Carlo study was carried out to evaluate the performance of these two methods.     

Large Sample Theory for the Bounds on the Gini and Related Indices of Inequality Estimated From Grouped Data

The joint asymptotic distribution of the upper and lower bounds for the Gini index derived by Gastwirth for grouped data are obtained. From them a conservative asymptotically distribution-free confidence interval for the population Gini index is presented. The methods also yield similar results for other indices of inequality (e.g., Theil's and Atkinson's).     

Nonparametric kernel density estimation for general grouped data

Interval-grouped data are defined, in general, when the event of interest cannot be directly observed and it is only known to have been occurred within an interval. In this framework, a nonparametric kernel density estimator is proposed and studied. The approach is based on the classical Parzen–Rosenblatt estimator and on the generalisation of the binned kernel density estimator. The asymptotic bias and variance of the proposed estimator are derived under usual assumptions, and the effect of using non-equally spaced grouped data is analysed. Additionally, a plug-in bandwidth selector is proposed. Through a comprehensive simulation study, the behaviour of both the estimator and the plug-in bandwidth selector considering different scenarios of data grouping is shown. An application to real data confirms the simulation results, revealing the good performance of the estimator whenever data are not heavily grouped.     

CSISZAR DIVERGENCE FROM CONSTANT FAILURE RATE MODEL FOR GROUPED DATA

We propose a measure of divergence in failure rates of a system from the constant failure rate model for a grouped data situation. We use this measure to compare the divergences of several systems from the constant failure rate model and find the asymptotic distributions of the test statistics. Several applications are discussed to illustrate the procedure. In the context of testing the goodness-of-fit with the constant failure rate model, we conduct a simulation study which shows that this procedure compares favorably with the Pearson chi-square test and the likelihood ratio test procedures.     

Semiparametric Analysis With Grouped Dependent Variables and Application to Physicians' Provision of Charity Care

We present estimators for semiparametric regression models where the dependent variable is grouped, that is, known to fall in a specified group with observable thresholds while its true value remains latent. Income, weeks unemployed, and treatment length are examples of such variables. Because the model is not amenable to direct estimation, estimators are derived from a transform in which the index emerges as the partially linear component in a vector of identities. $\sqrt{n}$ asymptotic normality of the proposed estimator is derived. The analytical results are applied to study physicians' provision of charity care, using data in which charity care is grouped.     

Testing randomness against ordered alternatives in a multinomial experiment with grouped frequencies

A test is derived for homogeneity of probabilities of a multi nomial trial against ordered alternatives, applicable to cases in which only the frequencies of grouped categories are known. Its asymptotic null distribution is obtained.     

Progressively censored tests for clinical experiments and life testing problems based on weighted empirical distributions

In the context of time-sequential studies, progressively censored tests for a simple regression model based on weighted empirical distributions are considered for ungrouped as well as grouped data situations. Early decision rules based on such tests are formulated. The asymptotic theory of the proposed tests rests on a construction of suitable empirical processes and their convergence (in distribution) to appropriate Gaussian functions. Critical values of the proposed test statistics are obtained by simulation, For a hypothetical example (of practical interest), a comparative study is made for the empirical powers and stopping times for some rival tests.     

Mean-Based Iterative Procedures in Linear Models with General Errors and Grouped Data

Abstract.  We present in this paper iterative estimation procedures, using conditional expectations, to fit linear models when the distributions of the errors are general and the dependent data stem from a finite number of sources, either grouped or non-grouped with different classification criteria. We propose an initial procedure that is inspired by the expectation-maximization (EM) algorithm, although it does not agree with it. The proposed procedure avoids the nested iteration, which implicitly appears in the initial procedure and also in the EM algorithm. The stochastic asymptotic properties of the corresponding estimators are analysed.     

Planning Life Tests Based on Progressively Type-I Grouped Censored Data from the Weibull Distribution

In this article, we apply the simulated annealing algorithm to determine optimally spaced inspection times for the two-parameter Weibull distribution for any given progressive Type-I grouped censoring plan. We examine how the asymptotic relative efficiencies of the estimates are affected by the position of the monitoring points and the number of monitoring points used. A comparison of different inspection plans is made that will enable the user to select a plan for a specified quality goal. Using the same algorithm, we can also determine an optimal progressive Type-I grouped censoring plan when the inspection times and the expected proportions of total failures in the experiment are pre-fixed. Finally, we discuss the sample size and the acceptance constant of the progressively Type-I grouped censored reliability sampling plan when the optimal inspection times are used.     

A fiducial approach to multiple comparisons

Comparing treatment means from populations that follow independent normal distributions is a common statistical problem. Many frequentist solutions exist to test for significant differences amongst the treatment means. A different approach would be to determine how likely it is that particular means are grouped as equal. We developed a fiducial framework for this situation. Our method provides fiducial probabilities that any number of means are equal based on the data and the assumed normal distributions. This methodology was developed when there is constant and non-constant variance across populations. Simulations suggest that our method selects the correct grouping of means at a relatively high rate for small sample sizes and asymptotic calculations demonstrate good properties. Additionally, we have demonstrated the flexibility in the methods ability to calculate the fiducial probability for any number of equal means. This was done by analyzing a simulated data set and a data set measuring the nitrogen levels of red clover plants that were inoculated with different treatments.     

Grouped data exponentially weighted moving average control charts

In the manufacture of metal fasteners in a progressive die operation, and other industrial situations, important quality dimensions cannot be measured on a continuous scale, and manufactured parts are classified into groups by using a step gauge. This paper proposes a version of exponentially weighted moving average (EWMA) control charts that are applicable to monitoring the grouped data for process shifts. The run length properties of this new grouped data EWMA chart are compared with similar results previously obtained for EWMA charts for variables data and with those for cumulative sum (CUSUM) schemes based on grouped data. Grouped data EWMA charts are shown to be nearly as efficient as variables-based EWMA charts and are thus an attractive alternative when the collection of variables data is not feasible. In addition, grouped data EWMA charts are less affected by the discreteness that is inherent in grouped data than are grouped data CUSUM charts. In the metal fasteners application, grouped data EWMA charts were simple to implement and allowed the rapid detection of undesirable process shifts.     

Estimation efficiency of grouped and censored observation schemes for a generalised regression model

A multiple regression model is considered in which the density of the response variable is a member of a very wide family which includes many well-known distributions. Schemes of observation in which the response observations are grouped or type 1 right censored are examined. Results on the asymptotic variance efficiencies of the maximum likelihood estimators of the regression coefficients and standard deviation of the error distribution are presented for the two schemes.     

Group and within-group variable selection for competing risks data

Variable selection in the presence of grouped variables is troublesome for competing risks data: while some recent methods deal with group selection only, simultaneous selection of both groups and within-group variables remains largely unexplored. In this context, we propose an adaptive group bridge method, enabling simultaneous selection both within and between groups, for competing risks data. The adaptive group bridge is applicable to independent and clustered data. It also allows the number of variables to diverge as the sample size increases. We show that our new method possesses excellent asymptotic properties, including variable selection consistency at group and within-group levels. We also show superior performance in simulated and real data sets over several competing approaches, including group bridge, adaptive group lasso, and AIC / BIC-based methods.     

具有组群异方差结构的面板数据模型及其应用研究

面板数据由不同个体的时间序列数据汇聚而成。已有大量研究表明面板数据个体之间存在组群结构,并且普遍存在模型的异方差现象。本文借鉴组群异质性的研究成果,构建模型误差项组群结构的面板数据模型,基于模型假定条件,提出惩罚伪最大似然函数估计法(PQMLE),该方法能够同时进行结构识别和参数估计;证明了估计量具有Oracle渐近性质;蒙特卡洛模拟验证了该方法有效的样本性质;进一步应用该方法对我国股市进行Fama-French三因子模型的实证分析,验证了理论模型的应用效果。     

Regularized robust estimation in binary regression models

In this paper, we investigate robust parameter estimation and variable selection for binary regression models with grouped data. We investigate estimation procedures based on the minimum-distance approach. In particular, we employ minimum Hellinger and minimum symmetric chi-squared distances criteria and propose regularized minimum-distance estimators. These estimators appear to possess a certain degree of automatic robustness against model misspecification and/or for potential outliers. We show that the proposed non-penalized and penalized minimum-distance estimators are efficient under the model and simultaneously have excellent robustness properties. We study their asymptotic properties such as consistency, asymptotic normality and oracle properties. Using Monte Carlo studies, we examine the small-sample and robustness properties of the proposed estimators and compare them with traditional likelihood estimators. We also study two real-data applications to illustrate our methods. The numerical studies indicate the satisfactory finite-sample performance of our procedures.     

Bridge regression: Adaptivity and group selection

In high-dimensional regression problems regularization methods have been a popular choice to address variable selection and multicollinearity. In this paper we study bridge regression that adaptively selects the penalty order from data and produces flexible solutions in various settings. We implement bridge regression based on the local linear and quadratic approximations to circumvent the nonconvex optimization problem. Our numerical study shows that the proposed bridge estimators are a robust choice in various circumstances compared to other penalized regression methods such as the ridge, lasso, and elastic net. In addition, we propose group bridge estimators that select grouped variables and study their asymptotic properties when the number of covariates increases along with the sample size. These estimators are also applied to varying-coefficient models. Numerical examples show superior performances of the proposed group bridge estimators in comparisons with other existing methods.     

Statistical Analysis of Exponential Lifetimes Under an Integrated Type-Ii Interval Censoring Scheme

In this paper, we propose a new type of censoring scheme which combines the features of grouped censoring and Type-II censoring. Statistical analysis of exponentially distributed lifetimes observed under this scheme is considered. The MLE of the model parameter and its asymptotic variance are derived. Furthermore, expressions for the expected experiment time and the expected number of failures are given. A numerical study is conducted to study these quantities and the results are compared with those under a Type-II censored plan. This comparison provides useful insight on the choice of these plans in designing a life test.