Restricted minimax estimation in semiparametric linear models

Abstract

In this article we develop the minimax estimation approach of general linear models to the semiparametric linear models when the parameters are simultaneously constrained by an ellipsoid and linear restrictions. Combining sample information and prior constraints the minimax estimator is obtained and compared with partially least square estimator by theoretical and simulation methods.     

Influence Diagnostics on Testing Linear Hypothesis in Linear Models with Correlated Errors

To assess the influence of observations on the parameter estimates, case deletion diagnostics are commonly used in linear regression models. For linear models with correlated errors we study the influence of observations on testing a linear hypothesis using single and multiple case deletions. The change in likelihood ratio test and F test theoretically is derived and it is shown these tests to be completely determined by two proposed generalized externally studentized residuals. An illustrative example of a real data set is also reported.     

Mixed Levels of Uncertainty in Complex Policy Models

The characterization and treatment of uncertainty poses special challenges when modeling indeterminate or complex coupled systems such as those involved in the interactions between human activity, climate and the ecosystem. Uncertainty about model structure may become as, or more important than, uncertainty about parameter values. When uncertainty grows so large that prediction or optimization no longer makes sense, it may still be possible to use the model as a behavioral test bed to examine the relative robustness of alternative observational and behavioral strategies. When models must be run into portions of their phase space that are not well understood, different submodels may become unreliable at different rates. A common example involves running a time stepped model far into the future. Several strategies can be used to deal with such situations. The probability of model failure can be reported as a function of time. Possible alternative surprises can be assigned probabilities, modeled separately, and combined. Finally, through the use of subjective judgments, one may be able to combine, and over time shift between models, moving from more detailed to progressively simpler order-of-magnitude models, and perhaps ultimately, on to simple bounding analysis.     

Developing a measure of contentment in an Arab Muslim country: implications for cross-cultural research in social work

This is one in a series of papers that report on a programme of research focusing on the psychosocial consequences of Kuwaitis in the wake of the 1990 invasion and occupation by Iraq. The research team chose to focus on contentment as the obverse of trauma effects and develop a new measure that more closely represents Kuwait society due to cultural sensitivity. The paper briefly discusses the programme of research and the need for a new measure of Kuwaiti contentment. The Kuwaiti Raha Scale (KRS), was developed to serve as the primary dependent variable for a post-war national survey of mental health in Kuwait. The KRS emerged from a multi-method approach first administered to a convenience sample of 560 undergraduate university students enrolled in eight different classes. The results reported here note that no differences were found according to the variable of gender, as was expected. Four factors emerged, with Cronbach's Alphas ranging from 0.850 to 0.709 after eliminating three items. The total twenty-eight-item KRS measure yielded a Cronbach's Alpha of 0.906. Conclusions: The present findings suggest that the four subscales are a psychometrically sound measure of contentment, and would be useful in studies of Arabic-speaking cultures by social workers, and other investigators, concerned about culture-based well-being. Implications for European social professions are discussed.     

Testing Normality Using Transformed Data

In this article, we first present a characterization of the normal distribution and then we introduce an exact goodness of fit test for normal distribution. The power of the proposed test under various alternatives is compared with the existing tests, by simulation.     

The modified permutation entropy-based independence test of time series

Abstract

In time series, it is essential to check the independence of data by means of a proper method or an appropriate statistical test before any further analysis. Therefore, among different independence tests, a powerful and productive test has been introduced by Matilla-García and Marín via m-dimensional vectorial process, in which the value of the process at time t includes m-histories of the primary process. However, this method causes a dependency for the vectors even when the independence assumption of random variables is considered. Considering this dependency, a modified test is obtained in this article through presenting a new asymptotic distribution based on weighted chi-square random variables. Also, some other alterations to the test have been made via bootstrap method and by controlling the overlap. Compared with the primary test, it is obtained that not only the modified test is more accurate but also, it possesses higher power.     

General treatment of goodness-of-fit tests based on Kullback–Leibler information

This paper introduces a general goodness-of-fit test based on the estimated Kullback–Leibler information. The test uses the Vasicek entropy estimate. Two special cases of the test for location–scale and shape families are discussed. The results are used to introduce goodness-of-fit tests for the uniform, Laplace, Weibull and beta distributions. The critical values and powers for some alternatives are obtained by simulation.     

Application of the Hyper‐Poisson Generalized Linear Model for Analyzing Motor Vehicle Crashes

The hyper‐Poisson distribution can handle both over‐ and underdispersion, and its generalized linear model formulation allows the dispersion of the distribution to be observation‐specific and dependent on model covariates. This study's objective is to examine the potential applicability of a newly proposed generalized linear model framework for the hyper‐Poisson distribution in analyzing motor vehicle crash count data. The hyper‐Poisson generalized linear model was first fitted to intersection crash data from Toronto, characterized by overdispersion, and then to crash data from railway‐highway crossings in Korea, characterized by underdispersion. The results of this study are promising. When fitted to the Toronto data set, the goodness‐of‐fit measures indicated that the hyper‐Poisson model with a variable dispersion parameter provided a statistical fit as good as the traditional negative binomial model. The hyper‐Poisson model was also successful in handling the underdispersed data from Korea; the model performed as well as the gamma probability model and the Conway‐Maxwell‐Poisson model previously developed for the same data set. The advantages of the hyper‐Poisson model studied in this article are noteworthy. Unlike the negative binomial model, which has difficulties in handling underdispersed data, the hyper‐Poisson model can handle both over‐ and underdispersed crash data. Although not a major issue for the Conway‐Maxwell‐Poisson model, the effect of each variable on the expected mean of crashes is easily interpretable in the case of this new model.     

A new estimator of Kullback–Leibler information and its application in goodness of fit tests*

We propose here a general statistic for the goodness of fit test of statistical distributions. The proposed statistic is constructed based on an estimate of Kullback–Leibler information. The proposed test is consistent and the limiting distribution of the test statistic is derived. Then, the established results are used to introduce goodness of fit tests for the normal, exponential, Laplace and Weibull distributions. A simulation study is carried out for examining the power of the proposed test and to compare it with those of some existing procedures. Finally, some illustrative examples are presented and analysed, and concluding comments are made.     

Bayesian composite Tobit quantile regression

Composite quantile regression models have been shown to be effective techniques in improving the prediction accuracy [H. Zou and M. Yuan, Composite quantile regression and the oracle model selection theory, Ann. Statist. 36 (2008), pp. 1108–1126; J. Bradic, J. Fan, and W. Wang, Penalized composite quasi-likelihood for ultrahighdimensional variable selection, J. R. Stat. Soc. Ser. B 73 (2011), pp. 325–349; Z. Zhao and Z. Xiao, Efficient regressions via optimally combining quantile information, Econometric Theory 30(06) (2014), pp. 1272–1314]. This paper studies composite Tobit quantile regression (TQReg) from a Bayesian perspective. A simple and efficient MCMC-based computation method is derived for posterior inference using a mixture of an exponential and a scaled normal distribution of the skewed Laplace distribution. The approach is illustrated via simulation studies and a real data set. Results show that combine information across different quantiles can provide a useful method in efficient statistical estimation. This is the first work to discuss composite TQReg from a Bayesian perspective.