Estimation in the presence of incidental parameters

This paper considers the estimation of “structural” parameters when the number of unknown parameters increases with the sample size. Neyman and Scott (1948) had demonstrated that maximum likelihood estimators (MLE) of structural parameters may be inconsistent in this case. Patefield (1977) further observed that the asymptotic covariance matrix of the MLE is not equal to the inverse of the information matrix. In this paper we establish asymptotic properties of estimators (which include in particular the MLE) obtained via the usual likelihood approach when the incidental parameters are first replaced by their estimates (which are allowed to depend on the structural parameters). Conditions for consistency and asymptotic normality together with a proper formula for the asymptotic covariance matrix are given. The results are illustrated and applied to the problem of estimating linear functional relationships, and mild conditions on the incidental parameters for the MLE (or an adjusted MLE) to be consistent and asymptotically normal are obtained. These conditions are weaker than those imposed by previous authors.     

Corrected p-values for tests based on estimated nuisance parameters

In some situations the asymptotic distribution of a random function T _n() that depends on a nuisance parameter is tractable when has known value. In that case it can be used as a test statistic, if suitably constructed, for some hypothesis. However, in practice, often needs to be replaced by an estimator S _n. In this paper general results are given concerning the asymptotic distribution of T _n(S _n) that include special cases previously dealt with. In particular, some situations are covered where the usual likelihood theory is nonregular and extreme values are employed to construct estimators and test statistics.     

川东北山前高陡构造地应力精细计算方法

摘 要：川东北地质构造极其复杂，80% 以上都是山前高陡构造。复杂的构造条件给油气资源的勘探开发带来了极大的挑战，特别是对该区地应力大小、方向及展布规律的认识不清，给油气建井带来了很大困难。充分利用测井资料的连续性、经济性和高分辨率等优势，综合运用数理统计方法以及计算机综合成图技术，对该区的岩石力学参数和地应力进行了精细计算与研究，重点建立起适合川东北高陡构造的垂向应力离散分析模型以及水平应力精细求解公式。同时，提出了平均水平应力的概念和取值范围，并针对研究工区实际地质情况进行了深入计算和检验。所取得的成果大幅度提高了对川东北山前高陡构造地应力的计算精度和展布规律的认识     

The percentile residual life up to time t0: Ordering and aging properties

Motivated by practical issues, a new stochastic order for random variables is introduced by comparing all their percentile residual life functions until a certain instant. Some interpretations of these stochastic orders are given, and various properties of them are derived. The relationships to other stochastic orders are studied and also an application in reliability theory is described. Finally, we present some characterization results of the decreasing percentile residual life up to time t₀ aging notion.     

Simplified Likelihood Based Goodness-of-fit Tests for the Weibull Distribution

The aim of this paper is to present new likelihood based goodness-of-fit tests for the two-parameter Weibull distribution. These tests consist in nesting the Weibull distribution in three-parameter generalized Weibull families and testing the value of the third parameter by using the Wald, score, and likelihood ratio procedures. We simplify the usual likelihood based tests by getting rid of the nuisance parameters, using three estimation methods. The proposed tests are not asymptotic. A comprehensive comparison study is presented. Among a large range of possible GOF tests, the best ones are identified. The results depend strongly on the shape of the underlying hazard rate.     

Concomitant record ranked set sampling

In this work, we define a new method of ranked set sampling (RSS) which is suitable when the characteristic (variable) Y of primary interest on the units is jointly distributed with an auxiliary characteristic X on which one can take its measurement on any number of units, so that units having record values on X alone are ranked and retained for making measurement on Y. We name this RSS as concomitant record ranked set sampling (CRRSS). We propose estimators of the parameters associated with the variable Y of primary interest based on observations of the proposed CRRSS which are applicable to a very large class of distributions viz. Morgenstern family of distributions. We illustrate the application of CRRSS and our estimation technique of parameters, when the basic distribution is Morgenstern-type bivariate logistic distribution. A primary data collected by CRRSS method is demonstrated and the obtained data used to illustrate the results developed in this work.     

Empirical Bayes estimates of finite mixture of negative binomial regression models and its application to highway safety

The empirical Bayes (EB) method is commonly used by transportation safety analysts for conducting different types of safety analyses, such as before–after studies and hotspot analyses. To date, most implementations of the EB method have been applied using a negative binomial (NB) model, as it can easily accommodate the overdispersion commonly observed in crash data. Recent studies have shown that a generalized finite mixture of NB models with K mixture components (GFMNB-K) can also be used to model crash data subjected to overdispersion and generally offers better statistical performance than the traditional NB model. So far, nobody has developed how the EB method could be used with finite mixtures of NB models. The main objective of this study is therefore to use a GFMNB-K model in the calculation of EB estimates. Specifically, GFMNB-K models with varying weight parameters are developed to analyze crash data from Indiana and Texas. The main finding shows that the rankings produced by the NB and GFMNB-2 models for hotspot identification are often quite different, and this was especially noticeable with the Texas dataset. Finally, a simulation study designed to examine which model formulation can better identify the hotspot is recommended as our future research.     

The use of multilevel modeling and the level two residual file to explore the relationship between middle years programme student performance and diploma programme student performance

Multilevel modeling has recently found a substantial niche in the context of educational research, although several details about the methodological application of these models have yet to be explored in an achievement data framework. This paper makes use of data provided by the International Baccalaureate (IB) in order to investigate modeling decisions and certain applications of the level two residual file in an effort to increase understanding about the way linear and logistic multilevel models function. The focus of this research is on the relationship between performances in two IB programmes: the Middle Years Programme (MYP) and the Diploma Programme (DP). The impact of predictors on the interpretation of the unconditional and conditional variance-covariance matrix as well as the reliability coefficients is discussed. Empirical findings suggest that students who perform better during MYP moderation tend to perform better on DP exams.     

A forecasting and policy simulation oriented small macro-model for the Indian economy

The design of macro-models for the purposes of derivation of macroeconomic stabilization policies and obtaining forecasts is an important area of theoretical and empirical economic research. This is because such a stance presents an ideal blend of skillfully interweaving the essential theoretical ingredients of the contemporary macroeconomic paradigms with specific structural features of the country under reference. The use of macro-models enables the policy makers to build alternative policy evidences and thus this approach proves to be far superior to the alternative approaches based on intuitive or judgmental criteria. It is against this background that a macro-model for the Indian economy is estimated in an error-correction framework. Based on it, some policy options are evaluated. ECM and time varying parameter based forecasts are obtained for inflation and growth for the Indian economy for the year 2004–2005.     

Burnout and Wellbeing: Testing the Copenhagen Burnout Inventory in New Zealand Teachers

The Copenhagen Burnout Inventory (CBI) is a public domain questionnaire measuring the degree of physical and psychological fatigue experienced in three sub-dimensions of burnout: personal, work-related, and client-related burnout. This study first examines the reliability and validity of the CBI in measuring burnout in New Zealand secondary school teachers, and then the relationship between burnout and wellbeing among this population. The CBI had acceptable reliability (internal consistency and homogeneity) as well as factorial and criterion-related validity. As expected, burnout was negatively related to wellbeing measures (wellbeing index, school connection, and perceived general health). The findings indicate that this burnout questionnaire is a valid instrument to use with New Zealand secondary teachers, and also highlight the potential impact of burnout on the health and wellbeing of teachers.