A Note on the Moment Generating Function

A simple proof is given to show that there always exists a neighborhood of zero in which a moment generating function has a power series expansion. Thus, the relation between moments and derivatives of the moment generating function at zero can be obtained without resorting to postcalculus theorems.     

A Paradox on Compartmental Models with Poisson Immigration

Even to the initiated, statistical calculations based on Bayes's Theorem can be daunting because of the numerical integrations required in all but the simplest applications. Moreover, from a teaching perspective, introductions to Bayesian statistics—if they are given at all—are circumscribed by these apparent calculational difficulties. Here we offer a straightforward sampling-resampling perspective on Bayesian inference, which has both pedagogic appeal and suggests easily implemented calculation strategies.     

Review of Teaching Statistical Concepts

A χ² test with a rejection region in the low tail is sometimes used to test whether data could plausibly have been generated by random sampling. A data set, taken from the statistical literature, is exhibited, which is suitable for demonstrating this test in the classroom.     

Chi-Squared Goodness-of-Fit Tests for Parametric Accelerated Failure Time Models

We give chi-squared goodness-of fit tests for parametric regression models such as accelerated failure time, proportional hazards, generalized proportional hazards, frailty models, transformation models, and models with cross-effects of survival functions. Random right censored data are used. Choice of random grouping intervals as data functions is considered.     

Optimal design for quasi-likelihood estimation in Poisson regression with random coefficients

Count data may be described by a Poisson regression model. If random coefficients are involved, maximum likelihood is not feasible and alternative estimation methods have to be employed. For the approach based on quasi-likelihood estimation a characterization of design optimality is derived and optimal designs are determined numerically for an example with random slope parameters.     

管理信息系统中随机制表研究

随机制表以一个数据库为基础,随机制作一个或多个二维表格以供输出。制表的核心部分是对表头进行编码,其规律是从左到右,从上到下,第一层用一个字母,第二层用两个字母,依次类推。     

Asymptotic study of the change-point mle in multivariate Gaussian families under contiguous alternatives

The problem of estimating an unknown change-point in the mean vector or covariance matrix of a sequence of independent multivariate Gaussian random variables is considered. Adapting the estimation methodology that Hinkley pursued for the case of abrupt changes, we develop theory for deriving the asymptotic distribution of the maximum likelihood estimator of the change-point when the amount of change is a function of the sample size and goes to zero in a smooth fashion as the sample size goes to infinity, yielding a contiguous change-point model. Simulations have been performed to illustrate the closeness of the asymptotic distribution with the empirical distribution, and to evaluate its robustness to departures from normality for reasonable sample sizes as well as parameter changes. Finally, we apply the methodology to estimate the change-point in the daily log-returns data of BLS (BellSouth) and VZ (Verizon) from NYSE.     

Choosing colleges: Identifying and modeling choice sets

Although largely ignored in the growing literature about college choice that adopts a random utility modeling framework, there is reason to believe that the estimates are sensitive to the criteria used to define the choice sets. Accordingly, this paper examines the methodological and substantive implications of using merit (class rank) and socioeconomic (high school strata) to define college choice sets. Using Texas as a case study, results show that criteria used to constrain choice sets—and type of high school attend in particular—not only produce quite different post-secondary institutional profiles, but also different estimates of institutional attributes on students’ top choice. These findings have methodological implications for future research about college choice and substantive importance for the prospects that the Texas top 10% law, which guarantees automatic admission to students who graduate in the top decile of their high school class, will equalize access to the state’s competitive public institutions.     

Some efficient classes of estimators of population mean in two-phase successive sampling under random non response

In this paper, an attempt has been made to present some efficient classes of estimators of population mean on current occasion in two-occasion successive sampling under random non response in two-phase setup. Effectiveness of the proposed classes of estimators has been studied under the assumptions that sampling units follow a distribution under the random non response. To check the performances, the proposed classes of estimators are compared with an estimator under the similar situation under the complete response. Results are demonstrated through empirical studies which show the reliable nature of the proposed classes of estimators. Suitable recommendations have been made to the survey practitioners.     

Effectual variance estimation strategy in two-occasion successive sampling in presence of random non response

Present investigation deals with the problem of random non response in estimation of population variance on current occasion in two-occasion successive sampling. To reduce the negative impact of random non response on both occasions, regression type imputation method has been suggested. Using auxiliary information, efficient estimation strategies have been developed for estimation of population variance on the current occasion. Estimator for the population variance is also derived as a special case when random non response occurs only on the current occasion. Empirical studies are carried out to show the dominance of suggested estimators over sample variance and exponential type estimators. Results are interpreted.