Tests for the variance parameter in the Fay–Herriot model

The Fay–Herriot model is a linear mixed model that plays a relevant role in small area estimation (SAE). Under the SAE set-up, tools for selecting an adequate model are required. Applied statisticians are often interested on deciding if it is worthwhile to use a mixed effect model instead of a simpler fixed-effect model. This problem is not standard because under the null hypothesis the random effect variance is on the boundary of the parameter space. The likelihood ratio test and the residual likelihood ratio test are proposed and their finite sample distributions are derived. Finally, we analyse their behaviour under simulated scenarios and we also apply them to real data.     

On Box–Muller Transformation and Simulation of Normal Record Data

Record data are commonly encountered in many fields such as sports, geography, finance, and reliability. In this article, we use the well-known Box–Muller transformation to develop an efficient method of simulating record data from the normal distribution. Another method based on exponential records is also discussed. Then, the performance of these algorithms is compared with some standard simulation methods.     

Short confidence intervals for variance components

Four approximate methods are proposed to construct confidence intervals for the estimation of variance components in unbalanced mixed models. The first three methods are modifications of the Wald, arithmetic and harmonic mean procedures, see Harville and Fenech (1985), while the fourth is an adaptive approach, combining the arithmetic and harmonic mean procedures. The performances of the proposed methods were assessed by a Monte Carlo simulation study. It was found that the intervals based on Wald's method maintained the nominal confidence levels across all designs and values of the parameters under study. On the other hand, the arithmetic (harmonic) mean method performed well for small (large) values of the variance component, relative to the error variance component. The adaptive procedure performed rather well except for extremely unbalanced designs. Further, compared with equal tails intervals, the intervals which use special tables, e.g., Table 678 of Tate and Klett (1959), provided adequate coverage while having much shorter lengths and are thus recommended for use in practice.     

A functional approach to estimating finite population distribution functions

Existing estimators of a finite population distribution function that utilize auxiliary information are often constructed by a point wise argument. As a result, these estimators are not always monotone. We adopt a functional approach to the problem and propose two estimators based on compositions of functions. Asymptotic variance formulae are derived for the proposed es-timators. Comparisons are made with existing estimators in a simulation study using three natural populations.     

Dynamic Bayesian analysis for irregularly and incompletely observed contingency tables

Pre-election surveys are usually conducted several times to forecast election results before the actual voting. It is common that each survey includes a substantial number of non-responses and that the successive survey results are seen as a stochastic multinomial time series evolving over time. We propose a dynamic Bayesian model to examine how multinomial time series evolve over time for the irregularly observed contingency tables and to determine how sensitively the dynamic structure reacts to an unexpected event, such as a candidate scandal. Further, we test whether non-responses are non-ignorable to determine if non-responses need to be imputed for better forecast. We also suggest a Bayesian method that overcomes the boundary solution problem and show that the proposed method outperforms the previous Bayesian methods. Our dynamic Bayesian model is applied to the two pre-election surveys for the 2007 Korea presidential candidate election and for the 1998 Ohio general election.     

Random effects regression models for count data with excess zeros in caries research

We extend the family of Poisson and negative binomial models to derive the joint distribution of clustered count outcomes with extra zeros. Two random effects models are formulated. The first model assumes a shared random effects term between the conditional probability of perfect zeros and the conditional mean of the imperfect state. The second formulation relaxes the shared random effects assumption by relating the conditional probability of perfect zeros and the conditional mean of the imperfect state to two different but correlated random effects variables. Under the conditional independence and the missing data at random assumption, a direct optimization of the marginal likelihood and an EM algorithm are proposed to fit the proposed models. Our proposed models are fitted to dental caries counts of children under the age of six in the city of Detroit.     

Cox regression for current status data with mismeasured covariates

Covariate measurement error problems have been extensively studied in the context of right‐censored data but less so for current status data. Motivated by the zebrafish basal cell carcinoma (BCC) study, where the occurrence time of BCC was only known to lie before or after a sacrifice time and where the covariate (Sonic hedgehog expression) was measured with error, the authors describe a semiparametric maximum likelihood method for analyzing current status data with mismeasured covariates under the proportional hazards model. They show that the estimator of the regression coefficient is asymptotically normal and efficient and that the profile likelihood ratio test is asymptotically Chi‐squared. They also provide an easily implemented algorithm for computing the estimators. They evaluate their method through simulation studies, and illustrate it with a real data example. The Canadian Journal of Statistics 39: 73–88; 2011 © 2011 Statistical Society of Canada     

Asymptotic expansions for the moments of serial correlation coefficients

This work is concerned with evaluating the moments of a number of serial correlation coefficients which arise in various ways and where the observations are from the first order autoregressive Gaussian process with known zero mean. The forms considered have biases whose main parts (of order 0(n^-1) , where n is the sample size) are substantially different. They are the intra-class correlation,the maximum likelihood estimators and an estimator whose main part of the bias is sere. The moments are obtained as asymptotic expansions in terms of the parameter of the process and to terms of order 0(n^-3). It is found that removing certain end terms in the denominator of a serial correlation has the effect of reducing the magnitude of the main part of its bias considerably and in one case completely eliminating it. This work extends the results of various authors,e.g.Kandall(1954), Marriott and pope(1954) and white (1961) in the special cases of the first order autogressive process.     

On comparing several straight lines under heteroscedasticity and robustness with respect to departure from normality

This article considers the problem of testing slopes in k straight lines with'heterogeneous variances. The statistic Fβ is proposed and the null and non-null distributions of Fβ derived under normality assumption. The power function values are then approximated by Laguerre polynomial expansion for normal and non-normal universes. For the example given in Graybill ‘1976, p. 295’, it is shown that the Satterthwaite approximation provides a close approximation to the null and non-null distributions in all the cases; it is also shown that the Fβ test is quite robust with respect to departure from normality in the case of mixtures of two normals.