Communications in Statistics: Theory and Methods

Timm, Neil H.; Al-Subaihi, Ali A.

doi: 10.1081/STA-100002137pmid: N/A

In this paper a new test statistic is developed to evaluate model specification for nonnested seemingly unrelated regression (SUR) models. The new statistic is compared with Cox's modified likelihood ratio test for comparing two nonnested models. The statistic maintains the size of the test at the nominal level α, may be used with very small sample sizes, has an exact chi-square distribution when the covariance structure is known, converges to a normal distribution when the covariance structure is unknown, and is slightly more powerful than Cox's test for small sample sizes.

Letón, E.; Zuluaga, P.

doi: 10.1081/STA-100002138pmid: N/A

In this paper we describe 10 expressions of score and weighted tests, in such a way that the numerators and the denominators are completely specified, including always the possibility of tied observations. We establish the equivalence between score and weighted tests in the general setting of ties. Based upon this equivalence we enunciate two new tests, which complete the jigsaw of the classification of these non-parametric tests in Survival Analysis.

Choi, ByoungSeon

doi: 10.1081/STA-100002139pmid: N/A

The Yule-Walker estimators of the AR coefficients of a causal multidimensional AR model are obtained by replacing the autocovariances with their estimators in the Yule-Walker equations. It is shown that only unbiased-type estimators of the autocovariances yield consistency of the Yule-Walker estimators. Also, the asymptotic joint distribution of the Yule-Walker estimators is presented.

Montopoli, George; Anderson, Donald A.

doi: 10.1081/STA-100002140pmid: N/A

In a stated preference discrete choice experiment each subject is typically presented with several choice sets, and each choice set contains a number of alternatives. The alternatives are defined in terms of their name (brand) and their attributes at specified levels. The task for the subject is to choose from each choice set the alternative with highest utility for them. The multinomial is an appropriate distribution for the responses to each choice set since each subject chooses one alternative, and the multinomial logit is a common model. If the responses to the several choice sets are independent, the likelihood function is simply the product of multinomials. The most common and generally preferred method of estimating the parameters of the model is maximum likelihood (that is, selecting as estimates those values that maximize the likelihood function). If the assumption of within-subject independence to successive choice tasks is violated (it is almost surely violated), the likelihood function is incorrect and maximum likelihood estimation is inappropriate. The most serious errors involve the estimation of the variance-covariance matrix of the model parameter estimates, and the corresponding variances of market shares and changes in market shares. In this paper we present an alternative method of estimation of the model parameter coefficients that incorporates a first-order within-subject covariance structure. The method involves the familiar log-odds transformation and application of the multivariate delta method. Estimation of the model coefficients after the transformation is a straightforward generalized least squares regression, and the corresponding improved estimate of the variance-covariance matrix is in closed form. Estimates of market share (and change in market share) follow from a second application of the multivariate delta method. The method and comparison with maximum likelihood estimation are illustrated with several simulated and actual data examples. Advantages of the proposed method are: 1) it incorporates the within-subject covariance structure; 2) it is completely data driven; 3) it requires no additional model assumptions; 4) assuming asymptotic normality, it provides a simple procedure for computing confidence regions on market shares and changes in market shares; and 5) it produces results that are asymptotically equivalent to those produced by maximum likelihood when the data are independent.

Manatunga, Amita K.; Williamson, John M.

doi: 10.1081/STA-100002141pmid: N/A

A latent variable model is considered for the analysis of twin data with an ordinal response. The underlying latent multivariate normally distributed variable is expressed in terms of genetic and environmental effects, and the variance components associated with these effects are estimated. We illustrate this approach with analysis of the NHLBI Twin Study. Model assessment is ascertained by proposing a goodness-of-fit test for ordered categorical data. Extensions of this approach for the investigation of how genetic effects vary over time are discussed.

Kuk, Anthony Y. C.; Mak, T. K.; Li, W. K.

doi: 10.1081/STA-100002142pmid: N/A

We consider surveys with one or more callbacks and use a series of logistic regressions to model the probabilities of nonresponse at first contact and subsequent callbacks. These probabilities are allowed to depend on covariates as well as the categorical variable of interest and so the nonresponse mechanism is nonignorable. Explicit formulae for the score functions and information matrices are given for some important special cases to facilitate implementation of the method of scoring for obtaining maximum likelihood estimates of the model parameters. For estimating finite population quantities, we suggest the imputation and prediction approaches as alternatives to weighting adjustment. Simulation results suggest that the proposed methods work well in reducing the bias due to nonresponse. In our study, the imputation and prediction approaches perform better than weighting adjustment and they continue to perform quite well in simulations involving misspecified response models.

Katsis, Athanassios

doi: 10.1081/STA-100002143pmid: N/A

This paper examines the problem of calculating the optimal sample size in the general case of a hypothesis test among many binomial proportions. The methodology follows the Bayesian point of view. Initially, an upper bound on the posterior risk is imposed. Since this is a pre-experimental process, a similar constraint is set on the probability of the unknown data not satisfying the previous condition. We examine the cases when the proportions are equal to a fixed or a random value and analyze the results for three binomial populations.

Luceño, Alberto

doi: 10.1081/STA-100002144pmid: N/A

The standard application of Shewhart monitoring charts often requires that several repeated observations should be made and averaged at each sampling time. This paper analyzes the adequacy of using the same policy in the context of discrete feedback adjustment schemes with dead band. When observational errors are present, we show that, by increasing the sample size and reducing the sampling frequency, it is often possible to increase the average interval between adjustments and simultaneously reduce the mean squared deviation from target.

Pulcini, Gianpaolo

doi: 10.1081/STA-100002145pmid: N/A

This paper deals with the prediction, from a Bayes viewpoint, of future failures for a repairable equipment subjected both to minimal repairs and periodic overhauls. The effect of major overhauls on the reliability of the equipment is modeled by a proportional age reduction model, while the failure process between two successive overhaul epochs is modeled by the power law process. Prediction both of the future failure times and of the number of failures in a future time interval are provided on the basis of the observed data and of a number of suitable prior densities, which reflect different degrees of belief on the failure mechanism and overhaul effectiveness. Finally, a numerical application illustrates the proposed prediction procedures and their use in assessing the adequacy of the model to describe the observed data set.

Sun, Yanqing; Sun, Shan; Diao, Yuanan

doi: 10.1081/STA-100002146pmid: N/A

The smooth nonparametric estimator of a quantile function Q(p) is defined as the solution of , where is the distribution function corresponding to a kernel estimator of a density function. The asymptotic properties of the smooth quantile process, , based on randomly right censored lifetime data are studied. The bootstrap approaches to approximate the distributions of the smooth quantile processes are investigated and are used to construct simultaneous confidence bands for quantile functions. Data-based selection of the bandwidth required for computing is also investigated using bootstrap methods. A Monte Carlo simulation is carried out to assess small sample performance of the proposed confidence bands. An application to construct confidence bands for the quantile function of the time between a manuscript's submission and its first review is provided using a JASA data set. The developed results can be applied to construct simultaneous confidence bands for the difference of two quantile functions and to check whether there is a location shift or scale change for two distributions under study.