Communications in Statistics: Theory and Methods

Kim, Won Kyung; Billard, L.

doi: 10.1080/03610929008830255pmid: N/A

For the first-order bilinear time series model where {et} is a sequence of independent normal random variables with mean 0 and variance σ2, the asymptotic distribution of the sample autocorrelation function is obtained and shown to follow a normal distribution. The variance of the asymptotic distribution is of a complicated form and hence a bootstrap estimate of the variance is proposed for large sample inference. This result can be used to distinguish between different bilinear models. Finally, we obtain moment estimators of the parameters and derive their asymptotic distribution.

Maeshiro, Asatoshi

doi: 10.1080/03610929008830256pmid: N/A

This study reveals that contrary to the conventional wisdom among econometricians, the bias of the OLS estimator can be quite small when the estimator is applied to a geometrically distributed lag model, yt<ce:glyph name="dbnd6"/> α + βx t+ λy t-1. + ut, with autocorrelated disturbances, be they AR(1), MA(1), MA(2), AR(2), and ARMA(1,1). This happens when λ is large and xtis smoothly trended (e.g., a real GNP series). In fact, the bias of the OLS estimator becomes zero at one parameter combination, and the OLS estimator performs well over a wide range around this parameter combination. By decomposing the disturbance term into two parts, the paper also explains why OLS shows such an unexpected property. These findings have both pedagogical and practical significance.

Draper, Norman R.

doi: 10.1080/03610929008830257pmid: N/A

The 25-page Bibliography in Applied Regression Analysis, 2nd edition, by N.R. Draper and H. Smith, published by Wiley in 1981, is extended by a list of selected references available during 1988-89, and a few older references inadvertently omitted from previous lists. It is hoped that this will be useful to regression practictioners. Items were chosen on the basis of their perceived relevance to practical applications (sometimes rather widely interpreted). The classification system used is that of the book. The references were selected mostly from the issues of these journals: Annals of Statistics; Applied Statistics: Biometrika; Canadian Journal of Statistics; Bulletin of the International Statistical Institute; Journal of the American Statistical Association; Journal of Quality Technology; Journal of the Royal Statistical Society, Series A and B; and Technometrics. The author would appreciate being notified of errors, however slight, so that these do not persist in future compilations.

Choi, Byoung-Chul; Owen, Donald B.

doi: 10.1080/03610929008830258pmid: N/A

A new process capability index is proposed that takes into account the location of the process mean between the two specification limits, the proximity to the target value, and the process variation when assessing process performance. The proposed index is compared to other indices on several properties. The proposed index is estimated based on a random sample of observations from the production process when the process is assumed to be normally distributed. The 95% lower confidence limits for the proposed index are derived for given sample sizes and its estimates.

Chandra, Nimai Kumar; Chaudhuri, Arijit

doi: 10.1080/03610929008830259pmid: N/A

In estimating the shape parameter of a two-parameter Weibull distribution from a failure-censored sample, a recently popular procedure is to employ a testimator which is a shrinkage estimator based on a preliminary hypothesis test for a guessed value of the parameter. Such an adaptive testimator is a linear compound of the guessed value and a statistic. A new compounding coefficient is numerically shown to yield higher efficiency in many situations compared to some of the existing ones.

Bremer, Ronald

doi: 10.1080/03610929008830260pmid: N/A

In 1970 Rao introduced the minimum norm, quadratic, unbiased estimators for estimating variance components. These estimators have been expanded into a class of estimators. This paper will present computational considerations for calculating the small sample variance of estimators in this class and present a numerical study of the small sample variances. The study is designed to examine the small sample properties of a one-step iterative form of the MINQUE estimators, also.

Martinez, José Raúl; Valparaísoy, AV; Martínez, R.

doi: 10.1080/03610929008830261pmid: N/A

The purpose of this work is to display optimal conditions, in terms of the Mean Square Error criterion of the (r,k) class estimators. This will be done with respect to the ordinary ridge repression, principal components and ordinary least squares estimate.

Godbole, Anant P.

doi: 10.1080/03610929008830262pmid: N/A

Let Nn.k.g.d be the hypergeometric random variable of order k≥1, equal to the number of success runs of length k contained in an ordered without replacement sample of size n drawn from a dichotomous urn with g good items and d defectives. We give an alternative formula for that is computationally simpler than the one in Panaretos and Xekalaki (1986). Distributions of the longest success run and of waiting times for r≥1 runs of length k are also derived. We call the latter the waiting time hypergeometric r.v. of order.

Ong, S.H.

doi: 10.1080/03610929008830263pmid: N/A

This paper considers further mixture formulations of the bivariate negative binomial (BNB) distribution of Edwards and Gurland (1961) and Subrahmaniam (1966). These formulations and some known ones are applied (1) to obtain a bivariate generalized negative binomial (BGNB) distribution of Bhattacharya (1966), (2) to establish a connection between the accident-proneness models given by the BNB, BGNB and Bhattacharya's bivariate distributions, and (3) to compute the grade correlation and distribution function of the Wicksell-Kibble bivariate gamma distribution.

Tanaka, Yutaka; Tostado Castaño, Eduardo

doi: 10.1080/03610929008830264pmid: N/A

The influence function of the covariance matrix is decomposed into a finite number of components. This decomposition provides a useful tool to develop efficient methods for computing empirical influence curves related to various multivariate methods. It can also be used to characterize multivariate methods from the sensitivity perspective. A numerical example is given to demonstrate efficient computing and to characterize some procedures of exploratory factor analysis.