Communications in Statistics: Theory and Methods

Barnett, Vic; Kenward, Mike G.

doi: 10.1080/03610929608831708pmid: N/A

An interesting feature of successive inter-event times in a Poisson renewal process, when observed through a superimposed (possibly random) grid, can be interpreted as an extended form of the ‘inspection paradox’. Probabilistic measures are determined and an estimation and testing procedure is outlined which could be used to examine possible departure from randomness (Poisson form). The problem arose from study of security systems and the results have important applications in that field.

Hinkle, John E.; Stromberg, Arnold J.

doi: 10.1080/03610929608831709pmid: N/A

Many statistical techniques require that computations be done on all subsets of size r in a data set of size n. Typically, this is done lexographically, i.e., with nested for-loops. If an exchange one point update formula is available, then it is used on the inner loop. In this paper we discuss a method of counting through all subsets of size r in a data set of size n by changing only one element between successive subsets. Such methods have been studied in the applied mathematics literature but are mostly unknown to statisticians. The advantage of such methods is that an update formula can be used at every step, thus potentially saving computation time. The method used to compute the next subset in the list requires some computation time, and thus the new method will only be faster if the update formula is sufficiently faster than doing the computation from scratch.

Esteban, M.D.

doi: 10.1080/03610929608831710pmid: N/A

Using divergence measures based on entropy functions, a procedure to test statistical hypotheses is proposed. Replacing the parameters by suitable estimators in the expresion of the divergence measure, the test statistics are obtained. Asymptotic distributions for these statistics are given in several cases when maximum likelihood estimators are considered, so they can be used to construct confidence intervals and to test statistical hypotheses based on one or more samples. These results can also be applied to multinomial populations. Tests of goodness of fit and tests of homogeneity can be constructed.

Yafune, Akifumi; Ishiguro, Makio; Kitagawa, Genshiro

doi: 10.1080/03610929608831711pmid: N/A

When an appropriate parametric model and a prior distribution of its parameters are given to describe clinical time courses of a dynamic biological process, Bayesian approaches allow us to estimate the entire profiles from a few or even a single observation per subject. The goodness of the estimation depends on the measurement points at which the observations were made. The number of measurement points per subject is generally limited to one or two. The limited measurement points have to be selected carefully. This paper proposes an approach to the selection of the optimum measurement point for Bayesian estimations of clinical time courses. The selection is made among given candidates, based on the goodness of estimation evaluated by the Kullback-Leibler information. This information measures the discrepancy of an estimated time course from the true one specified by a given appropriate model. The proposed approach is applied to a pharmacokinetic analysis, which is a typical clinical example where the selection is required. The results of the present study strongly suggest that the proposed approach is applicable to pharmacokinetic data and has a wide range of clinical applications.

Thompson, Peter

doi: 10.1080/03610929608831712pmid: N/A

The admissibility of testing procedures is examined when the loss function used is an increasing function of the p-value rather than the standard 0–1 loss. It is shown that the class of admissible procedures using the new approach is a subset of the class of admissible procedures using the 0–1 loss.

Byrne, Philip J.

doi: 10.1080/03610929608831713pmid: N/A

This paper addresses the problem of testing the multivariate linear hypothesis when the errors follow an antedependence model (Gabriel, 1961, 1962). Antedependence can be formulated as a nonstationary autoregressive model of general order. Three test statistics are derived that provide analogs to three commonly used MANOVA statistics: Wilks' Lambda, the Lawley-Hotelling Trace, and Pillai's Trace. Formulas are given for each of these statistics that show how they can be obtained From any statistical computing package that calculates the usual MANOVA statistics. These antedependent statistics would be appropriate in analyzing certain multivariate data sets in which repeated measurements are taken on the same subjects over a period of time.

Yokoyama, Takahisa

doi: 10.1080/03610929608831714pmid: N/A

This paper is concerned with profilc analysis of growth curves of several groups. Two extended growth curve models introduced by Verbyla and Venables (1988) are considered. The first is a growth curve model with covariates, which has a random-effects covariance structure based on a single response variable; the second is a multivariate growth curve model with parallel profiles, which has a multivariate random-effects covariance structure based on several response variables. Test statistics for testing hypotheses about mean parameters are suggested under the random-effects covariance structures.

Calabria, R.; Pulcini, G.

doi: 10.1080/03610929608831715pmid: N/A

In this paper, Bayes estimates of the parameters and functions thereof in the left-truncated exponential distribution are derived. Asymmetric loss functions are used to reflect that, in most situations of interest, overestimation of a parameter does not produce the same economic consequence than underestimation. Both the non-informative prior and an informative prior on the reliability level at a prefixed time value are considered, and the statistical performances of the Bayes estimates are compared to those of the maximum likelihood ones through the risk function.

Reschenhofer, Erhard

doi: 10.1080/03610929608831716pmid: N/A

Recent results (Kass and Wasserman, 1995, Reschenhofer, 1995) concerning the approximation of posterior probabilities are used to develop further the Bayesian prediction criterion proposed by San Martini and Spezzaferri (1984).

El-Saidi, Mohammed A.; Dimitrov, Boyan; Chukova, Stefanka

doi: 10.1080/03610929608831717pmid: N/A

In this paper we discuss an extended form of the logistic distribution and refer to it as the reversed generalized logistic distribution. We study some moment properties, and derive exact and explicit formulas for the mean, median, mode, variance, coefficients of skewness and kurtosis, and percentage points of this distribution. In addition, we study its limiting distributions as the shape parameter tends to zero or infinity. We also discuss some possible applications in bioassays through logistic regression approach.