Showing papers in "Communications in Statistics - Simulation and Computation in 1985"
TL;DR: In this article, the partial least squares (PLS) prediction method is compared to the predictor based on principal component regression (PCR), both theoretical considerations and computations on artificial and real data are presented.
Abstract: In this paper we discuss the partial least squares (PLS) prediction method. The method is compared to the predictor based on principal component regression (PCR). Both theoretical considerations and computations on artificial and real data are presented.
164 citations
TL;DR: In this article, a two-stage sampling procedure for selecting a subset of size m containing the t best of k independent normal populations, when the ranking parameters are the population means, is presented.
Abstract: In this paper we state and justify a two-stage sampling procedure for selecting a subset of size m containing the t best of k independent normal populations, when the ranking parameters are the population means. We do not assume that the variances of the populations are known or equal. Discrete event simulation studies are often concerned with choosing one or more system designs which are best in some sense. We present empirical results from a typical simulation application for which the observations are not normally distributed.
134 citations
TL;DR: In this paper, the problem of estimating the linear parameters of a generalized linear model (GLM) when the explanatory variable is subject to measurement error is considered, and it is shown that in this situation the induced linear parameters can be approximated by a Gaussian distribution.
Abstract: This paper considers the problem of estimating the linear parameters of a Generalised Linear Model (GLM) when the explanatory variable is subject to measurement error. In this situation the induced...
129 citations
TL;DR: In this article, the generalized Poisson distribution (GPD) was used to fit data arising in various situations and in many fields, and the truncation error for most cases is negligible and that the model can be used without any correction for truncation.
Abstract: The generalized Poisson distribution (GPD), containing two parameters and studied by many researchers, was found to fit data arising in various situations and in many fields. It is generally assumed that both parameters (θ,λ) are non-negative, and hence the distribution will have a variance larger than the mean. However, it appears that the distribution, as a descriptive model, fits many data for negative values of λ, which implies that the mean must be greater than the variance. Thetruncation of the GPD, proposed to remedy the deficiency in the model in this case, is investigated on the basis of the error analysis on the computer and it is suggested that the truncation error for most of the cases is negligible and that the model can be used without any correction for truncation.
60 citations
TL;DR: In this paper, the effect of truncation on the performance of an open vector-at-a-time sequential sampling procedure (P* B) for selecting the multinomial event which has the largest probability was studied.
Abstract: In this article we study the effect of truncation on the performance of an open vector-at-a-time sequential sampling procedure (P* B) proposed by Bechhofer, Kiefer and Sobel , for selecting the multinomial event which has the largest probability. The performance of the truncated version (P* B T) is compared to that of the original basic procedure (P* B). The performance characteristics studied include the probability of a correct selection, the expected number of vector-observations (n) to terminate sampling, and the variance of n. Both procedures guarantee the specified probability of a correct selection. Exact results and Monte Carlo sampling results are obtained. It is shown that P* B Tis far superior to P* B in terms of E{n} and Var{n}, particularly when the event probabilities are equal.The performance of P* B T is also compared to that of a closed vector-at-a-time sequential sampling procedure proposed for the same problem by Ramey and Alam; this procedure has here to fore been claimed to be the bes...
41 citations
TL;DR: In this article, a joint k-variate normal distribution with zero means, common unknown varianceσ2 and known correla- tion matrix (ρij) where ρi j = ρ for all i ≠ j.
Abstract: Let X1,…X,k have a joint k-variate normal distribution with zero means, common unknown varianceσ2and known correla- tion matrix (ρij) where ρi j = ρ for all i ≠ j. Let s2 be distributed independently of the X1 such that vs2/σ2 has a chisquared distribution with v degrees of freedom. New tables with wider coverage and more accuracy than the previously published ones are given for the percentage points of . Some basic theoretical results are given in Section.
38 citations
TL;DR: In this paper, a simulation structured as an experimental design allows statistical testing of the various missing data estimators for the various regression criteria as well as different regression specifications, and the results indicate that although no missing estimator is globally best many of the computationally simpler first order methods perform well as the more expensive higher order estimators, contrary to some previous findings.
Abstract: Previous simulations have reported second order missing data estimators to be superior to the more straightforward first order procedures such as mean value replacement. These simulations however were based on deterministic comparisonsbetween regression criteria even though simulated sampling is a random procedure. In this paper a simulation structured asan experimental design allows statistical testing of the various missing data estimators for the various regression criteria as well as different regression specifications. Our results indicate that although no missing data estimator is globally best many of the computationally simpler first order methods perform as well as the more expensive higher order estimators, contrary to some previous findings.
23 citations
TL;DR: In this article, the authors examined the performance of a likelihood ratio statistic and a Kolmogorov ratio statistic for ambient air quality concentration and proposed a procedure for increasing the probability of correct selection.
Abstract: Methods for selecting a distributional model for a random variable such as ambient air quality concentration are examined. Specific consideration is given to identification of a model from the exponential, lognormal, Weibull and gamma distributions. The performance of a likelihood ratio statistic and a Kolmogorov ratio statistic are examined by Monte Carlo simulation. On the basis of these results a procedure for increasing the probability of correct selection is proposed.
23 citations
TL;DR: In this article, a Monte Carlo investigation into the small sample robustness and power of an aligned rank transformation statistic (ART) was conducted for detecting treatment effects in balanced incomplete block (BIB) designs.
Abstract: This paper is concerned primarily with a Monte Carlo investigation into the small sample robustness and power of an aligned rank transformation statistic. The aligned rank transformation statistic (ART) is compared to the classical F-test and to Durbin's (1951) rank test for its ability to detect treatment effects in balanced incomplete block (BIB) designs.
21 citations
TL;DR: An algorithm which is often referred as the EM algorithm is presented, which utilizes the technique of analysis of covariance for analysing growth curve data with missing values.
Abstract: This paper considers a computational method for analysing growth curve data with missing values. We present an algorithm which is often referred as the EM algorithm. The procedure proposed here utilizes the technique of analysis of covariance.
19 citations
TL;DR: In this article, a minimum point set requirement for two-factor rotatable designs is established, thus enabling one to form an infinity of such designs, and some difficulties in obtaining deLigns for k>2 are described.
Abstract: Fourth order rotatable designs are discussed. A general k, design moment inequality is given. The variance function for two-factor designs is derived, and plotted for a specific design. A minimum point set requirement for two-factor designs is established, thus enabling one to form an infinity of such designs. Some difficulties in obtaining deLigns for k>2 are described. Some questions are posed for future work.
TL;DR: In this paper, an empirical performance study of outlier detection procedures for Weibull or extreme value distributions using a mixture model in which a known number of randomly chosen observations are contaminated was carried out.
Abstract: We carried out an empirical performance study of outlier detection procedures for Weibull or extreme–value distributions using a mixture model in which a known number of randomly chosen observations are contaminated. Procedures studied were: L(L') based on leaps (differences of adjacent observations divided by expectation), V, Q and W (Mann, 1982), R1(R'1), R2(R'2), R3(R'3) (Dixon, 1950) and G(G') (Grubbs, 1950). Percentage points for statistics L(L'), R1(R'1), R2(R'2), R3(R'3) and G(G') were computed empirically for the extreme-value distribution and are tabulated. The procedures L(L') (or equivalently in power V) performed best, with few exceptions, for the contaminated model tested. The Grubb statistic G' performed well in testing for lower outliers. Mann's W , which was best for the labeled slippage was substantially poorer than the others for the mixture model. Dixon's R1(R'1)is recommended as a generally useful test for sample sizes in the range investigated (n=5,20)
TL;DR: This paper provides extended sets of correct constants and associated performance characteristics of Ramey and Alam's closed sequential procedure, and describes the methods that were used to calculate them.
Abstract: Ramey and Alam 1979 proposed a closed sequential procedure for selecting that one of k >2 multinomial events which has the largest probability. They provided tables of constants necessary to implement their procedure and, based on these constants, they calculated certain performance characteristics of their procedure. In the course of devising a fundamentally different procedure and studying its performance, we had occasion to check their constants and associated performance characteristics. We found quite a few of them to be incorrect. In the present paper we provide extended sets of correct constants and associated performance characteristics (some of which were not provided by Ramey and Alam), and describe the methods that we used to calculate them.
TL;DR: In this article, the problem of comparing several means under heteroscedasticity and nonnormality was considered, and several robust procedures were developed; these procedures were compared through computer simulation studies with the Tan-Tabatabai procedure which was developed by combining Tiku's MML estimators with the Brown-Forsythe test.
Abstract: In this paper we consider the problem of comparing several means under heteroscedasticity and nonnormality. By combining Huber‘s M-estimators with the Brown-Forsythe test, several robust procedures were developed; these procedures were compared through computer simulation studies with the Tan-Tabatabai procedure which was developed by combining Tiku's MML estimators with the Brown-Forsythe test. The numerical results indicate clearly that the Tan-Tabatabai procedure is considerably more powerful than tests based on Huber's M-estimators over a wide range of nonnormal distributions.
TL;DR: In this article, the response variances, var(yi), are estimated using replications for each experimental condition, and the resulting estimated variances can be used to derive the correct variances of the Ordinary A 2 Least Squares (OLS) estimators β.
Abstract: Response variances, var(yi), are estimated using replications for each experimental condition. The resulting estimated variances can be used to derive the correct variances of the Ordinary A 2 Least Squares (OLS) estimators β. The estimates si can also be used to compute the Estimated Weighted Least Squares (EWLS) estimators β* . The asymptotic covariance formula for EWLS might be utilized to test the EWLS estimators. The type I and type I1 errors of this test procedure are compared to the corresponding A errors for the OLS estimators β.
TL;DR: An algorithm is presented for computing the probability value associated with a recently-developed test of statistical inference for matched pairs.
Abstract: An algorithm is presented for computing the probability value associated with a recently-developed test of statistical inference for matched pairs. The exact probability value is provided for small samples; otherwise, an approximate probability value is computed.
TL;DR: In this article, the authors consider several procedures for estimating the sites of multiple changepoints in the distribution of a sequence of independent, continuous observations, each of these estimation schemes is based on the statistic proposed by Schechtman (1982) for testing hypotheses about a single change-point, in conjunction with a variety of techniques for detecting local maxima.
Abstract: In this paper we consider several procedures for estimating the sites of multiple changepoints in the distribution of a sequence of independent, continuous observations. Each of these estimation schemes is based on the statistic proposed by Schechtman (1982) for testing hypotheses about a single change-point, in conjunction with a variety of techniques for detecting local maxima in a sequence of data. The results of an extensive Monte Carlo investigation are presented and used to provide guidelines for selecting a particular estimation procedure for a specific application.
TL;DR: In this paper, two families of parameter estimation procedures for the stable laws based on a variant of the characteristic function are provided, which may be described as a modified weighted chi-squared minimization procedure, and both explicitly take account of constraints on the parameter space.
Abstract: Two families of parameter estimation procedures for the stable laws based on a variant of the characteristic function are provided. The methodology which produces viable computational procedures for the stable laws is generally applicable to other families of distributions across a variety of settings. Both families of procedures may be described as a modified weighted chi-squared minimization procedure, and both explicitly take account of constraints on the parameter space. Influence func-tions for and efficiencies of the estimators are given. If x1, x2, …xn random sample from an unknown distribution F , a method for determining the stable law to which F is attracted is developed. Procedures for regression and autoregres-sion with stable error structure are provided. A number of examples are given.
TL;DR: In this paper, a Monte Carlo study of OLS and GLS based adaptive ridge estimators for regression problems in which the independent variables are collinear and the errors are autocorrelated is presented.
Abstract: This paper presents the results of a Monte Carlo study of OLS and GLS based adaptive ridge estimators for regression problems in which the independent variables are collinear and the errors are autocorrelated. It studies the effects of degree of collinearity, magnitude of error variance, orientation of the parameter vector and serial correlation of the independent variables on the mean squared error performance of these estimators. Results suggest that such estimators produce greatly improved performance in favorable portions of the parameter space. The GLS based methods are best when the independent variables are also serially correlated.
TL;DR: In this article, the inverse wishart matrices were generated by generating inverse wish-art vectors from a single wishart matrix, and the authors presented a method to generate a wishart vector from a pair of wishart vectors.
Abstract: (1985). Generating inverse wishart matrices. Communications in Statistics - Simulation and Computation: Vol. 14, No. 2, pp. 511-514.
TL;DR: In this paper, the lack of a generally accepted measure of the degree of severity of heteroskedasticity is shown to have caused some Monte Carlo studies to draw misleading conclusions.
Abstract: The lack of a generally-accepted measure of the degree of severity of heteroskedasticity is shown to have caused some Monte Carlo studies to draw misleading conclusions. An attractive measure of heteroskedasticity is suggested.
TL;DR: In this article, two statistics are suggested for testing the equality of two normal percentiles where population means and variances are unknown. The first is based on the generalized likelihood ratio test (LRT), the second on Cochran's statistic used in the Behrens-Fisher problem, and size and power comparisons are made by using simulation and asympototic theory.
Abstract: Two statistics are suggested for testing the equality of two normal percentiles where population means and variances are unknown. The first is based on the generalized likelihood ratio test (LRT), the second on Cochran's statistic used in the Behrens-Fisher problem. Size and power comparisons are made by using simulation and asympototic theory.
TL;DR: In this article, a Monte Carlo study was made of the effects of using simple linear regression, on the appropriate probability paper, to estimate parameters, quantiles and cumulative probability for several distributions.
Abstract: A Monte Carlo study was made of the effects of using simple linear regression, on the appropriate probability paper, to estimate parameters, quantiles and cumulative probability for several distributions. These distributions were the Normal, Weibull (shape parameters 1, 2, and 4) and the Type I largest extreme-value distributions. The specific objective was to observe differences arising from choice of plotting positions. Plotting positions used were i/(n+l), (i−3)/(n+.04), (i−.5)/n, either (i−.375)/(n+.25) or (i−.4)/(n+.2), and either F[E(Yi)] or F[E(£n Y)]. For each combination of 4 sample sizes (n=10(10)(40)), distribution, and plotting position, regression lines were found for each of N =9999 samples. Each regression line was used to estimate: (1) quantiles of 9 specific probabilities, (2) probabilities of 9 specific quantiles, and (3) return periods corresponding to 9 specific quantiles. Compa[rgrave]ison of the mean, variances, mean square error and medians of these estimates and of the regression c...
TL;DR: In this article, the small sample properties of the size-corrected W, LM and LR tests were examined by Monte Carlo experiments and it was shown that the performances of these tests are very good.
Abstract: In this paper, we examine by Monte Carlo experiments the small sample properties of the W (Wald), LM (Lagrange Multiplier) and LR (Likelihood Ratio) tests for equality between sets of coefficients in two linear regressions under heteroscedasticity. The small sample properties of the size-corrected W, LM and LR tests proposed by Rothenberg (1984) are also examined and it is shown that the performances of the size-corrected W and LM tests are very good. Further, we examine the two-stage test which consists of a test for homoscedasticity followed by the Chow (1960) test if homoscedasticity is indicated or one of the W, LM or LR tests if heteroscedasticity should be assumed. It is shown that the pretest does not reduce much the bias in the size when the sizecorrected citical values are used in the W, LM and LR tests.
TL;DR: In this paper, the authors consider the determination of Bayesian life test acceptance sampling plans for finite lots when the underlying lifetime distribution is the two parameter exponential and assume that the costs associated with the actions accept and reject are known functions of the lifetimes of the items, and the cost of testing a sample is proportional to the duration of the test.
Abstract: In this paper we consider the determination of Bayesian life test acceptance sampling plans for finite lots when the underlying lifetime distribution is the two parameter exponential. It is assumed that the prior distribution is the natural conjugate prior, that the costs associated with the actions accept and reject are known functions of the lifetimes of the items, and that the cost of testing a sample is proportional to the duration of the test. Type 2 censored sampling is considered where a sample of size n is observed only until the rth failure occurs and the decision of whether to accept or reject the remainder of the lot is made on the basis of the r observed lifetimes. Obtaining the optimal sample size and the optimal censoring number are difficult problems when the location parameter of the distribution is restricted to be non-negative. The case when the positivity restriction on the location parameter is removed has been investigated. An example is provided for illustration.
TL;DR: In this article, the relative performances of randomised block, balanced lattice squares and Papadakis nearest neighbor analyses were compared on two simulated fields whose soil heterogeneity profiles were generated, one with a few evenly spaced contours and the other with many unevenly spaced contour.
Abstract: The relative performances of randomised block, balanced lattice squares and Papadakis nearest neighbour analyses were compared on two simulated fields whose soil heterogeneity profiles were generated, one with a few evenly spaced contours and the other with many unevenly spaced contours. Four levels of random error were generated to simulate different proportions of random error and soil heterogeneity. Dummy treatments, corresponding to 7 x 7 and 11 x 11 balanced lattice squares were applied to the fields. The results from simulated experiments showed an interaction of error mean square (EMS) between size of experiment (7 x 7, 11 x 11) and levels of soil heterogeneity in the lattice analyses, but no such interaction in the Papadakis analyses. The Papadakis EMS decreased as random error decreased but at a rate depending on the map andthe ratio of soil heterogeneity to random error.
TL;DR: In this paper, the percentage points of a new distribution involving a confluent-hypergeometric distribution obtained by Khatri and Rao (1985) are tabulated and the use of the tabulated values in obtaining a lower confidence bound for the realized signal to noise ratio based on an estimated discriminant function for signal detection is explained.
Abstract: Percentage points of a new distribution involving a confluent-hypergeometric distribution obtained by Khatri and Rao (1985) are tabulated. The use of the tabulated values in obtaining a lower confidence bound for the realized signal to noise ratio based on an estimated discriminant function for signal detection is explained.
TL;DR: In this article, the authors consider the estimation of Poisson regression models in which structural variation in a subset of the parameters is permitted and propose an alternative algorithm that implements partitioned matrix inversion and thereby avoids restictions on the size of the model.
Abstract: We consider the estimation of Poisson regression models in which structural variation in a subset of the parameters is permitted. It is noted that coventional estimation algorithms are likely to impose restrictions on the number of explanatory variables and the number of structural regimes. We propose an alternative algorithm that implements partitioned matrix inversion and thereby avoids restictions on the size of the model. The algorithm is applied to a model of shopping behavior Adjustments in the algorithm necessary for dealing with censored data are detailed.
TL;DR: In this paper, the authors compare two estimators via analytic results and a simulation study, and compare their estimators with the estimators of Olkin, Sobel, and Tong.
Abstract: In the problem of selecting the best of k populations, Olkin, Sobel, and Tong (1976) have introduced the idea of estimating the probability of correct selection. In an attempt to improve on their estimator we consider anempirical Bayes approach. We compare the two estimators via analytic results and a simulation study.
TL;DR: In this article, seven estimators for the probabilities of misclassification associated with the linear discriminant function are considered and an empirical investigation is conducted to evaluate the relative merits of these estimators.
Abstract: Seven estimators for the probabilities of misclassifi-cation associated with the linear discriminant function are considered. Four of them are known in the literature. The remaining three are constructed through the Jackknife Pro-cedure. An empirical investigation is conducted to evalu-ate the relative merits of these estimators. Summary of the results is presented.