Showing papers in "Journal of Statistical Computation and Simulation in 1982"
TL;DR: It is shown that three problems from computational statistics are n p- hard: cluster analysis, subset selection in regression and D-optimal exact design of experiments.
Abstract: A theory of algorithmic complexity from computer science allows one to examine the properties of algorithms for the solution of computational problems and, in particular, the relationship between the size of an instance of the generic problem and the time required for computation The theory identifies certain problems as n p- complete or n p-hard, two classes of problems thought to be intractable. We show that three problems from computational statistics are n p- hard: cluster analysis, subset selection in regression and D-optimal exact design of experiments.
145 citations
TL;DR: In this article, a generalization of the block replacement policy (BRP) is proposed and analyzed, where at failure epochs the replacement of the failed unit is not mandatory and instead a minimal repair can be made.
Abstract: A generalization of the block replacement policy (BRP) is proposed and analysed. The new policy differs from the ordinary BRP in that at failure epochs the replacement of the failed unit is not mandatory and instead a minimal repair can be made. The choice between these two possible actions is based on the repair cost which is assumed to be random. Planned replacements are carried out at timesk T(k=1,2,3….), like in the ordinary BRP, and the aim of the paper is to find the optimal block interval T which minimizes the long run expected cost per unit time of the policy.
56 citations
TL;DR: In this article, the critical angles proposed by Krzanowski (1979) were investigated as a means of comparing principal component analyses done on two sets of individuals, each of which has had the same p responses measured on it.
Abstract: Sampling distributions arc Investigated for the critical angles proposed by Krzanowski (1979) as a means of comparing principal component analyses done on two sets of individuals, each of which has had the same p responses measured on it A summary of the distributions is presented, by giving mean angles and 95% points The emphasis is on the null case, when the two sets of individuals are assumed to be independent samples from the same population, but a limited study is also made of the case where the two samples come from different populations
50 citations
TL;DR: In this article, a class of generalized ML estimates, indexed by a parameter τ, which contain REML and ordinary ML estimates as special limiting cases are introduced, which enables a single set of iterative EM equations which yields either ML or REML estimates of the variance components, depending upon the value specified for τ.
Abstract: In their paper on maximum likelihood will) Incomplete data. Dempster. Laird, and Rubin (1977) noted that both maximum likelihood (ML) and restricted ML (REML) estimators of variance components in the mixed model analysis oi variance can be computed via the LM algorithm. Thi-follows from treating the random effects as missing data and using the incomplete data framework outlined in Dempster, et al. (1977). We elaborate on this idea, introducing a class of generalized ML estimates, indexed by a parameter τ, which contain REML and ordinary ML estimates as special limiting cases. This device enables us to derive a single set of iterative EM equations which yields either ML or REML estimates of the variance components, depending upon the value specified for τ.
48 citations
42 citations
39 citations
TL;DR: In this article, a smooth empirical Bayes estimation technique based on nonparametric maximum likelihood estimation of the prior distribution is presented, which can be easily calculated for a variety of sampling situations.
Abstract: This paper presents a smooth empirical Bayes estimation technique based on nonparametric maximum likelihood estimation of the prior distribution Posterior means based on this estimate of the prior are shown to be easily calculated for a variety of sampling situations Examples involving normal and binomial sampling are given.
34 citations
TL;DR: In this article, the studentized absolute maximum deviation from the mean statistic is modified by replacing the sample standard deviation with a biweight estimator of σ 2, and simple approximate formulas for the 90 and 95th percentage points are found through the use of the Monte Carlo technique.
Abstract: The studentized absolute maximum deviation from the mean statistic is modified by replacing the sample standard deviation with a biweight estimator of σ 2. Simple approximate formulas for the 90 and 95th percentage points are found through the use of the Monte-Carlo technique. A comparison is made between the proposed procedure, the one using the sample standard deviation and the kurtosis measure (b2 ), as methods for detecting one or more outliers. For normal slippage alternatives the use of the proposed procedure seems better than using standard deviation and about the same as using b2 . For more general alternatives b2 seems to be far more conservative than the proposed method. In addition, the proposed procedure can be used in one stage to detect multiple outliers, with only slight loss of power, as compared to consecutive use.
33 citations
TL;DR: In this paper, the problem of computing binomial probabilities when the trial probabilities are unequal is investigated, and an algorithm for computing such probabilities is formulated by expanding the probability generating function and collecting the appropriate coefficients via a recursive scheme.
Abstract: The problem of computing binomial probabilities when the trial probabilities are unequal is investigated. An algorithm for computing such probabilities is formulated by expanding the probability generating function and collecting the appropriate coefficients via a recursive scheme. Various examples are given, and comparisons are made with calculations of such probabilities using the probability distribution.
31 citations
TL;DR: In this article, the authors point out that to obtain the theoretical autocovariances of any vector ARMA process, they need to solve a smaller system of equations than in Ansley (1980).
Abstract: We point out that to obtain the theoretical autocovariances of any vector ARMA process we need to solve a smaller system of equations than in Ansley (1980). This implies a substantial reduction in computation time. As an application, we consider obtaining the likelihood of a stationary ARMA process. To speed up the computation, we suggest a stable fixed point iteration.
31 citations
TL;DR: The computer simulation of two stochastic hard core models, the Kelly-Ripley model and the SSI model, using a spatial birth and death process and a new method of simulation, which is considerably faster than the existing method at high densities of discs, is described.
Abstract: A commonly used model for spatial point patterns exhibiting inhibition between points is the hard core model, in which the points of the pattern may be regarded as being the centres of non-overlapping discs of fixed diameter. It is often necessary in spatial statistics to be able to simulate many realisations of various models for point patterns. In this paper, the computer simulation of two stochastic hard core models is considered. The first of these, the Kelly-Ripley model, is simulated using a spatial birth and death process, while, for the second, the “SSI” model, a birth process is used. In each case, a new method of simulation, which is considerably faster than the existing method at high densities of discs, is described. Both algorithms use the Dirichlet tessellation of the points. The properties of the algorithm for simulating the SSI process make it possible to investigate random sequential packing of discs in a rectangular container. An estimate of the limiting packing density at complete packi...
TL;DR: In this article, the small sample properties of several related test statistics are investigated via Monte Carlo techniques and the covariance matrix is estimated by each of three non-iterative methods.
Abstract: Kleinbaum (1973) developed a generalized growth curve model for analyzing incomplete longitudinal data. In this paper the small sample properties of several related test statistics are investigated via Monte Carlo techniques. The covariance matrix is estimated by each of three non-iterative methods. The null and non-null distributions of these test statistics are examined.
TL;DR: In this article, the authors used Khintchine's theorem to construct new multivariate distributions which are easy to simulate and which cover a broad range of dependence structures, which are then used to construct a multivariate distribution.
Abstract: Khintchine's theorem is used to construct new multivariate distributions which are easy to simulate and which cover a broad range of dependence structures.
TL;DR: In this article, a comparison of the power of the two-sample equal sample size Wilcoxon test over an extensive practical range of domains is presented, and the power is evaluated for two values of the noncentrahty parameter △ (values which produce powers of 0.50 and 0.95 for the corresponding r-test under normality).
Abstract: The present study has as its object an accurate evaluation of the power of the two-sample equal sample size Wilcoxon test over an extensive practical range of uismnmioriv The method is thai o! a large Monte Carlo study over the Pearson ay item of dmnbuUoiia. β1 = 0.0(0.4)2.0, β2 = 1.4(0.4)7.8 (negative and positive skewness) and equal sample sizes N = 5(5)30. The power is evaluated for two values of the noncentrahty parameter △ (values which produce powers of 0.50 and 0.95 for the corresponding r-test under normality) and these probabilities are evaluated from 40,000 generated values of the test statistic. Since the ingredients of this study are identical to those of a similar earlier study of the t-test, a comparison of the power of the Wilcoxon and the t-test is provided to determine the range of the Pearson system in which the power function of one test is superior to that of the other. The stutly is restricted to equal sample size tests and the results may not apply to more than moderate departures fr...
TL;DR: In this article, a new method for reducing the variance in simalation experiments is presented and evaluated, which can be regarded as an extension of the antithetic variates principle.
Abstract: A new method for reducing the variance in simalation experiments is presented and evaluated. The method can be regarded as an extension of the antithetic variates principle. We create negative correlation within all pairs of random number while the original mcihod creates correlation only within some pairs. Our method is compared to ihe antithetic variates and crude Monte-Carlo techniques by repeated simulations. The results obtained are ail in favour of our method.
TL;DR: In this paper, the authors consider the problem of finding the maximum likelihood estimate for a certain class of discrete sampling models using convex optimization theory, including aspects of equivalence theory, duality theory, and iterative procedures.
Abstract: In this article we consider the pioblem of finding the maximum likelihood estimate for a certain class of discrete sampling models. Methods are adapted from parts of convex optimization theory, includiug aspects of equivalence theory, duality theorv and iterative procedures Their application is illustrated through example.
TL;DR: In this article, the probability that the estimated between-group covariance matrix is not positive definite is computed exactly under certain conditions given in Hill and Thompson (1978) for the balanced single classification multi-vanate analysis of variance with random effects.
Abstract: The probability that the estimated between-group covariance matrix is not positive definite is computed exactly under certain conditions given in Hill and Thompson (1978) for the balanced single classification multi-vanate analysis of variance with random effects. The computation is done using the Pfaffian method. This method can also be used more generally to calculate the cummulative distribution function of the largest root of the matrix where S1 and S2 are independent central Wishart matrices with common covariance matrices. The Pfaffian method is found to be a rapid and highly practical alternative to an algorithm of Venables (1974).
TL;DR: In this article, the usefulness of the total variation criterion is pointed out, and some examples are given when the total variance is hard to compute, good upper bounds can be used in its place.
Abstract: If random variates with density fare needed in simulations, but random variates with density g (close to f) are used instead, how does one measure the error committed? The usefulness of the total variation criterion is pointed out, and some examples are given When the total variation is hard to compute, good upper bounds can be used in its place Some inequalities are reviewed that link the total variation to other quantities such as the rejection and composition constants, the uniform deviation, the divergence and so forth
TL;DR: In this article, the maximum approximation error of a normal approximation to the exact conditional power function of the Manic!-Haenszcl one degree of freedom chi-squared procedure is investigated.
Abstract: The accuracy of a normal approximation to the exact conditional power function of the Manic!-Haenszcl one degree ni freedom chi-squared procedure is nnesugaied The maximum approximation error over the parameter space is studied for designs with equal numbers of cases and controls within and across strata. An empirical rule is provided for the estimation of the maximum error, the rule performs well over a range of design constants of importance in stratified case-control studies.
TL;DR: In this article, a rank statistic is considered which may be used for testing for total independence in a p-variate exponential distribution with equal correlation coefficients, and the small sample power performance of the rank test relative to that of the locally most powerful similar measure under the exponential alternative is evaluated.
Abstract: A rank statistic is considered which may be used for testing for total independence in a p-variate exponential distribution with equal correlation coefficients. Critical values for the statistic are provided for p = 3.4 and sample sizes less than or equal to 20. Finally, the small sample power performance of the rank test relative to that of the locally most powerful similar lest under the exponential alternative is evaluated.
TL;DR: In this paper, the problem of predicting, on the basis of an observed sample from an inverse Gaussian distribution, the mean of a future random sample from the same distribution is considered.
Abstract: The problem of predicting, on the basis of an observed sample from an inverse Gaussian distribution, the mean of a future random sample from the same distribution is considered. Approximate prediction intervals are proposed, and their accuracy is investigated via extensive Monte Carlo simulations. The results are useful for predicting the mean of future first passage times for a Brownian motion with positive drift or mean failure time of m future items having inverse Gaussian life distribution.
TL;DR: In this paper, Gaussian-quadrature formulas for Gaussian quadrature formulas have been proposed for statistical computing and simulation, and they have been applied to the problem of statistical clustering.
Abstract: (1982). Gaussian-quadrature formulas for. Journal of Statistical Computation and Simulation: Vol. 15, No. 2-3, pp. 155-160.
TL;DR: In this article, the distributions of the Brown-Forsythe F * statistic for a one-way ANOVA model with heterogeneous variances are derived and approximated by Laguerre polynomial expansions.
Abstract: This article considers a one-way ANOVA model as given in (1.1) with heterogeneous variances. The distributions of the Brown-Forsythe F * statistic for this model are derived and approximated by Laguerre polynomial expansions. The Type 1 error and power function values are then evaluated for both normal and mixtures of two normals populations. For the example with k=3n 1=8,n 2=10 and n 3=12. it is shown that the Satterthwaite approximation provides a close approximation to the null and non-null distributions in most o\ the cases. It is shown that the F * is quite robust with respect to departure from normality for Type 1 error in the case of mixtures of two normals.
TL;DR: The posterior distribution of the cross-ratio measure of association has been found under a Dirichlet prior for the population parameters as mentioned in this paper, which is readily evaluated in terms of elementary functions.
Abstract: The posterior distribution of the cross-ratio measure of association has been found under a Dirichlet prior for the population parameters. This distribution is readily evaluated in terms of elementary functions.
TL;DR: In this article, a computer simulation study of power and robustness of three competitor tests for comparing scales, for use with correlated data: Rothstein, Richardson and Bell (RRB), Arvesen, and Pitman, is presented.
Abstract: Results of a computer simulation study of power and robustness of three competitor tests for comparing scales, for use with correlated data: Rothstein, Richardson and Bell (RRB), Arvesen, and Pitman, are presented. It is found that unless one could improve the approximate null distributions for Arvesen's and Pitman's test, RRB's procedure is best, having simulated probabilities of Type I error closest to the test's nominal α and being reasonably robust and powerful, for all distributions considered.
TL;DR: In this paper, a test statistic based on the signed ranks of the data is discussed and investigated, which is obtained by computing Hotelling's T 2 statistic as a function of the signed rank and is equivalent to a statistic of Puri and Sen (1971).
Abstract: In the multivariate one-sample location problem, the size of Hotelling's T 2 test fluctuates widely from nominal alpha as the distributions deviate from multinormality due to skewness or the distributions have tails heavier than multinormal distributions. For skewed distributions, several modifications of Hotelling's T 2 are available to adjust for skewness. In this paper for symmetric distributions, a test statistic based on the signed ranks of the data is discussed and investigated. The proposed test statistic is obtained by computing Hotelling's T 2 statistic as a function of the signed ranks and is equivalent to a statistic of Puri and Sen (1971). An approximation to its null distribution is derived by moment matching criterion. Monte Carlo results are presented to compare several test statistics. For various multidimensional distributions the Monte Carlo results indicate the robustness of the proposed statistics. For bivariate normal, uniform and Cauchy distributions, the results of a power compariso...
TL;DR: This article showed that the Mantel-Valand statistic does not have the asymptotic moments of a normal distribution for the important case where the two samples are of equal size and that the normal distribution provides a poor fit for relatively small sample sizes.
Abstract: The Mantel–Valand statistic is used to measure the “distance” between p-variate samples from two possibly different distributions. We show that while this statistic can be approximated by a normal distribution for many large sample cases, it does not have the asymptotic moments of a normal distribution for the important case where the two samples are of equal size. In addition, the normal distribution provides a poor fit for relatively small sample sizes. The exact first four moments of this statistic for a single variable (p= 1) are derived and fitted curves of the Pearson series are shown to better approximate the tail areas of simulated sampling distributions than do the corresponding normal fits. Exact critical values are presented for n 1, and n 2 up to .
TL;DR: In this paper, an algorithm for computing the bivariate cumulants of a multinomial sample under the null hypothesis is given. But the algorithm is based on an unproved but certainly true conjecture concerning the characteristic polynomial of the matrix product.
Abstract: Pearson's chi-squared for a multinomial sample is defined as where An analogous or supplementary statistic Yt: is defined as .The statistic Y t , should be powerful when the alternative hypotheses:are obtained from the null hypothesis by adding to it bumps or dips wider than the bin width. Algorithms are supplied for calculating the cumulants of Y 1 especially when the null hypothesis is Most of the formulae depend on an unproved but certainly true conjecture concerning the characteristic polynomial of the matrix product Formulae for the bivariate cumulants of X 2,Y 1 are also provided.
TL;DR: In this paper, four MANOVA tests (Wilk's Lambda, Roy's Largest Root Test, Hotelling-Lawley Trace and Pillai-Bartlett Trace) were compared by examining bias at critical points and fluctuations in the standard error of the empirical distributions.
Abstract: Four MANOVA tests (Wilk's Lambda, Roy's Largest Root Test, the Hotelling-Lawley Trace and the Pillai-Bartlett Trace) were studied when restricted sample data were drawn from normal populations Robustness was compared by examining bias at critical points and fluctuations in the standard error of the empirical distributions The Wilk's Lambda statistic was found to be the least affected by the restricted sampling