Showing papers in "Communications in Statistics - Simulation and Computation in 1986"
TL;DR: In this paper, the authors proposed estimators of a and c are similar to those of Fama and Roll, except that the small asymptotic bias in their estimators has been eliminated, and their restrictions that a be no less than 1.0 and that the distribution be symmetrical have been relaxed.
Abstract: The four parameters of a stable distribution may be estimated consistently from five pre-determined sample quantiles with the aid of the accompanying tables, for a in the range [0.6, 2.0] and g in the range [-1, 1]. The problem of the discontinuity of the traditional location parameter in the asymmetrical cases as a passes unity is resolved. The proposed estimators of a and c are similar to those of Fama and Roll, except that the small asymptotic bias in their estimators has been eliminated, and their restrictions that a be no less than 1.0 and that the distribution be symmetrical have been relaxed. The proposed estimators can provide good initialization values for other more efficient, but computer-intensive, methods.
660 citations
TL;DR: In this paper, the effect of using F or W only after a significant test for equal variances has been obtained, and new results on the robustness of the F test are described.
Abstract: Because the usual F test for equal means is not robust to unequal variances, Brown and Forsythe (1974a) suggest replacing F with the statistics F or W which are based on the Satterthwaite and Welch adjusted degrees of freedom procedures. This paper reports practical situations where both F and W give * unsatisfactory results. In particular, both F and W may not provide adequate control over Type I errors. Moreover, for equal variances, but unequal sample sizes, W should be avoided in favor of F (or F ), but for equal sample sizes, and possibly unequal variances, W was the only satisfactory statistic. New results on power are included as well. The paper also considers the effect of using F or W only after a significant test for equal variances has been obtained, and new results on the robustness of the F test are described. It is found that even for equal sample sizes as large as 50 per treatment group, there are practical situations where the F test does not provide adequately control over the probability...
133 citations
TL;DR: In this paper, a concise representation of the UMVUE and several representations for the MLE are derived and large-sample results are given and numerical comparison of the two point estimators is made.
Abstract: We consider estimation of P(Y
96 citations
TL;DR: In this paper, the authors compared three estimators for R = P(Y < X) when Y and X are two independent but not identically distributed random variables, i.e., the minimum variance unbiased, the maximum likelihood and the Bayes estimators.
Abstract: This paper provides a simulation study which compares three estimators for R = P(Y
91 citations
TL;DR: In this article, the authors presented two simple non-Gaussian first-order autoregressive markovian Markovian processes which are easy to simulate via a computer and were constructed according to the stochastic difference equation Xn:=Vn:Xn−1+∊n:, where ∊n:} is an i.i.d.
Abstract: This paper presents two simple non-Gaussian first-order autoregressive markovian processes which are easy to simulate via a computer. The autoregressive Gamma process {Xn:} is constructed according to the stochastic difference equation Xn:=Vn:Xn−1+∊n:, where {∊n:} is an i.i.d. Exponential sequence and {Vn:} is i.i.d. with Power-function distribution defined on the interval [0,1). The autoregressive Weibull process {Xn:} is constructed from the probabilistic model Xn:= k.min (Xn−1:, Yn:) where {Yn:} is an i.i.d. Weibull sequence and k > 1.
48 citations
TL;DR: In this article, the size and power of a test for the equality of the coefficients of variation from r normal populations were compared with two tests developed by Doornbos and Dijkstra and the test statistic is simpler to compute.
Abstract: Simulation study results are given for the size and power of a test for the equality of the coefficients of variation from r normal populations. Independent samples of equal and unequal size from the normal and three other distributions were used. The size and power of the test compare favorably to two tests developed by Doornbos and Dijkstra and the test statistic is simpler to compute.
43 citations
TL;DR: In this paper, the effects of one or more missing values in a response surface design are examined and a number of robustness criteria considered and central composite designs with a second order model are used to illustrate the selection of designs which are robust to one or two missing observations.
Abstract: The effects of one or more missing values in a response surface design are examined and a number of robustness criteria considered. Central composite designs with a second order model are used to illustrate the selection of designs which are robust to one or two missing observations. These designs are compared with other designs such as rotatable designs and the outlier-robust designs of Box and Draper.
39 citations
TL;DR: In this paper, the authors studied the performance of a truncated version of a vector-at-a-time sequential sampling procedure proposed by Bechhofer, Kiefer and Sobel for selecting the multinomial event which has the largest probability.
Abstract: In an earlier article the authors studied the performance of a truncated version of a vector-at-a-time sequential sampling procedure proposed by Bechhofer, Kiefer and Sobel for selecting the multinomial event which has the largest probability Among the performance characteristics studied for both the original (open) basic procedure (P*B:) and the truncated (closed) procedure (P*B:T:) were the achieved probability of a correct selection, and BT the expected number of vector-observations (n) to terminate sampling when the event probabilities are in the so-called least-favorable and equal-parameter configurations These were compared with the same quantities for a competing (closed) procedure of Ramey and Alam (R-A) All three procedures guarantee the same requirement on the probability of a correct selection The truncated procedure was shown to be greatly superior to the untruncated version both in terms of E{n} and Var{n}, and also to be superior to the R-A procedure¶A limited set of truncation numbers
30 citations
TL;DR: This article showed that the quadratic approximation of Johnson's test is superior to the linear and quadratically approximated version of the Johnson test, respectively, for the mean of an asymmetric distribution.
Abstract: Confidence intervals for the mean of an asymmetric distribution can be based on Student's t statistic or on Johnson's modified t statistic; Johnson's statistic has two variants, based on a linear and a quadratic approximation respectively. The quadratic approximation is complicated and is first investigated geometrically, which results in new insight. Next Monte Carlo experiments yield estimates of the coverage and power of several variations on Johnson's test. These experiments show that the quadratic approximation is superior.
24 citations
TL;DR: In this article, a simple least square method for estimating a change in mean of a sequence of independent random variables is studied, and all estimates are consistent, and those for the initial level and change are shown to be asymptotically jointly normal.
Abstract: A simple least squares method for estimating a change in mean of a sequence of independent random variables is studied. The method first tests for a change in mean based on the regression principle of constrained and unconstrained sums of squares. Conditionally on a decision by this test that a change has occurred, least squares estimates are used to estimate the change point, the initial mean level (prior to the change point) and the change itself. The estimates of the initial level and change are functions of the change point estimate. All estimates are shown to be consistent, and those for the initial level and change are shown to be asymptotically jointly normal. The method performs well for moderately large shifts (one standard deviation or more), but the estimates of the initial level and change are biased in a predictable way for small shifts. The large sample theory is helpful in understanding this problem. The asymptotic distribution of the change point estimator is obtained for local shifts in m...
22 citations
TL;DR: In this paper, a test based on Tiku's modified maximum likelihood estimators is developed for testing that the population correlation coefficient is zero, and compared with various other tests and shown to have good Type I error robustness and power for numerous symmetric and skew bivariate populations.
Abstract: A test based on Tiku's MML (modified maximum likelihood) estimators is developed for testing that the population correlation coefficient is zero. The test is compared with various other tests and shown to have good Type I error robustness and power for numerous symmetric and skew bivariate populations.
TL;DR: In this article, a general class of models for discrete data is introduced that includes log-linear, linear, and product models as special cases, and maximum likelihood equations are developed to yield a Fisher scoring algorithm for fitting the models to both complete and incomplete data.
Abstract: A very general class of models for discrete data is introduced that includes log-linear, linear, and product models as special cases. Maximum likelihood equations are developed to yield a Fisher scoring algorithm for fitting the models to both complete and incomplete data. Two examples serve to underscore the usefulness of these models.
TL;DR: In this article, a smooth nonparametric estimator of the quantile function Q (p) is given by Qn(p)=h 1jjQn(t)K((t-p)/h)dt, where QR(p) denotes the product-limit quantile functions.
Abstract: Based on right-censored data from a lifetime distribution F , a smooth nonparametric estimator of the quantile function Q (p) is given by Qn(p)=h 1jjQn(t)K((t-p)/h)dt, where QR(p) denotes the product-limit quantile function. Extensive Monte Carlo simulations indicate that at fixed p this kernel-type quantile estimator has smaller mean squared error than (L(p) for a range of values of the bandwidth h. A method of selecting an "optimal" bandwidth (in the sense of small estimated mean squared error) based on the bootstrap is investigated yielding results consistent with the simulation study. The bootstrap is also used to obtain interval estimates for Q (p) after determining the optimal value of h.
TL;DR: In this article, two approaches to the problem of goodness-of-fit with nuisance parameters are presented, both based on modifications of the Kolmogorov-Smirnov statistics.
Abstract: Two approaches to the problem of goodness-of-fit with nuisance parameters are presented in this paper, both based on modifications of the Kolmogorov-Smirnov statistics. Improved tables of critical values originally computed by Lilliefors and Srinivasan are presented in the normal and exponential cases. Also given are tables for the uniform case, normal with known mean and normal with known variance. All tables were computed using Monte Carlo simulation with sample size n = 20000.
TL;DR: In this paper, an approximate 1 −α upper, lower and two sided confidence intervals for the respective ratios of the individual variances, to the total variation are found for the balanced two-factor crossed components-of-variance model with interaction.
Abstract: Approximate 1 −α upper, lower and two sided confidence intervals for the respective ratios of the individual variances , to the total variation are found for the balanced two-factor crossed components-of-variance model with interaction. Results of a simulation study, performed to estimate the confidence levels of these approximate confidence intervals, are given.
TL;DR: In this paper, a series of Monte Carlo studies was performed to investigate the possible use of these estimators and their standard errors in estimating the common degree of inject control of a number of blocks.
Abstract: The current estimator of the degree of insect control by an insecticide in a field experiment laid out in randomized blocks is equal to one minus the cross-product ratio of a two way table of total insect counts over blocks Since much work has been done on estimation of the common odds ratio of a number of strata in medical studies, a series of Monte Carlo studies was performed to investigate the possible use of these estimators and their standard errors in estimating the common degree of inject control of a number of blocks Maximum likelihood, Mantel-Haenszel, and empirical logit estimators were evaluated and compared with back-transformed means over blocks, of cross-product ratios on the arithmetic, logarithmic, and arcsine scales Maximum likelihood and Mantel-Haenszel estimators had the smallest mean squared errors, but their standard error estimates were only appropriate when sampling distributions were approximately Poisson and there was little heterogeneity among plots within blocks in the natura
TL;DR: In this article, one-sided B-content tolerance intervals for the two-parameter double exponential distribution are considered and Monte Carlo tolerance factors along with estimates of their asymptotic standard deviations are presented.
Abstract: One-sided B-content tolerance intervals for the two-parameter double exponential distribution are considered. Monte Carlo tolerance factors along with estimates of their asymptotic standard deviations are presented. Smoothing the Monte Carlo results using least squares regression is investigated. Comparisons among the approximate, Monte Carlo and smoothed tolerance factors are also investigated.
TL;DR: In this article, a method for obtaining conservative simultaneous confidence intervals for the K parameters in a linear regression model, or for K linear contrasts, is based on the percentage points of the Studentized maximum modulus distribution.
Abstract: A well known method for obtaining conservative simultaneous confidence intervals for the K parameters in a linear regression model, or for K linear contrasts, is based on the percentage points of the Studentized maximum modulus distribution. From an inequality due to Sidak, conservative yet uniformly shorter confidence intervals would be possible if the percentage points of a particular form of the multivariate t distribution were available. The purpose of this paper is to provide the required percentage points. For K<8 the resulting confidence intervals can be substantially shorter.
TL;DR: In this article, Tiku's MML robust procedure was applied to Brown and Forsythe's (1974) statistic for comparing several means under hetero-scedasticity and nonnormality.
Abstract: By applying Tiku's MML robust procedure to Brown and Forsythe's (1974) statistic, this paper derives a robust and more powerful procedure for comparing several means under hetero-scedasticity and nonnormality. Some Monte Carlo studies indicate clearly that among five nonnormal distributions, except for the uniform distribution, the new test is more powerful than the Brown and Forsythe test under nonnormal distributions in all cases investigated and has substantially the same power as the Brown and Forsythe test under normal distribution.
TL;DR: In this article, simple low-storage algorithms for generating samples from the bivariate Binomial, negative binomial and Pascal distributions are examined, based on stochastic models that lead to these distributions.
Abstract: Simple low-storage algorithms for generating samples from the bivariate Binomial, Negative Binomial and Pascal distributions are examined. The methods are based on stochastic models that lead to these distributions and involve generating univariate random variables and combining them in various ways.
TL;DR: The algorithm is efficient in solving fairly well-behaved, small, residual nonlinear LP: -norm estimation problems when 1 > p > ∞ and only first-order partial derivatives need be considered.
Abstract: In this paper an algorithm for solving nonlinear LP: -norm estimation problems is derived. It uses the structure of the LP: -norm problem and is an extension of the classical Gauss-Newton method designed to solve nonlinear least squares problems. It is shown that the Gauss-Newton method is imbedded within this new algorithm and hence only first-order partial derivatives need be considered. The use of second-order derivative information, which is costly from a computational point of view, is ignored. Expressions for the first- and second-order partial derivatives will be obtained using a compact matrix notation. The algorithm is efficient in solving fairly well-behaved, small, residual nonlinear LP: -norm estimation problems when 1 > p > ∞.
TL;DR: Andrews (1972) introduced a method of plotting high-dimensional data in two dimensions that is exploited as a graphical technique for the detection of the period and outliers in time series data.
Abstract: Andrews (1972) introduced a method of plotting high-dimensional data in two dimensions. This method is exploited as a graphical technique for the detection of the period and outliers in time series data. Some examples are given.
TL;DR: In this article, the authors propose two simple approximate confidence interval procedures as alternatives to both Satterthwaite!s and Naikfs procedures, and compare the new procedures to the standard procedures.
Abstract: The analysis of variance table does not always yield the appropriate error term for tests of hypotheses or confidence interval estimation. When the design is balanced, an approximation due to Satterthwaite (19^6) is often employed. While this works well in many cases it does not always produce the expected results. The three-factor mixed model is a case in point. Naik (197M proposed an interval estimation procedure for this model which is conservative. In this paper we propose two simple approximate confidence interval procedures as alternatives to both Satterthwaite!s and Naikfs procedures. Simulation results comparing the new procedures to the standard procedures are also reported.
TL;DR: In this article, the authors focus on an evaluation of misclassification probabilities when the power transformation could have been used to achieve at least approximate normality and equal covariance matrices in the sampled populations for the distribution of the observed random variables.
Abstract: The linear discriminant function (LDF) is known to be optimal in the sense of achieving an optimal error rate when sampling from multivariate normal populations with equal covariance matrices. Use of the LDF in nonnormal situations is known to lead to some strange results. This paper will focus on an evaluation of misclassification probabilities when the power transformation could have been used to achieve at least approximate normality and equal covariance matrices in the sampled populations for the distribution of the observed random variables. Attention is restricted to the two-population case with bivariate distributions.
TL;DR: In this paper, a power study of the standard Kolmogorov-Smirnov, Anderson-Darling, and Cramer-bon Mises tests for the logistic distribution with unknown location and scale parameters is presented.
Abstract: The standard Kolmogorov-Smirnov, Anderson-Darling, and Cramer-bon Mises tests require continuous underlying distributions with known parameters. When the parameters are not known, but must be estimated from the sample data, the standard tables are no longer valid. This paper gives tables of critical values for the logistic distribution with unknown location and scale parameters. The powers of these tests are given for a number of alternative distributions. The results of the power study indicate that the modified tests do well at distinguishing between a logistic distribution and a distribution that has a very different shape. However, the powers are not very good when trying to distinguish between the logistic and a similar-shaped distribution, such as the normal.
TL;DR: In this paper, it is proved that in computing percentage points of a distribution, Halley's method yields convergent solutions under most conditions, and demonstrate the efficiency of the method with some examples.
Abstract: In this note, it is proved that in computing percentage points of a distribution, Halley's method yields convergent solutions under most conditions, and we demonstrate the efficiency of the method with some examples.
Journal Article•
TL;DR: On definit une generalisation de la distribution logistique et de ses cumulants ce qui permet une approximation precise de the distribution de Student as mentioned in this paper, i.e.
Abstract: On definit une generalisation de la distribution logistique et de ses cumulants ce qui permet une approximation precise de la distribution de Student
TL;DR: Algorithms for computing the maximum likelihood estimators and the estimated covariance matrix of the estimators of the factor model are derived and are particularly suitable for large matrices and for samples that give zero estimates of some error variances.
Abstract: Algorithms for computing the maximum likelihood estimators and the estimated covariance matrix of the estimators of the factor model are derived The algorithms are particularly suitable for large matrices and for samples that give zero estimates of some error variances A method of constructing estimators for reduced models is presented The algorithms can also be used for the multivariate errors-in-variables model with known error covariance matrix
TL;DR: Considering X and Y as two independent generalized Poisson variates with distributions P x:(θ1:;,λ) and Py:θ2:,λ, where, x = 0,1,2, … and θ > 0, 0 < A < 1, the probability distribution of D = X−Y is derived and some differential difference equations are given as discussed by the authors.
Abstract: Considering X and Y as two independent generalized Poisson (GP) variates with distributions P x:(θ1:;,λ) and Py:(θ2:,λ), where , x = 0,1,2, … and θ > 0, 0 < A < 1, the probability distribution of D = X−Y is derived and some differential difference equations are given. The probability generating function and the cumulant generating function for the distribution of D are obtained. A recurrence relation for all the cumulants has been established. Also, the first five cumulants, β1:, and β2: have been derived.