On the accuracy and cost of numerical integration in several variables ∗

Identical numerical integration experiments are performed on a CYBER 205 and an IBM 3081 in order to gauge the relative performance of several methods of integration. The methods employed are the general methods of Gauss-Legendre, iterated Gauss-Legendre, Newton-Cotes, Romberg and Monte Carlo as well as three methods, due to Owen, Dutt, and Clark respectively, for integrating the normal density. The bi- and trivariate normal densities and four other functions are integrated; the latter four have integrals expressible in closed form and some of them can be parameterized to exhibit singularities or highly periodic behavior. The various Gauss-Legendre methods tend to be most accurate (when applied to the normal density they are even more accurate than the special purpose methods designed for the normal) and while they are not the fastest, they are at least competitive. In scalar mode the CYBER is about 2-6 times faster than the IBM 3081 and the speed advantage of vectorised to scalar mode ranges from 6 to 15. Large scale econometric problems of the probit type should now be routinely soluble.     

Latin hypercube sampling with multidimensional uniformity

Complex models can only be realized a limited number of times due to large computational requirements. Methods exist for generating input parameters for model realizations including Monte Carlo simulation (MCS) and Latin hypercube sampling (LHS). Recent algorithms such as maximinLHS seek to maximize the minimum distance between model inputs in the multivariate space. A novel extension of Latin hypercube sampling (LHSMDU) for multivariate models is developed here that increases the multidimensional uniformity of the input parameters through sequential realization elimination. Correlations are considered in the LHSMDU sampling matrix using a Cholesky decomposition of the correlation matrix. Computer code implementing the proposed algorithm supplements this article. A simulation study comparing MCS, LHS, maximinLHS and LHSMDU demonstrates that increased multidimensional uniformity can significantly improve realization efficiency and that LHSMDU is effective for large multivariate problems.     

Fractiles of an extended multiple outlier test

The widely-used Tietjen—Moore multiple outlier statistic has a defect as originally proposed in that it may test the wrong observations as outliers. The defect is corrected by redefinition and the statistic extended to make use of possible additional information on underlying variance. Results of simulation of the revised statistic are presented.     

Comparison of performance measures for multivariate discrete models

For multivariate probit models, Spiess and Tutz suggest three alternative performance measures, which are all based on the decomposition of the variation. The multivariate probit model can be seen as a special case of the discrete copula model. This paper proposes some new measures based on the value of the likelihood function and the prediction-realization table. In addition, it generalizes the measures from Spiess and Tutz for the discrete copula model. Results of a simulation study designed to compare the different measures in various situations are presented.     

Learning in experiments: Dynamic interaction of policy variables designed to deter tax evasion

While neoclassical economic theory sheds insight into the way that audit rates and penalty rates interact when individuals decide to declare income for taxation, it predicts far lower levels of compliance than observed levels of compliance. This paper analyses experimental responses to explore a dynamic interaction between audit and penalty rates as individuals learn how to comply with taxation. It compares the responses of subjects in experiments with responses that are predicted when individuals rely on an adaptive learning process (that offers information feedback about decision payoffs). This comparison suggests that learning is an important consideration when explaining differences between predicted and observed levels of tax compliance.     

On the use of the scholz-sievers method for dlstribution-free inference about the difference in slopes of two regression lines

A simple adaptation of a distribution-free method due to Scholz (1978) and Sievers (1978) for inference in a single regression setting is proposed for inference about the difference in slopes of two regression lines. We assume that the data are obtained from a designed experiment with common regression constants. A comparison of the proposed method to its competitors-one due to Hollander and the other due to Rao and Gore-indicates superiority of the new method.     

Effect of a new selection procedure on adaptive estimation

Adaptive estimation of parameters of some failure time distributionsis considered. A new procedure named the F-procedure has beendeveloped for selecting an appropriate model out of two possible models by Pandey et.al. (1991). Applying this F-procedure adaptive estimatorsof parameters of exponential, Wei bull, inverse Gaussian (IG) and Wald failure time distributions have been proposed in this paper. Comparison of these estimators has been undertaken with MLE's of the respective parameters and with some previous adaptiveestimators by simulation of samples using the Monte Carlo method.Adaptive estimation of parameters of some failure time distributions is considered. A new procedure named the F-procedure has been developedfor selecting an appropriate model out of two possible models by Pandey et.al. (1991). Applying this F-procedure adaptive estimators of parameters of exponential, Wei bull, inverse Gaussian (IG) and Wald failure time distributions have been proposed in this paper. Comparison of these estimators has been undertaken with MLE's of the respective parameters and with some previous adaptive estimators by simulation of samples using the Monte Carlo method.     

A statistical measure of internal consistency

A test for homogeneity of several populations against the simple tree alternative is proposed when the observations in various groups are subject to the same pattern of random right-censorship. The test is a generalization of the one proposed by Slivka (1970) which is useful when testing time is expensive so that an early termination of an experiment is desirable. The power of the test is examined in a simulation study.     

A simulation study of the nearest neighbour analysis method of papadakis

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.