A monte carlo evaluation of response surface analysis based on paired-comparison data

The use of the logit transformation on paired-comparison data in the weighted least squares analysis of response surfaces for aesthetic qualities of products is discussed. Monte Carlo simulations are employed to investigate the small sample properties of the estimators and test statistics. A secondary objective of the Monte Carlo simulations is the comparison of two transformation procedures. The simulations are of standard-item paired-compar-ison experiments in which ties are not allowed.     

On a preliminary test estimator for one of the parameters of the log-zero-poisson distribution

A discrete distribution called the log-zero-Poisson distribution has been recommended by Katti (c.f. Biometrics 1970) as an alternate to the negative binomial and other distributions usually called "contagious" distributions.A major problem in the use of this and all other contagious distributions has been the difficulty of obtaining the maximum likelihood esti-mates. A custom-made ad hoc estimator, λ, has been proposed for the parameter λ of this distribution in Katti and Khedr (1980). In this paper, its efficiency relative to Fisher information is studied, only to discover that λ can be 30 times better than the maximum likelihood estimate in some parts of the parameter space and much weaker in other parts.A preliminary test is recommended to choose between the estimates, and the efficiency of the procedure is tabulated. As it is to be expected, the resultant estimator equals the better of the two estimators with some error at the values of the parameters where the two estimators are equivalent.     

Inferences on regression coefficients in a regression model under heteroscedasticity and robustness with respect to departure from normality

In this paper we consider a simple linear regression model under heteroscedasticity and nonnormality. A statistical test for testing the regression coefficient is then derived by assuming normality for the random disturbances and by applying Welch's method. Some Monte Carlo studies are generated for assessing robustness of this test. By combining Tiku's robust procedure with the new test, a robust but more powerful test is developed.     

A generating algorithm for linear trend-free and nearly linear trend-free block designs

The theory and properties of trend-free (TF) and nearly trend-free (NTF) block designs are wel1 developed. Applications have been hampered because a methodology for design construction has not been available.

This article begins with a short review of concepts and properties of TF and NTF block designs. The major contribution is provision of an algorithm for the construction of linear and nearly linear TF block designs. The algorithm is incorporated in a computer program in FORTRAN 77 provided in an appendix for the IBM PC or compatible microcomputer, a program adaptable also to other computers. Three sets of block designs generated by the program are given as examples.

A numerical example of analysis of a linear trend-free balanced incomplete block design is provided.     

An Extension of the Normal/Independent Family for Studies of Robust Estimators

The family of normal scale mixture distributions, also called the Normal/Independent family, has been used for efficient Monte Carlo studies of robust estimators. The distributions in this family are unimodal. The Normal/Independent family is extended by introducing a location mixing in addition to the scale mixing. Distributions in this extension may be nonunimodal. The asymptotic variances of robust estimators of location are compared using the distributions from the extension. A Monte Carlo swindle similar to the one used in the Princeton study is given for the extended family. A small simulation study demonstrates the efficiency of the swindle. The swindle is compared with other swindle methods based on Fisher's score function and regression.     

Small sample properties of parameter estimation in the dirichlet distribution

A numerically feasible algorithm is proposed for maximum likelihood estimation of the parameters of the Dirichlet distribution. The performance of the proposed method is compared with the method of moments using bias ratio and squared errors by Monte Carlo simulation. For these criteria, it is found that even in small samples maximum likelihood estimation has advantages over the method of moments.     

Robust estimation methods for exponential data: a monte-carlo comparison

We compare the performance of seven robust estimators for the parameter of an exponential distribution. These include the debiased median and two optimally-weighted one-sided trimmed means. We also introduce four new estimators: the Transform, Bayes, Scaled and Bicube estimators. We make the Monte Carlo comparisons for three sample sizes and six situations. We evaluate the comparisons in terms of a new performance measure, Mean Absolute Differential Error (MADE), and a premium/protection interpretation of MADE. We organize the comparisons to enhance statistical power by making maximal use of common random deviates. The Transform estimator provides the best performance as judged by MADE. The singly-trimmed mean and Transform method define the efficient frontier of premium/protection.     

Issues in blinded sample size re-estimation

The utility of blinded sample size re-estimation for clinical trials depends on the ability to estimate variability without providing information about the true treatment difference, and on some reasonable assurance that the method is not likely to cause the sample size to be increased when the treatment effect is better than anticipated. We show that violations of these properties are unlikely to occur in practice.     

The 'improved' brown and forsythe test for mean equality: some things can't be fixed

Mehrotra (1997) presented an ‘;improved’ Brown and Forsythe (1974) statistic which is designed to provide a valid test of mean equality in independent groups designs when variances are heterogeneous. In particular, the usual Brown and Fosythe procedure was modified by using a Satterthwaite approximation for numerator degrees of freedom instead of the usual value of number of groups minus one. Mehrotra then, through Monte Carlo methods, demonstrated that the ‘improved’ method resulted in a robust test of significance in cases where the usual Brown and Forsythe method did not. Accordingly, this ‘improved’ procedure was recommended. We show that under conditions likely to be encountered in applied settings, that is, conditions involving heterogeneous variances as well as nonnormal data, the ‘improved’ Brown and Forsythe procedure results in depressed or inflated rates of Type I error in unbalanced designs. Previous findings indicate, however, that one can obtain a robust test by adopting a heteroscedastic statistic with the robust estimators, rather than the usual least squares estimators, and further improvement can be expected when critical significance values are obtained through bootstrapping methods.