A monte carlo comparison of regression trimmed means

Two proposals are made for constructing adaptive estimators of the parameters in a linear regression model. These estimators are based on regression trimmed means and use an idea of Jaeckel [(1971) Ann Math Statist 42, 1540-1552] and the bootstrap respectively. These adaptive trimmed means as well as some nonadaptive trimmed means are studied by Monte Carlo. A one-step biweight is also included for comparison purposes.     

A robust procedure for comparing several means under heteroscedasticity and nonnormality

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.     

A Simulator for Twenty20 Cricket

This paper develops a Twenty20 cricket simulator for matches between sides belonging to the International Cricket Council. As input, the simulator requires the probabilities of batting outcomes which are dependent on the batsman, the bowler, the number of overs consumed and the number of wickets lost. The determination of batting probabilities is based on an amalgam of standard classical estimation techniques and a hierarchical empirical Bayes approach where the probabilities of batting outcomes borrow information from related scenarios. Initially, the probabilities of batting outcomes are obtained for the first innings. In the second innings, the target score obtained from the first innings affects the aggressiveness of batting during the second innings. We use the target score to modify batting probabilities in the second innings simulation. This gives rise to the suggestion that teams may not be adjusting their second innings batting aggressiveness in an optimal way. The adequacy of the simulator is addressed through various goodness‐of‐fit diagnostics.     

Modified cramer-von mises and anderson-darling tests for weibull distributions with unknown location and scale parameters

The standard Cramer-von Mises and Anderson-Darling goodness-of-fit tests require continuous underlying distributions with known parameters. In this paper, tables of critical values are generated for both tests for Weibull distributions with unknown location and scale parameters and known shape parameters. The powers of the Cramer-von Mises, Anderson-Darling, Kolmogorov-Smirnov, and Chi-Square tests for this situation are investigated. The Cramer-von Mises test has most power when the shape is 1.0 and the Anderson-Darling test has most power when the shape is 3.5. Finally, a relation between critical value and inverse shape parameter is presented.     

A note on the linear discriminant function when group means are equal

The performance of the sample linear discriminant function with known, proportional, covariance matrices and equal but unknown mean vectors is considered. Unconditional misclassification rates are obtained from the Student-t distribution. These results can be used as an aid in verifying simulation programs incorporating the linear discriminant function when Gaussian densities with unequal covariance matrices are used.     

Robust hierarchical Bayes estimation of exchangeable means

Estimation of the mean of a multivariate normal distribution is considered. The components of the mean vector θ are assumed to be exchangeable; this is modelled in a hierarchical fashion with independent Cauchy distributions as the first-stage prior. The resulting generalized Bayes estimator is calculated and shown to be robust with respect to the presence of outlying means. Alternative estimators that have similar behaviour but are cheaper to compute are also derived.     

A test statistic based on ranked set sampling for two normal means

In this study, we considered a hypothesis test for the difference of two population means using ranked set sampling. We proposed a test statistic for this hypothesis test with more than one cycle under normality. We also investigate the performance of this test statistic, when the assumptions hold and are violated. For this reason, we investigate the type I error and power rates of tests under normality with equal and unequal variances, non-normality with equal and unequal variances. We also examine the performance of this test under imperfect ranking case. The simulation results show that derived test performs quite well.     

Size distortion of asymmetric unit root tests in the presence of level shifts

The finite-sample size properties of momentum-threshold autoregressive (MTAR) asymmetric unit root tests are examined in the presence of level shifts under the null hypothesis. The original MTAR test using a fixed threshold is found to exhibit severe size distortion when a break in level occurs early in the sample period, leading to an increased probability of an incorrect inference of asymmetric stationarity. For later breaks the test is also shown to suffer from undersizing. In contrast, the use of consistent-threshold estimation results in a test which is relatively robust to level shifts.     

Regenerative Markov Chain Monte Carlo for Any Distribution

While Markov chain Monte Carlo (MCMC) methods are frequently used for difficult calculations in a wide range of scientific disciplines, they suffer from a serious limitation: their samples are not independent and identically distributed. Consequently, estimates of expectations are biased if the initial value of the chain is not drawn from the target distribution. Regenerative simulation provides an elegant solution to this problem. In this article, we propose a simple regenerative MCMC algorithm to generate variates for any distribution.     

Numerical computation of multivariate t-probabilities with application to power calculation of multiple contrasts

A new method to calculate the multivariate t-distribution is introduced. We provide a series of substitutions, which transform the starting q-variate integral into one over the (q—1)-dimensional hypercube. In this situation standard numerical integration methods can be applied. Three algorithms are discussed in detail. As an application we derive an expression to calculate the power of multiple contrast tests assuming normally distributed data.     

A monte carlo study of robust estimators of location

Andrews et al (1972) carried out an extensive Monte Carlo study of robust estimators of location. Their conclusions were that the hampel and the skipped estimates, as classes, seemed to be preferable to some of the other currently fashionable estimators. The present study extends this work to include estimators not previously examined. The estimators are compared over short-tailed as well as long-tailed alternatives and also over some dependent data generated by first-order autoregressive schemes. The conclusions of the present study are threefold. First, from our limited study, none of the so-called robust estimators are very efficient over short-tailed situations. More work seems to be necessary in this situation. Second, none of the estimators perform very well in dependent data situations, particularly when the correlation is large and positive. This seems to be a rather pressing problem. Finally, for long-tailed alternatives, the hampel estimators and Hogg-type adaptive versions of the hampels are the strongest classes. The adaptive hampels neither uniformly outperform nor are they outperformed by the hampels. However, the superiority in terms of maximum relative efficiency goes to the adaptive hampels. That is, the adaptive hampels, under their worst performance.     

Multivariate trimmed means based on the Tukey depth

In univariate statistics, the trimmed mean has long been regarded as a robust and efficient alternative to the sample mean. A multivariate analogue calls for a notion of trimmed region around the center of the sample. Using Tukey's depth to achieve this goal, this paper investigates two types of multivariate trimmed means obtained by averaging over the trimmed region in two different ways. For both trimmed means, conditions ensuring asymptotic normality are obtained; in this respect, one of the main features of the paper is the systematic use of Hadamard derivatives and empirical processes methods to derive the central limit theorems. Asymptotic efficiency relative to the sample mean as well as breakdown point are also studied. The results provide convincing evidence that these location estimators have nice asymptotic behavior and possess highly desirable finite-sample robustness properties; furthermore, relative to the sample mean, both of them can in some situations be highly efficient for dimensions between 2 and 10.     

Bayesian expectile regression with asymmetric normal distribution

In this paper, we adopt the Bayesian approach to expectile regression employing a likelihood function that is based on an asymmetric normal distribution. We demonstrate that improper uniform priors for the unknown model parameters yield a proper joint posterior. Three simulated data sets were generated to evaluate the proposed method which show that Bayesian expectile regression performs well and has different characteristics comparing with Bayesian quantile regression. We also apply this approach into two real data analysis.     

Comparison of the bias of trimmed and Winsorized means

ABSTRACT

We derive sharp upper and lower projection bounds on the bias of two-sided Winsorized means. To determine the projection of appropriate function, we consider new analytic condition which describes the form of the corresponding greatest convex minorant. Then we compare numerically obtained bounds for trimmed and Winsorized means. We conclude that if we have no information about the underlying distribution then Winsorized means are better than the trimmed ones.     

Adaptive Step Size Selection for Hessian‐Based Manifold Langevin Samplers

In this paper, I explore the usage of positive definite metric tensors derived from the second derivative information in the context of the simplified manifold Metropolis adjusted Langevin algorithm. I propose a new adaptive step size procedure that resolves the shortcomings of such metric tensors in regions where the log‐target has near zero curvature in some direction. The adaptive step size selection also appears to alleviate the need for different tuning parameters in transient and stationary regimes that is typical of Metropolis adjusted Langevin algorithm. The combination of metric tensors derived from the second derivative information and the adaptive step size selection constitute a large step towards developing reliable manifold Markov chain Monte Carlo methods that can be implemented automatically for models with unknown or intractable Fisher information, and even for target distributions that do not admit factorization into prior and likelihood. Through examples of low to moderate dimension, I show that the proposed methodology performs very well relative to alternative Markov chain Monte Carlo methods.     

Estimation of group means using Bayesian generalized linear mixed models

Generalized linear mixed models (GLMM) are commonly used to model the treatment effect over time while controlling for important clinical covariates. Standard software procedures often provide estimates of the outcome based on the mean of the covariates; however, these estimates will be biased for the true group means in the GLMM. Implementing GLMM in the frequentist framework can lead to issues of convergence. A simulation study demonstrating the use of fully Bayesian GLMM for providing unbiased estimates of group means is shown. These models are very straightforward to implement and can be used for a broad variety of outcomes (eg, binary, categorical, and count data) that arise in clinical trials. We demonstrate the proposed method on a data set from a clinical trial in diabetes.     

A multivariate parallelogram and its application to multivariate trimmed means

This paper introduces a multivariate parallelogram that can play the role of the univariate quantile in the location model, and uses it to define a multivariate trimmed mean. It assesses the asymptotic efficiency of the proposed multivariate trimmed mean by its asymptotic variance and by Monte Carlo simulation.     

Bayesian multivariate GARCH models with dynamic correlations and asymmetric error distributions

The main goal in this paper is to develop and apply stochastic simulation techniques for GARCH models with multivariate skewed distributions using the Bayesian approach. Both parameter estimation and model comparison are not trivial tasks and several approximate and computationally intensive methods (Markov chain Monte Carlo) will be used to this end. We consider a flexible class of multivariate distributions which can model both skewness and heavy tails. Also, we do not fix tail behaviour when dealing with fat tail distributions but leave it subject to inference.     

A new nonlinear asymmetric cointegration approach using error correction models

In this article, two new powerful tests for cointegration are proposed. The general idea is based on an intuitively appealing extension of the traditional, rather restrictive cointegration concept. In this article, we allow for a nonlinear, but most importantly a different, asymmetric convergence process to account for negative and positive changes in our cointegration approach. Using Monte Carlo simulations we verify, that the estimated size of the first test depends on the unknown value of a signal-to-noise ratio q. However, our second test—which is based on the original ideas of Kanioura and Turner—is more successful and robust in the sense that it works in all of the different evaluated situations. Furthermore it is shown to be more powerful than the traditional residual based Enders and Siklos method. The new optimal test is also applied in an empirical example in order to test for potential nonlinear asymmetric price transmission effects on the Swedish power market. We find that there is a higher propensity for power retailers to rapidly and systematically increase their retail electricity prices subsequent to increases in Nordpool's wholesale prices, than there is for them to reduce their prices subsequent to a drop in wholesale spot prices.