Abstract: This article provides a review of research involving least absolute value (LAV) regression. The review is concentrated primarily on research published since the survey article by Dielman (Dielman, T. E. (1984). Least absolute value estimation in regression models: An annotated bibliography. Communications in Statistics – Theory and Methods, 4, 513–541.) and includes articles on LAV estimation as applied to linear and non-linear regression models and in systems of equations. Some topics included are computation of LAV estimates, properties of LAV estimators and inferences in LAV regression. In addition, recent work in some areas related to LAV regression will be discussed.

Abstract: Many multivariate statistical methods call upon the assumption of multivariate normality (MVN). However, many researchers fail to test this assumption. This omission could be due to either ignorance of the existence of tests of MVN or confusion about which test to use. Although at least 50 tests of MVN exist, relatively little is known about the power of these procedures. The purpose of this study was to examine the power of 13 promising tests of MVN with a Monte Carlo study. Ten thousand data sets were generated from several multivariate distributions. The test statistic for each procedure was calculated and compared with the appropriate critical value. The number of rejections of the null hypothesis of MVN was tabled for each situation. No single test was found to be the most powerful in all situations. The use of the Henze–Zirkler test is recommended as a formal test of MVN. Supplementary procedures such as Mardia's skewness and kurtosis measures and the chi-square plot are also recommended for diagnos...

Abstract: We introduce a new statistical quantity, the energy, to test whether two samples originate from the same distributions. The energy is a simple logarithmic function of the distances of the observations in the variate space. The distribution of the test statistic is determined by a resampling method. The power of the energy test in one dimension was studied for a variety of different test samples and compared to several nonparametric tests. In two and four dimensions, a comparison was performed with the Friedman–Rafsky and nearest neighbor tests. The two-sample energy test was shown to be especially powerful in multidimensional applications.

Abstract: In this paper, we perform an empirical comparison of the classification error of several ensemble methods based on classification trees. This comparison is performed by using 14 data sets that are ...

Abstract: The two-parameter generalized exponential (GE) distribution was introduced by Gupta and Kundu [Gupta, R.D. and Kundu, D., 1999, Generalized exponential distribution. Australian and New Zealand Journal of Statistics, 41(2), 173–188.]. It was observed that the GE can be used in situations where a skewed distribution for a nonnegative random variable is needed. In this article, the Bayesian estimation and prediction for the GE distribution, using informative priors, have been considered. Importance sampling is used to estimate the parameters, as well as the reliability function, and the Gibbs and Metropolis samplers data sets are used to predict the behavior of further observations from the distribution. Two data sets are used to illustrate the Bayesian procedure.

Abstract: Statisticians seek tests which have maximum power amongst tests of size α. In both numerical and theoretical studies, the standard approach is to compare the powers of competing tests which have the same nominal size α*. In most cases, α and α* differ; and in this case, the differing size biases of the tests contaminate any comparisons of their power. For instance, two nominal 5% tests with actual sizes 4% and 6% should not have their powers naively compared. In this paper, the basic problem of trading-off size for power is approached through the existing theory of receiver operating characteristic curves. This leads us to a simple way of estimating power adjusted for size, not only for a fixed nominal size, but also for a range of relevant nominal sizes. The calculations required are both familiar and simple. We recommend that the methods be routinely applied to simulations studies that compare alternative tests of the same hypotheses.

Abstract: In this article, we propose a new empirical information criterion (EIC) for model selection which penalizes the likelihood of the data by a non-linear function of the number of parameters in the model. It is designed to be used where there are a large number of time series to be forecast. However, a bootstrap version of the EIC can be used where there is a single time series to be forecast. The EIC provides a data-driven model selection tool that can be tuned to the particular forecasting task. We compare the EIC with other model selection criteria including Akaike’s information criterion (AIC) and Schwarz’s Bayesian information criterion (BIC). The comparisons show that for the M3 forecasting competition data, the EIC outperforms both the AIC and BIC, particularly for longer forecast horizons. We also compare the criteria on simulated data and find that the EIC does better than existing criteria in that case also.

Abstract: Ranked set sampling is a sampling technique that provides substantial cost efficiency in experiments where a quick, inexpensive ranking procedure is available to rank the units prior to formal, expensive and precise measurements. Although the theoretical properties and relative efficiencies of this approach with respect to simple random sampling have been extensively studied in the literature for the infinite population setting, the use of ranked set sampling methods has not yet been explored widely for finite populations. The purpose of this study is to use sheep population data from the Research Farm at Ataturk University, Erzurum, Turkey, to demonstrate the practical benefits of ranked set sampling procedures relative to the more commonly used simple random sampling estimation of the population mean and variance in a finite population. It is shown that the ranked set sample mean remains unbiased for the population mean as is the case for the infinite population, but the variance estimators are unbiased...

Abstract: Owing to the growing concerns over data confidentiality, many national statistical agencies are considering remote access servers to disseminate data to the public. With remote servers, users submit requests for output from statistical models fit using the collected data, but they are not allowed access to the data. Remote servers also should enable users to check the fit of their models; however, standard diagnostics like residuals or influence statistics can disclose individual data values. In this article, we present diagnostics for categorical data regressions that can be safely and usefully employed in remote servers. We illustrate the diagnostics with simulation studies.

Abstract: Perakis and Xekalaki 2002, A process capability index that is based on the proportion of conformance. Journal of Statistical Computation and Simulation, 72(9), 707–718. introduced a process capability index that is based on the proportion of conformance of the process under study and has several appealing features. One of its advantages is that it can be used not only for continuous processes, as is the case with the majority of the indices considered in the literature, but also for discrete processes as well. In this article, the use of this index is investigated for discrete data under two alternative models, which are frequently considered in statistical process control. In particular, distributional properties and estimation of the index are considered for Poisson processes and for processes resulting in modeling attribute data. The performance of the suggested estimators and confidence limits is tested via simulation.

Abstract: We discuss analytical bias corrections for maximum likelihood estimators in a regression model where the errors are Student-t distributed with unknown degrees of freedom. We propose a reparameterization of the number of degrees of freedom that produces a bias corrected estimator with very good small sample properties. This unknown number of degrees of freedom is assumed greater than 1, to guarantee a bounded likelihood function. We discuss some special cases of the general model and present some simulations which show that the corrected estimates perform better than their corresponding uncorrected versions in finite samples.

Abstract: The question of how to estimate the number of specie in a region given the species frequency distribution for a sample of animals from the region has been of interest for more than 60 years Data analyses indicate that the inferential problem is a difficult one when there are many rare species and a few abundant ones In this article simulation is used to study the properties of data sets generated by a generalized multinomial model proposed for this setting by Boender and Rinnooy Kan [Boender, CGE and Rinnooy Kan, AHG, 1987, A multinomial Bayesian approach to the estimation of population and vocabulary size Biometrika, 74, 849–856] In addition, the performance of Bayesian methods for drawing inferences about the parameters of the generalized multinomial model is evaluated by simulation

Abstract: Problems of practical implementation of the computer intensive subsampling methodology are addressed by Monte Carlo simulations of a situation typical for atmospheric time series. The motivating data were collected under Lake-Effect Snow Studies Project in the winter of 1983–1984 over Lake Michigan. Certain enhancements of subsampling methodology are suggested specifically on the issue of optimal block size choice.

Abstract: In the last fifty years, a great deal of research effort has been made on the construction of simultaneous confidence bands for a linear regression function. Two most frequently quoted confidence bands in the statistics literature are the Scheffe type and constant width bands over a given rectangular region of the predictor variables. For the constant width bands, a method is given by Gafarian [Gafarian, A.V., 1964, Confidence bands in straight line regression. Journal of the American Statistical Association, 59, 182–213.] for the calculation of critical constants only for the special case of one predictor variable. In this article, a method is proposed to construct constant width bands when there are any number of predictor variables. A new criterion for assessing a confidence band is also proposed; it is the probability that a confidence band excludes a false regression function and can be viewed as the power function of a test associated, naturally, with a confidence band. Under this criterion, a numer...

Abstract: The restricted minimum φ-divergence estimator, [Pardo, J.A., Pardo, L. and Zografos, K., 2002, Minimum φ-divergence estimators with constraints in multinomial populations. Journal of Statistical Planning and Inference, 104, 221–237], is employed to obtain estimates of the cell frequencies of an I×I contingency table under hypotheses of symmetry, marginal homogeneity or quasi-symmetry. The associated φ-divergence statistics are distributed asymptotically as chi-squared distributions under the null hypothesis. The new estimators and test statistics contain, as particular cases, the classical estimators and test statistics previously presented in the literature for the cited problems. A simulation study is presented, for the symmetry problem, to choose the best function φ2 for estimation and the best function φ1 for testing.

Abstract: In this article, we investigate an algorithm for the fast O(N) and approximate simulation of long memory (LM) processes of length N using the discrete wavelet transform. The algorithm generates stationary processes and is based on the notion that we can improve standard wavelet-based simulation schemes by noting that the decorrelation property of wavelet transforms is not perfect for certain LM process. The method involves the simulation of circular autoregressive process of order one. We demonstrate some of the statistical properties of the processes generated, with some focus on four commonly used LM processes. We compare this simulation method with the white noise wavelet simulation scheme of Percival and Walden [Percival, D. and Walden, A., 2000, Wavelet Methods for Time Series Analysis (Cambridge: Cambridge University Press).].

Abstract: Inference procedures for γ = P(T 2 < T 1) are considered when T 1 and T 2 are correlated and distributed as bivariate exponential. Under this model, asymptotic inference procedures based on maximum likelihood, the method of moments, and generalized estimating equations are developed. Exact confidence limits and the bootstrap BCa confidence on γ are also given. Monte Carlo methods are used to estimate the coverage probabilities with the aim of evaluating the alternative strategies. Two examples are given to illustrate these techniques.

Abstract: The method of control variates has been intensively used for reducing the variance of estimated (linear) regression metamodels in simulation experiments. In contrast to previous studies, this article presents a procedure for applying multiple control variates when the objective is to estimate and validate a nonlinear regression metamodel for a single response, in terms of selected decision variables. This procedure includes robust statistical regression techniques for estimation and validation. Assuming joint normality of the response and controls, confidence intervals and hypothesis tests for the metamodel parameters are obtained. Finally, results for measuring the efficiency of the use of control variates are discussed.

Abstract: The exact inference and prediction intervals for the K-sample exponential scale parameter under doubly Type-II censored samples are derived using an algorithm of Huffer and Lin [Huffer, F.W. and Lin, C.T., 2001, Computing the joint distribution of general linear combinations of spacings or exponen-tial variates. Statistica Sinica, 11, 1141–1157.]. This approach provides a simple way to determine the exact percentage points of the pivotal quantity based on the best linear unbiased estimator in order to develop exact inference for the scale parameter as well as to construct exact prediction intervals for failure times unobserved in the ith sample. Similarly, exact prediction intervals for failure times of units from a future sample can also be easily obtained.

Abstract: In this article, we introduce genetic algorithms (GAs) as a viable tool in estimating parameters in a wide array of statistical models We performed simulation studies that compared the bias and variance of GAs with classical tools, namely, the steepest descent, Gauss–Newton, Levenberg–Marquardt and don't use derivative methods In our simulation studies, we used the least squares criterion as the optimizing function The performance of the GAs and classical methods were compared under the logistic regression model; non-linear Gaussian model and non-linear non-Gaussian model We report that the GAs' performance is competitive to the classical methods under these three models

Abstract: We confirm that units root tests can exhibit substantial size distortion when breaks in mean are generated by a first-order Markov chain, but unlike previous literature, we find augmentation largely remedies this situation. However, considerable heterogeneity is evident in the size properties of the tests when faced with breaks in mean varying in duration, in number and in position within the sample. This heterogeneity will be hidden when a Markov chain is employed. For instance, when the transition probabilities generate single period outliers, rejection frequencies (RFs) rise substantially with the number of outliers, but augmentation results in approximately nominal RFs. Qualitatively similar results hold when a number of structural breaks are allocated randomly in the central section of the sample. Interestingly, very different behaviour is exposed by a design exploring the impact on the tests of two breaks imposed at a range of fixed intervals, RFs rising when break occur in the extremities of the sa...

Abstract: In this article, we develop inference tools for an effect size parameter in a paired experiment. A class of estimators is defined that includes natural, shrinkage and shrinkage preliminary test estimators. The shrinkage and preliminary test methods incorporate uncertain prior information on the parameter. This information may be available in the form of a realistic guess on the basis of the experimenter’s knowledge and experience, which can be incorporated into the estimation process to increase the efficiency of the estimator. Asymptotic properties of the proposed estimators are investigated both analytically and computationally. A simulation study is also conducted to assess the performance of the estimators for moderate and large samples. For illustration purposes, the method is applied to a data set.

Abstract: This study investigated the bias of factor loadings obtained from incomplete questionnaire data with imputed scores Three models were used to generate discrete ordered rating scale data typical of questionnaires, also known as Likert data These methods were the multidimensional polytomous latent trait model, a normal ogive item response theory model, and the discretized normal model Incomplete data due to nonresponse were simulated using either missing completely at random or not missing at random mechanisms Subsequently, for each incomplete data matrix, four imputation methods were applied for imputing item scores Based on a completely crossed six-factor design, it was concluded that in general, bias was small for all data simulation methods and all imputation methods, and under all nonresponse mechanisms Imputation method, two-way-plus-error, had the smallest bias in the factor loadings Bias based on the discretized normal model was greater than that based on the other two models

Abstract: Statistical modelling and inference for a single-ion channel have principally been carried out using finite-state space continuous-time Markov chains. Statistical inferences for the closed and open dwell times and the kinetic rate constants between states have then been arrived at via maximum likelihood methods, including the use of the EM algorithm. The fundamental assumption behind this theory is that one has the correct number of closed and open states, something which may not be easily determined by the use of current methods for modelling, say, the number of components in a mixture of exponential distributions used to fit, say, the ‘closed’ dwell times. Here, we show that the use of a robust L 2 estimator can outperform the EM algorithm both when the correct number of states is apparent and also when there are small deviations from the supposed models. After describing the statistical models used to demonstrate these results and how they lead to particular mixtures of exponential distributions the co...

Abstract: In 1998, Bowman and Shenton introduced an asymptotic formula for the third central moment of a maximum likelihood estimator of the parameter θα, a = 1, 2, …, s. From this moment, the asymptotic skewness can be set up using the standard deviation. Clearly, the skewness, measured in this way is location free, and scale free, so that shape is accounted for. The computer program is implemented by insertion of the values of expectations of products of logarithmic derivatives, a tiresome task. But now using Maple, the only input consists of the values of the parameters and the form of the density or probability function. Cases of up to four parameters have been implemented. However, in this paper we present two- and three-parameter cases in detail. Future improvements in handling Maple may lead to the implementation of the general case. Bowman and Shenton [Bowman, K.O. and Shenton, L.R., 1999, The asymptotic kurtosis for maximum likelihood estimators. Communications in Statistics, Theory and Methods, 28(11), 26...

Abstract: Very few specific stochastic differential equations have explicitly known solutions. The most common procedure to obtain a simulated path of a solution is based on a discretization of the stochastic differential equations. However, there are some cases where the discrete-time discretization cannot be used. In this article, we propose a new method to simulate the solution of a non-linear stochastic differential equation, which, in principle, is exempt from error of simulation and can be widely applied including in cases where the discrete-time discretization cannot be used.

Abstract: The method of target estimation developed by Cabrera and Fernholz [(1999). Target estimation for bias and mean square error reduction. The Annals of Statistics, 27(3), 1080–1104.] to reduce bias and variance is applied to logistic regression models of several parameters. The expectation functions of the maximum likelihood estimators for the coefficients in the logistic regression models of one and two parameters are analyzed and simulations are given to show a reduction in both bias and variability after targeting the maximum likelihood estimators. In addition to bias and variance reduction, it is found that targeting can also correct the skewness of the original statistic. An example based on real data is given to show the advantage of using target estimators for obtaining better confidence intervals of the corresponding parameters. The notion of the target median is also presented with some applications to the logistic models.

Abstract: It is well known that more powerful variants of Dickey–Fuller unit root tests are available. We apply two of these modifications, on the basis of simple maximum statistics and weighted symmetric estimation, to Perron tests allowing for structural change in trend of the additive outlier type. Local alternative asymptotic distributions of the modified test statistics are derived, and it is shown that their implementation can lead to appreciable finite sample and asymptotic gains in power over the standard tests. Also, these gains are largely comparable with those from GLS-based modifications to Perron tests, though some interesting differences do arise. This is the case for both exogenously and endogenously chosen break dates. For the latter choice, the new tests are applied to the Nelson–Plosser data.

Abstract: Bayesian change points analysis on the seismic activity in northeastern Taiwan is studied via the reversible jump Markov chain Monte Carlo simulation. An epidemic model is considered with Gamma prior distributions for the parameters. The prior distributions are essentially determined based on an earlier period of the seismic data in the same region. It is investigated that there exist two change points during the time period considered. This result is also confirmed by the BIC criteria.