Binomial AR(1) processes: moments,cumulants, and estimation

The modelling and analysis of count-data time series are areas of emerging interest with various applications in practice. We consider the particular case of the binomial AR(1) model, which is well suited for describing binomial counts with a first-order autoregressive serial dependence structure. We derive explicit expressions for the joint (central) moments and cumulants up to order 4. Then, we apply these results for expressing moments and asymptotic distribution of the squared difference estimator as an alternative to the sample autocovariance. We also analyse the asymptotic distribution of the conditional least-squares estimators of the parameters of the binomial AR(1) model. The finite-sample performance of these estimators is investigated in a simulation study, and we apply them to real data about computerized workstations.     

A comparison of robust regression techniques for the estimation of weibull parameters

In this paper several alternative robust reqression techniques are compared for estimating parameters of a Weibull distribution . In addition to the usual least squares (L₂) and least absolute deviation (L₁) methods, a number of one-step reweighting schemes based on the L₁residuals are considered. The results of an extensive series of Monte Carlo simulation experiments demonstrate that the Anscmbe reweighting scheme generally produces the best Weibull estimates over the range of sample sizes and parameter values studied.     

A hybrid bandwidth selection methodology for kernel density estimation

A bandwidth selection method that combines the concept of least-squares cross-validation and the plug-in approach is being introduced in connection with kernel density estimation. A simulation study reveals that this hybrid methodology outperforms some commonly used bandwidth selection rules. It is shown that the proposed approach can also be readily employed in the context of variable kernel density estimation. We conclude with two illustrative examples.     

Nonparametric point estimators for the change-point problem

Three nonparametric methods for estimating a change-point, and the mean function Pefore and after the change has occurred are developed for a restricted class of processes. The estimators which are developed are intuitive, and their asymptotic behavior is studied, Konte Cario cornparisoris are undertaKen for smali and moderate samples.     

Sensory analysis via multi-block multivariate additive PLS splines

In the last decade, much effort has been spent on modelling dependence between sensory variables and chemical–physical ones, especially when observed at different occasions/spaces/times or if collected from several groups (blocks) of variables. In this paper, we propose a nonlinear generalization of multi-block partial least squares with the inclusion of variable interactions. We show the performance of the method on a known data set.     

Computing the normalization factor in bingham distributions

A new method for calculating the confluent hypergeometric function of vector argument is presented. This function serves to normalize the integral which defines the Bingham distribution. By using a polynomial and series expansion, the double integral can be reduced to a single infinite summation whose coefficients may be computed recursively. A short c program implementing the method is included in the appendix.     

An Empirical Nonlinear Data-Fitting Approach for Transforming Data to Normality

A general method is proposed by which nonnormally distributed data can be transformed to achieve approximate normality. The method uses an empirical nonlinear data-fitting approach and can be applied to a broad class of transformations including the Box-Cox, arcsine, generalized logit, and Weibull-type transformations. It is easy to implement using standard statistical software packages. Several examples are provided.     

Variance Reduction Using Nonlinear Controls and Transformations

Nonlinear regression-adjusted control variables are investigated for improving variance reduction in statistical and system simulations. To this end, simple control variables are piecewise sectioned and then transformed using linear and nonlinear transformations. Optimal parameters of these transformations are selected using linear or nonlinear least-squares regression algorithms. As an example, piecewise power-transformed variables are used in the estimation of the mean for the twovariable Anderson-Darling goodness-of-fit statistic W ₂ ². Substantial variance reduction over straightforward controls is obtained. These parametric transformations are compared against optimal, additive nonparametric transformations obtained by using the ACE algorithm and are shown, in comparison to the results from ACE, to be nearly optimal.     

A Note on Estimation of Parameters for Branching Processes with Immigration

It is proved that under certain conditions the conditional least-squares estimator of the offspring mean for a sequence of nearly critical Ji?ina processes with immigration is consistent but not asymptotically normal and the conditional least-squares estimator of the immigration mean is not consistent. These results differ from the existing results in the case where the initial values are zero (see Ispány et al., 2005 Ispány , M. , Pap , G. , Zuijlen , M. V. ( 2005 ). Fluctuation limit of branching processes with immigration and estimation of the means . Adv. Appl. Probab. 37 : 523 – 538 . [Google Scholar]).     

Variance reduction for quantile estimates in simulations via nonlinear controls

Linear controls are a well known simple technique for achieving variance reduction in computer simulation. Unfortunately the effectiveness of a linear control depends upon the correlation between the statistic of interest and the control, which is often low. Since statistics often have a nonlinear relation-ship with the potential control variables, nonlinear controls offer a means for improvement over linear controls. This paper focuses on the use of nonlinear controls for reducing the variance of quantile estimates in simulation. It is shown that one can substantially reduce the analytic effort required to develop a nonlinear control from a quantile estimator by using a strictly monotone transformation to create the nonlinear control. It is also shown that as one increases the sample size for the quantile estimator, the asymptotic multivariate normal distribution of the quantile of interest and the control reduces the effectiveness of the nonlinear control to that of the linear control. However, the data has to be sectioned to obtain an estimate of the variance of the controlled quantile estimate. Graphical methods are suggested for selecting the section size that maximizes the effectiveness of the nonlinear control