Sample size determination of steel's nonparametric many-one test

We derive sample size formulas for the many-one test of Steel (1959) when the all-pairs power is preassigned. In this large sample approach we replace, similar to Noether (1987), the unknown variances and also the unknown correlation coefficients in the power expressions by their known values under the null hypotheses. We then obtain least favorable configurations for one-and two-sided comparisons. The reliability of our formulas is examined in computer simulations for different alternatives with various distributions.     

On Least Absolute Value Estimators for Poisson Processes

We consider the problem of parameter estimation for an inhomogeneous Poisson process observed on the time interval [0, τ]. We introduce the minimum L ₁-norm estimator of the unknown parameter and study the asymptotical behaviors of the estimates when the number of observations increases. It is established that this estimator is consistent and we show that the corresponding differences converge to certain variables. These limit variables are asymptotically normal as τ tends to infinity.     

Local Linear Least Squares Kernel Regression for Linear and Circular Predictors

We extend nonparametric regression models with local linear least squares fitting using kernel weights to the case of linear and circular predictors. We derive the asymptotic properties of the conditional bias and variance of bivariate local linear least squares kernel estimators. A small simulation study and a real experiment are given.     

Estimation in Singular Linear Models with Stochastic Linear Restrictions and Linear Equality Restrictions

This article is concerned with the parameter estimation in a singular linear regression model with stochastic linear restrictions and linear equality restrictions simultaneously. A new estimator is introduced and it is proved that the proposed estimator is superior to the least squares estimator and singular mixed estimator in the mean squared error sense under certain conditions.     

The Least Upper Bound on the Poisson-Negative Binomial Relative Error

In this article, basic mathematical computations are used to determine the least upper bound on the relative error between the negative binomial cumulative distribution function with parameters n and p and the Poisson cumulative distribution function with mean λ =nq = n(1 ? p). Following this bound, it is indicated that the negative binomial cumulative distribution function can be properly approximated by the Poisson cumulative distribution function whenever q is sufficiently small. Five numerical examples are presented to illustrate the obtained result.     

Model Selection for Vector Autoregressive Processes via Adaptive Lasso

Determination of the best subset is an important step in vector autoregressive (VAR) modeling. Traditional methods either conduct subset selection and parameter estimation separately or compute expensively. In this article, we propose a VAR model selection procedure using adaptive Lasso, for it is computational efficient and can select subset and estimate parameters simultaneously. By proper choice of tuning parameters, we can choose the correct subset and obtain the asymptotic normality of the non zero parameters. Simulation studies and real data analysis show that adaptive Lasso performs better than existing methods in VAR model fitting and prediction.     

Empirical Likelihood-based Inference for Stationary-ergodicity of the Generalized Random Coefficient Autoregressive Model

In this article, we consider the application of the empirical likelihood method to the generalized random coefficient autoregressive (GRCA) model. When the order of the model is 1, we derive an empirical likelihood ratio test statistic to test the stationary-ergodicity. Some simulation studies are also conducted to investigate the finite sample performances of the proposed test.     

Estimation in second order branching processes with application to swine flu data

Abstract

This paper discusses inferential issues related to estimation of offspring mean and variance in a second order branching process, when both the offspring distributions are assumed to have identical mean and variance. Estimating equation approach is used to find the estimator of the offspring mean and the fact that a second order branching process model can be modeled as an autoregressive process is utilized to obtain the estimator of the offspring variance. Both the estimators are shown to be consistent and asymptotically normal. The second order branching process model is applied to H1N1 data for Pune, India, and Mexico and is found to be a suitable model. The estimates obtained from this model are used to compute the proportion of vaccination required for elimination of the disease.     

A GRAPHICAL TECHNIQUE FOR DETECTING INFLUENTIAL CASES IN REGRESSION ANALYSIS

This paper presents a graphical technique for detecting influential cases in regression analysis. The idea is to decompose a diagnostic problem involving higher order dimensional regression problems, into a series of two-dimensional diagnostic sub-problems, such that the diagnoses of influential cases is undertaken by visually inspecting two-dimensional diagnostic plots of these sub-problems. An algorithm for the graphical procedure is proposed to reduce the computational effort. Practical examples are used to illustrate this graphical technique.     

Artificial neural networks for some macroeconomic series: A first report

There is a tendency for the true variability of feasible GLS estimators to be understated by asymptotic standard errors. For estimation of SUR models, this tendency becomes more severe in large equation systems when estimation of the error covariance matrix, C, becomes problematic. We explore a number of potential solutions involving the use of improved estimators for the disturbance covariance matrix and bootstrapping. In particular, Ullah and Racine (1992) have recently introduced a new class of estimators for SUR models that use nonparametric kernel density estimation techniques. The proposed estimators have the same structure as the feasible GLS estimator of Zellner (1962) differing only in the choice of estimator for C. Ullah and Racine (1992) prove that their nonparametric density estimator of C can be expressed as Zellner's original estimator plus a positive definite matrix that depends on the smoothing parameter chosen for the density estimation. It is this structure of the estimator that most interests us as it has the potential to be especially useful in large equation systems.

Atkinson and Wilson (1992) investigated the bias in the conventional and bootstrap estimators of coefficient standard errors in SUR models. They demonstrated that under certain conditions the former were superior, but they caution that neither estimator uniformly dominated and hence bootstrapping provides little improvement in the estimation of standard errors for the regression coefficients. Rilstone and Veal1 (1996) argue that an important qualification needs to be made to this somewhat negative conclusion. They demonstrated that bootstrapping can result in improvements in inferences if the procedures are applied to the t-ratios rather than to the standard errors. These issues are explored for the case of large equation systems and when bootstrapping is combined with improved covariance estimation.