Test for periodicity in restrictive EXPAR models

Abstract

This article is devoted to study the problem of test of periodicity in the restricted exponential autoregressive (EXPAR) model. The local asymptotic normality property, of this model, is shown via the adapted sufficient conditions due to Swensen (1985 Swensen, A.R. (1985). The asymptotic distribution of the likelihood ratio for autoregressive time series with a regression trend. J. Multivariate Anal. 16:54–70.[Crossref], [Web of Science ®] , [Google Scholar]). Using this result, in the case where the innovation density is specified, we obtain a parametric local asymptotic “most stringent” test.     

Recurrence formula on the joint distribution of sample skewness and kurtosis under normality

Abstract

Two recurrence relations with respect to sample size are given concerning the joint distribution of skewness and kurtosis of random observations from a normal population: one between the probability density functions and the other between the product moments. As a consequence, the latter yields a recurrence formula for the moments of sample kurtosis. The exact moments of Jarque-Bera statistic is also given.     

The limiting power of point optimal autocorrelation tests

This paper considers the point optimal tests for AR(1) errors in the linear regression model. It is shown that these tests have the same limiting power characteristics as the Durbin-Watson test. . The limiting power is zero or one when the regression has no intercept, but lies strictly between these values when an intercept is included.     

A new rank test for the K-Sample problem

The treatment sum of squares in the one-way analysis of variance can be expressed in two different ways: as a sum of comparisons between each treatment and the remaining treatments combined, or as a sum of comparisons between the treatments two at a time. When comparisons between treatments are made with the Wilcoxon rank sum statistic, these two expressions lead to two different tests; namely, that of Kruskal and Wallis and one which is essentially the same as that proposed by Crouse (1961,1966). The latter statistic is known to be asymptotically distributed as a chi-squared variable when the numbers of replicates are large. Here it is shown to be asymptotically normal when the replicates are few but the number of treatments is large. For all combinations of numbers of replicates and treatments its empirical distribution is well approximated by a beta distribution     

A note on stratification and gain in precision in estimating diversity from large samples

Several indices of entropy have been suggested in the literature as weighted diversity measures of a population with respect to a classification process. Among them, Shannon's entropy and Havrda -Charvát's non-additive entropies of order a, have been exhaustively used.

When the population is finite but too large to be censused, the diversity with respect to a given classification process must be estimated from a sample.

In this note, on the basis of an asymptotic study of the sample indices in the stratified random sampling, we are going to confirm that when we deal with large samples one can guarantee a gain in precision from stratified random over simple random sampling. This gain becomes considerable when the ‘inaccuracy" (as intended by Kerridge and Rathie and Kannapan) between the frequency vector in each stratum and that in the whole population, varies greatly from stratum to stratum.     

Estimating multivariate autoregressive moving average models by fitting long autoregressions

Some simple methods for the estimation of mixed multivariate autoregressive moving average time series models are introduced. The methods require the fitting of a long autoregression to the data and the computation of consistent initial estimates for the parameters of the model. After these preliminaries the estimators of the paper are obtained by applying weighted least squares to a multivariate auxiliary regression model. Two types of weight matrices are considered. Both of them yield estimators which are strongly consistent and asymptotically normally distributed. The first estimators are also asymptotically efficient while the second ones are not fully efficient but computationally simple. A simulation study is performed to illustrate the behaviour of the estimators in finite samples.     

A plug-in technique in nonparametric regression with dependence

The problem addressed is that of smoothing parameter selection in kernel nonparametric regression in the fixed design regression model with dependent noise. An asymptotic expression of the optimum bandwidth parameter has been obtained in recent studies, where this takes the form h = C ₀ n ^?1/5. This paper proposes to use a plug-in methodology, in order to obtain an optimum estimation of the bandwidth parameter, through preliminary estimation of the unknown value of C ₀.     

Generalized least squares estimation of multivariate nonlinear models with missing data

The method of estimated generalized least squares estimation of multiple response models is extended to the randomly missing date case. This estimation procedure is computationally simply when there are many missing data but the number of distinct patterns of missing data for the response vectors is small. The consistency and asymptotic normality of the proposed estimators are established.