Asymptotic distribution of (h, φ)-entropies

In this paper, (h,φ)-entropies are presented as a generalization of φ-entropies, Havrda-Charvat entropies and the Renyi entropy among others. For this functional, asymptotic distribution for simple random sampling and stratified .sampling with proportional affixing is obtained.     

Test of linear trend in eigenvalues of k covariance matrices with applications in common principal components analysis

A test for linear trend among a set of eigenvalues of k covariance matrices is developed. A special case of this test is Flury's (1986) test for the equality of eigenvalues. The linear trend hypothesis appears to be more relevant to data analysis than the equality hypothesis. Examples show how the linear trend hypothesis can be acceptable while the equality hypothesis is rejected.     

Asymptotic efficiency of model selection criteria: the nonzero mean gaussian ar(∞) case

Motivated by Shibata’s (1980) asymptotic efficiency results this paper dis-cusses the asymptotic efficiency of the order selected by a selection procedure for an infinite order autoregressive process with nonzero mean and unob servable errors that constitute a sequence of independent Gaussian random variables with mean zero and variance σ² The asymptotic efficiency is established for AIC–type selection criteria such as AIC’, FPE, and S_n(k). In addition, some asymptotic results about the estimators of the parameters of the process and the error–sequence are presented.     

The asymptotic distribution of the process capability index Cpmk

The main result of this paper is that under some regularity conditions, the distribution of an estimator of the process capability index C_pmk is asymptotically normal.     

Confidence bounds for the joint survival function in the dependent competing risks setup

In the competing risks set up with two dependent competing risks, the joint distribution of (X₁,X₂), the latent lifetimes of the system under the two risks, is not identifiable on the basis of the distribution of the actual observation (T, δ) where T = min(X₁, X₂) and δ = I(T=X₁), Using Peterson's (1976) bounds, we have obtained conservative pointwise as well as simultaneous confidence bounds for the unidentifiable joint survival function. In an example we evaluate the confidence bounds and Indicate where the estimated joint survival function in the independent case, lies within them.     

A note on umvu estimation in the transformed chi-square family

The transformed chi-square family includes many common one-parameter continuous distributions. In that family, we give conditions under which a given function of the mean admits a minimum variance unbiased estimator and an orthogonal expansion for this estimator in terms of the generalized Laguerre polynomials. We show that such expansion is useful for obtaining bounds for the variance and for the study of the asymptotic properties of the unbiased estimators.     

Asymptotic distribution for the order statistics of a truncated one-parameter family of distributions

In this article we have presented some of the asymptotic theorems related to one-truncation parameter family of distributions ? Comparison of performance of different estimators and other inferential problems have been tackled - Also applications of the main results have been given and illustrated their uses with examples.     

Self-weighted quasi-maximum exponential likelihood estimator for ARFIMA-GARCH models

In this paper, a local self-weighted quasi-maximum exponential likelihood estimator for ARFIMA-GARCH models is proposed, asymptotic normality of this estimator is derived under the existence of second moment including stationary and non-stationary cases. A simulation study is given to evaluate the performance of the proposed self-weighted QMELE under the stationary case.     

Hellinger distance estimation of general bilinear time series models

In the present paper, minimum Hellinger distance estimates for parameters of a bilinear time series model are presented. The probabilistic properties such as stationarity, existence of moments of the stationary distribution and strong mixing property of the model are well known (see for instance [J. Liu, A note on causality and invertibility of a general bilinear time series model, Adv. Appl. Probab. 22 (1990) 247–250; J. Liu, P.J. Brockwell, On the general bilinear time series model, J. Appl. Probab. 25 (1988) 553–564; D.T. Pham, The mixing property of bilinear and generalised random coefficients autoregressive models, Stoch. Process Appl. 23 (1986) 291–300]). We establish, under some mild conditions, the consistency and the asymptotic normality of the minimum Hellinger distance estimates of the parameters of the model.     

Estimation of a multiple-threshold AR(p) model

The present paper deals with the multiple-threshold p-order autoregressive model which has been introduced by Tong and Lim [H. Tong, K.S. Lim, Threshold autoregression, limit cycles and cyclical data, J. R. Stat. Soc. Ser. B 42 (1980) 245–292] in nonlinear system modelling. Under some conditions on the coefficients of the model which ensure the stationarity, the existence of moments and the strong mixing property of this process and under other mild assumptions, we establish the asymptotic properties (consistency and asymptotic normality) of the minimum Hellinger distance estimates of the autoregressive coefficients of the model.