Large sample estimation and prediction for explosive growth curve models

Asymptotic distributions of maximum likelihood estimators for the parameters in explosive growth curve models are derived. Limit distributions of prediction errors when the parameters are estimated are also obtained. The growth curve models are viewed as multivariate time-series models, and the usual time-series methods are used for prediction. Estimation constrained by a hypothesis of homogeneity of growth rates is also considered.     

Anderson's classification statistic based on a post-stratified training sample

The performance of Anderson's classification statistic based on a post-stratified random sample is examined. It is assumed that the training sample is a random sample from a stratified population consisting of two strata with unknown stratum weights. The sample is first segregated into the two strata by post-stratification. The unknown parameters for each of the two populations are then estimated and used in the construction of the plug-in discriminant. Under this procedure, it is shown that additional estimation of the stratum weight will not seriously affect the performance of Anderson's classification statistic. Furthermore, our discriminant enjoys a much higher efficiency than the procedure based on an unclassified sample from a mixture of normals investigated by Ganesalingam and McLachlan (1978).     

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     

Asymptotic equivalence of the harrell-davis median estimator and the sample median

This paper presents an asymptotic equivalence result with a sharp rate of convergence forthe sample median and the Harrell-Davis median estimator. The consequences of this result are discussed.     

Pseudo maximum likelihood estimation for the dirichlet-multinomial distribution

Pseudo maximum likelihood estimation (PML) for the Dirich-let-multinomial distribution is proposed and examined in this pa-per. The procedure is compared to that based on moments (MM) for its asymptotic relative efficiency (ARE) relative to the maximum likelihood estimate (ML). It is found that PML, requiring much less computational effort than ML and possessing considerably higher ARE than MM, constitutes a good compromise between ML and MM. PML is also found to have very high ARE when an estimate for the scale parameter in the Dirichlet-multinomial distribution is all that is needed.     

Exclusion restrictions in instrumental variables equations

In this paper we consider two-stage estimators of parameters of a structural equation in a model with recursive exclusion restrictions on the instrumental variables equations. The estimations considered are simple OLS and GLS estimators after substitution of estimates of the systematic part of the IV equations for the endogenous variables. It is known in the literature that neither imposing the restrictions in the first stage nor ignoring them will in general be more efficient than the alternative. We introduce a class of mixed instrumental variables estimators (MIV) with these possibilities as special cases which yields an estimator which is not only more efficient than the two stage estimators considered in the literature but as efficient as an efficient system estimator like 3SLS.     

BIVARIATE DISTRIBUTION WITH TRUNCATED POISSON MARGINAL DISTRIBUTIONS

ABSTRACT

A bivariate distribution, whose marginal distributions are truncated Poisson distributions, is developed as a product of truncated Poisson distributions and a multiplicative factor. The multiplicative factor takes into account the correlation, either positive or negative, between the two random variables. The distributional properties of this model are studied and the model is fitted to a real life bivariate data.     

HAZARD RATE ESTIMATION FOR CENSORED DATA BY WAVELET METHODS

ABSTRACT

We study the estimation of a hazard rate function based on censored data by non-linear wavelet method. We provide an asymptotic formula for the mean integrated squared error (MISE) of nonlinear wavelet-based hazard rate estimators under randomly censored data. We show this MISE formula, when the underlying hazard rate function and censoring distribution function are only piecewise smooth, has the same expansion as analogous kernel estimators, a feature not available for the kernel estimators. In addition, we establish an asymptotic normality of the nonlinear wavelet estimator.     

POISSON REGRESSION WITH A PERIODIC FUNCTION

ABSTRACT

Let {y_t } be a Poisson-like process with the mean μ _t which is a periodic function of time t. We discuss how to fit this type of data set using quasi-likelihood method. Our method provides a new avenue to fit a time series data when the usual assumption of stationarity and homogeneous residual variances are invalid. We show that the estimators obtained are strongly consistent and also asymptotically normal.     

Estimating the discovery rate in a continuous time recapture model

We consider a family of marked Poisson process models for the discovery of distinct errors in a computer program and also for sampling, in continu-ous time, a population containing an unknown number of distinct biological species. Captures (selections or discoveries) are assumed to occur at a con-stant rate, each event consisting of the discovery of a distinct process (error or species) or the recurrence of a previously discovered process. Using a generalization of Nayak’s (1988) model we derive confidence limits for the discovery rate. The limits are based on the asymptotic distribution of a scaled logarithmic function of the maximum likelihood estimator.