Non-ergodic martingale estimating functions and related asymptotics

Well-known estimation methods such as conditional least squares, quasilikelihood and maximum likelihood (ML) can be unified via a single framework of martingale estimating functions (MEFs). Asymptotic distributions of estimates for ergodic processes use constant norm (e.g. square root of the sample size) for asymptotic normality. For certain non-ergodic-type applications, however, such as explosive autoregression and super-critical branching processes, one needs a random norm in order to get normal limit distributions. In this paper, we are concerned with non-ergodic processes and investigate limit distributions for a broad class of MEFs. Asymptotic optimality (within a certain class of non-ergodic MEFs) of the ML estimate is deduced via establishing a convolution theorem using a random norm. Applications to non-ergodic autoregressive processes, generalized autoregressive conditional heteroscedastic-type processes, and super-critical branching processes are discussed. Asymptotic optimality in terms of the maximum random limiting power regarding large sample tests is briefly discussed.     

Higher-order and non-stationary properties of lampard's stochastic reversible counter system

Summary. In this paper we discuss higher-order and non-stationary properties of LAM-PAED'S (1968) stochastic reversible counter model whose output is a stochastic point process with MABKOV dependent time intervals. Statistical properties of the primed counter system, are also considered. A characterization of the probability density function of the interval lengths and the probability distribution of the counts by means of a mixed POXSSOH process is then derived. The distribution of counts of the primed counter system is shown to be mathematically equivalent to the birth-and-death process with immigration. A generalization of the problem when initial counts and incremental counts have independent distributions is also discussed     

Some exact tables for the squared ranks test

Since the squared ranks test was first proposed by Taha in 1964 it has been mentioned by several authors as a test that is easy to use, with good power in many situations. It is almost as easy to use as the Wilcoxon rank sum test, and has greater power when two populations differ in their scale parameters rather than in their location parameters. This paper discuss the versatility of the squared ranks test, introduces a test which uses squared ranks, and presents some exact tables     

Comparison of conditional and unconditional confidence intervals for the double exponential distribution

Conditional confidence intervals for the location parameter of the double exponential distribution based on maximum likelihood estimators conditioned on a set of ancillary statistics and the corresponding unconditional confidence intervals based on the maximum likelihood estimators alone are compared in two ways. Monte Carlo techniques are used and the conditional approach appears to give slightly better results although agreement as n becomes larger is noted     

CUSUM Hypothesis Tests and Alternative Response Probabilities for Finite Poisson Trials

This article develops a new cumulative sum statistic to identify aberrant behavior in a sequentially administered multiple-choice standardized examination. The examination responses can be described as finite Poisson trials, and the statistic can be used for other applications which fit this framework. The standardized examination setting uses a maximum likelihood estimate of examinee ability and an item response theory model. Aberrant and non aberrant probabilities are computed by an odds ratio analogous to risk adjusted CUSUM schemes. The significance level of a hypothesis test, where the null hypothesis is non-aberrant examinee behavior, is computed with Markov chains. A smoothing process is used to spread probabilities across the Markov states. The practicality of the approach to detect aberrant examinee behavior is demonstrated with results from both simulated and empirical data.     

On the Specification of Propensity Scores,With Applications to the Analysis of Trade Policies

A vector autoregression is fit to recent U.S. data on wheat prices, wheat export sales, wheat export shipments, and exchange rates. Forecast error decompositions and out-of-sample forecasts indicate that exchange rates have little influence on wheat sales and shipments.     

Amemiya‘s generalized least squares and tests of overidentification in simultaneous equation models with qualitative or limited dependent variables

Amemiya's generalized least squares method for the estimation of simultaneous equation modeis with qualitative or limited dependent variables is known to be efficient relative to many popular two stage estimators. This note points out that test statistics for overidentification restrictions can be obtained as by-products of Amerniya's generalized least squares procedure. Amemiya's procedure is shown to be a minimum chisquare method. The Amemiya procedure is valuable both for efficient estimation and for model evaluation of such models.     

New approximate confidence intervals for the difference between two Poisson means and comparison

The problem of estimating the difference between two Poisson means is considered. A new moment confidence interval (CI), and a fiducial CI for the difference between the means are proposed. The moment CI is simple to compute, and it specializes to the classical Wald CI when the sample sizes are equal. Numerical studies indicate that the moment CI offers improvement over the Wald CI when the sample sizes are different. Exact properties of the CIs based on the moment, fiducial and hybrid methods are evaluated numerically. Our numerical study indicates that the hybrid and fiducial CIs are in general comparable, and the moment CI seems to be the best when the expected total counts from both distributions are two or more. The interval estimation procedures are illustrated using two examples.     

Point estimation after early stopping in a repeated measures trial

When the individual measurements are statistically independent, the maximum likelihood estimator calculated at the end of a sequential procedure overestimates the underlying effect. There are many clinical trials in which we are interested in comparing changes in responses between two treatment groups sequentially. Lee and DeMets (1991, JASA 86, 757–762) proposed a group sequential method for comparing rates of change when a response variable is measured for eaeh patient at successive follow-up visits. They assumed that the response follows the linear mixed effects model and derived the asymptotic joint distribution of the sequentially computed statistics. In this article, we consider the maximum likelihood estimator (MLE), the median unbiased estimator (MUE) and the midpoint of a 100(1-α)% confidence interval as point estimators for the rate of change in the linear mixed effects model, and investigate their properties by Monte Carlo simulation.