COMPARING TESTS OF AUTOREGRESSIVE VERSUS MOVING AVERAGE ERRORS IN REGRESSION MODELS USING BAHADUR’S ASYMPTOTIC RELATIVE EFFICIENCY

ABSTRACT

The purpose of this paper is to use Bahadur's asymptotic relative efficiency measure to compare the performance of various tests of autoregressive (AR) versus moving average (MA) error processes in regression models. Tests to be examined include non-nested procedures of the models against each other, and classical procedures based upon testing both the AR and MA error processes against the more general autoregressive-moving average model.     

A NOTE ON THE HOMOGENETIC ESTIMATE FOR THE VARIANCE OF THE KAPLAN–MEIER ESTIMATE

ABSTRACT

The Greenwood estimate (GE) is commonly employed for estimating the variance of the Kaplan–Meier estimate (KME) even though it underestimates the variance. To reduce the bias of the GE, Zhao (1996) proposed an alternative, called the homogenetic estimate (HE). In this note, we point out that the HE actually esimates the variance of the reduced sample estimate (RE) and can seriously overestimate that of the KME. We also derive the explict relationship between the HE and the GE and discuss the use of the HE.     

HOW WELL DO SELECTION MODELS PERFORM? ASSESSING THE ACURACY OF ART AUCTION PRE-SALE ESTIMATES

Art auction catalogs provide a pre-sale prediction interval for the price each item is expected to fetch. When the owner consigns art work to the auction house, a reserve price is agreed upon, which is not announced to the bidders. If the highest bid does not reach it, the item is brought in. Since only the prices of the sold items are published, analysts only have a biased sample to examine due to the selective sale process. Relying on the published data leads to underestimating the forecast error of the pre-sale estimates. However, we were able to obtain several art auction catalogs with the highest bids for the unsold items as well as those of the sold items. With these data we were able to evaluate the accuracy of the predictions of the sale prices or highest bids for all item obtained from the original Heckman selection model that assumed normal error distributions as well as those derived from an alternative model using the t(2) distribution, which yielded a noticeably better fit to several sets of auction data. The measures of prediction accuracy are of more than academic interest as they are used by auction participants to guide their bidding or selling strategy, and similar appraisals are accepted by the US Internal Revenue Services to justify the deductions for charitable contributions donors make on their tax returns.     

A NOTE ON ‘A COMPARISON OF BAYES AND MAXIMUM LIKELIHOOD ESTIMATION OF THE INTRACLASS CORRELATION COEFFICIENT’

Palmer and Broemeling [1] Palmer, J. L. and Broemeling, L. D. 1990. A Comparison of Bayes and Maximum Likelihood Estimation of the Intraclass Correlation Coefficient. Comm. Statist.-Theory Meth, 19: 953–975. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar] compare Bayes and maximum likelihood estimates of the intraclass correlation (ICC). The prior information in their derivation of the Bayes estimator is placed on the variance components instead of the ICC itself. This paper finds a Bayes estimator of the ICC with the prior placed on the ICC. Bayes estimates based on three different priors are then compared to method of moments estimate.     

TESTING SUBHYPOTHESES AND ESTIMATING σ2 IN THE NONREPLICATED THREE-WAY MULTIPLICATIVE INTERACTION MODEL

ABSTRACT

Standard statistical techniques do not provide methods for analyzing data from nonreplicated factorial experiments. Such experiments occur for several reasons. Many experimenters may prefer conducting experiments having a large number of factor levels with no replications than conducting experiments with a few factor levels with replications particularly in pilot studies. Such experiments may allow one to identify factor combinations to be used in follow-up experiments. Another possibility is when the experimenter thinks that an experiment is replicated when in fact it is not. This occurs when a naive researcher believes that sub-samples are replicates when in reality they are not. Nonreplicated two-way experiments have been extensively studied. This paper discusses the analysis of nonreplicated three-way experiments. In particular, estimation of σ² is discussed and a test is derived for testing whether three-factor interaction is absent in sub-areas of three-way data using a nonreplicated three-way multiplicative interaction model with a single multiplicative term. Approximate null distribution of the derived test statistic is studied using Monte Carlo studies and results are illustrated through an example.