A non-bayesian approach to estimation using tested priors

A two stage sampling scheme for estimating the mean of a distribution, proposed by Katti (1962), is investigated and some of its properties are generalized. The method utilizes subjective information in the analysis, but is still within the classical framework. The generalized mean square error of the estimator is computed as the loss function and is compared with that of the usual classical approach. Modifications are suggested to improve the efficiency of the estimator by incorporating the uncertainty of the subjective information. The procedure, which is referred to as "the Method of Tested Priors" is an alternate way of using subjective information without necessarily agreeing with the philosophical aspect of the Bayesian approach.     

Choosing principal components for multivariate statistical process control

Principal components are useful for multivariate process control. Typically, the principal component variables are often selected to summarize the variation in the process data. We provide an analysis to select the principal component variables to be included in a multivariate control chart that incorporates the unique aspects of the process control problem (rather than using traditional principal component guidelines).     

Reply

Selection processes that are inherent in litigation complicate policy-oriented research of medical malpractice tort reforms. In regard to their deterrent impact, the range of potential inferences based on analyses of claim frequency is limited because plaintiffs only file a subset of potential claims. In regard to their impact on litigation costs, researchers often analyze data on claim disposition, but it is difficult to determine whether effects attributed to tort reforms reflect changes in litigant behavior or their influence on the selection of claims. In this article, we evaluate these problems and report results of our study of the effects of medical malpractice reforms on claim disposition.     

How Long Is a Spell of Unemployment? Illusions and Biases in the Use of CPS Data

Most data used to study the durations of unemployment spells come from the Current Population Survey (CPS), which is a point-in-time survey and gives an incomplete picture of the underlying duration distribution. We introduce a new sample of completed unemployment spells obtained from panel data and apply CPS sampling and reporting techniques to replicate the type of data used by other researchers. Predicted duration distributions derived from this CPS-like data are then compared to the actual distribution. We conclude that the best inferences that can be made about unemployment durations by using CPS-like data are seriously biased.     

Measuring Substitution in Monetary-Asset Demand Systems

The Allen elasticity of substitution (AES) is widely used to study monetary-asset substitution and structural demand stability. Blackorby and Russell showed that the AES is uninformative and that the Morishima elasticity of substitution (MES) is the appropriate measure, a point overlooked in the monetary literature. Use of improper measures can lead to incorrect inferences. This article considers five alternative measures of substitution—the AES, the MES, the Hicksian and Marshallian elasticities of demand, and Mundlak's unencountered, but appealing, constant-cost elasticity of substitution. Selection of the substitution measure appropriate to respective research questions is addressed.     

Testing the Null Hypothesis of Nonstationary Long Memory Against the Alternative Hypothesis of a Nonlinear Ergodic Model

Interest in the interface of nonstationarity and nonlinearity has been increasing in the econometric literature. This paper provides a formal method of testing for nonstationary long memory against the alternative of a particular form of nonlinear ergodic processes; namely, exponential smooth transition autoregressive processes. In this regard, the current paper provides a significant generalization to existing unit root tests by allowing the null hypothesis to encompass a much larger class of nonstationary processes. The asymptotic theory associated with the proposed Wald statistic is derived, and Monte Carlo simulation results confirm that the Wald statistics have reasonably correct size and good power in small samples. In an application to real interest rates and the Yen real exchange rates, we find that the tests are able to distinguish between these competing processes in most cases, supporting the long-run Purchasing Power Parity (PPP) and Fisher hypotheses. But, there are a few cases in which long memory and nonlinear ergodic processes display similar characteristics and are thus confused with each other in small samples.     

Variance reduction of estimators arising from Metropolis–Hastings algorithms

The Metropolis–Hastings algorithm is one of the most basic and well-studied Markov chain Monte Carlo methods. It generates a Markov chain which has as limit distribution the target distribution by simulating observations from a different proposal distribution. A proposed value is accepted with some particular probability otherwise the previous value is repeated. As a consequence, the accepted values are repeated a positive number of times and thus any resulting ergodic mean is, in fact, a weighted average. It turns out that this weighted average is an importance sampling-type estimator with random weights. By the standard theory of importance sampling, replacement of these random weights by their (conditional) expectations leads to more efficient estimators. In this paper we study the estimator arising by replacing the random weights with certain estimators of their conditional expectations. We illustrate by simulations that it is often more efficient than the original estimator while in the case of the independence Metropolis–Hastings and for distributions with finite support we formally prove that it is even better than the “optimal” importance sampling estimator.     

Neuropathology in Alzheimer's disease: awaking from a hundred-year-old dream

For one hundred years after Alois Alzheimer's first report of Alzheimer's disease (AD) in 1906, the pathological hallmarks of the disease, senile plaques and neurofibrillary tangles (NFTs), have been attractive targets for researchers. Therefore, not surprisingly, efforts to understand disease mechanisms have concentrated on the cell biology of amyloid-beta (Abeta) deposition as senile plaques or on the phosphorylation and aggregation of tau as NFTs. However, it now appears that this focus on pathology as a central contributor to disease may be misguided. Indeed, neurons associated with Abeta and NFTs in AD brain show a decrease in oxidative damage relative to those in vulnerable but morphologically intact areas of the brain, suggesting that neurodegenerative lesions are compensatory phenomena, and thus manifestations of cellular adaptation. That Abeta and tau accumulations indicate an age-related physiological reaction to chronic stress calls into question the rationale of current therapeutic efforts targeted toward lesion removal. Moreover, if this concept holds true for pathology in other neurodegenerative diseases, we may need to restructure our thinking and undergo a paradigm shift before substantial progress can be made in therapeutic intervention.     

Understanding risk and regulatory reform

There are few areas in regulation likely to cause more controversy than where risk, science and politics collide. While the case of Thalidomide shows that it is by no means an exclusively recent concern, David Vogel’s work confirms that it is an enduring theme of contemporary debate. Vogel has maintained that, while the American regulatory regime of the 1960s and 1970s may have been intensely contested, its European counterpart now displays significant similarities, so that the “Tortoise has now caught up with the Hare”. This article challenges such a view, suggesting that he has overstated the role of Precaution in European regulation, where it is qualified by other regulatory principles (BATNEEC, Proportionality and Subsidiarity) that embrace other socially valued objectives: economic growth, technological innovation and employment. Moreover, while the rhetoric of European regulation may evoke a concern with the role of science in regulation (often at the cutting edge, where precaution demands the evidentiary bar to intervention is lowered) in practise, its role (through risk assessments) has ensured that it is elevated.     

The effect of number of clusters and cluster size on statistical power and Type I error rates when testing random effects variance components in multilevel linear and logistic regression models

When using multilevel regression models that incorporate cluster-specific random effects, the Wald and the likelihood ratio (LR) tests are used for testing the null hypothesis that the variance of the random effects distribution is equal to zero. We conducted a series of Monte Carlo simulations to examine the effect of the number of clusters and the number of subjects per cluster on the statistical power to detect a non-null random effects variance and to compare the empirical type I error rates of the Wald and LR tests. Statistical power increased with increasing number of clusters and number of subjects per cluster. Statistical power was greater for the LR test than for the Wald test. These results applied to both the linear and logistic regressions, but were more pronounced for the latter. The use of the LR test is preferable to the use of the Wald test.