Minimum Divergence Estimators, Maximum Likelihood and the Generalized Bootstrap

This paper states that most commonly used minimum divergence estimators are MLEs for suited generalized bootstrapped sampling schemes. Optimality in the sense of Bahadur for associated tests of fit under such sampling is considered.

Informational Energy and Entropy Applied to Testing Exponentiality

The exponential distribution is widely used in reliability and life testing analysis. In this paper, two tests of fit for the exponential distribution based on Informational Energy and entropy are constructed. Consistency and other properties of the tests are proved. Using a simulation study, critical values of the proposed tests are obtained and then power values of tests are computed and compared with each other against various alternatives. Finally, we apply the tests for time between failures of secondary reactor pumps and waiting times for fatal plane accidents in the USA from 1983 to 1998.

A Revised Motor Activity Log Following Rasch Validation (Rasch-Based MAL-18) and Consensus Methods in Chronic Stroke and Multiple Sclerosis

Objectives. To derive a shorter version of the Motor Activity Log Quality-of-Movement Scale (MAL-28) with enhanced content and construct validity. Design. Validation cohort. Setting. Outpatient rehabilitation within an academic laboratory. Participants. Retrospective consecutive sample of 149 community-dwelling adults with chronic mild/moderate upper-extremity hemiparesis caused by stroke or multiple sclerosis (MS). Intervention. Not applicable. Methods. Participants received the MAL-28 at baseline and following upper-extremity rehabilitation. Rasch Measurement Theory informed threshold ordering of scoring categories, tests of fit, differential item functioning, targeting, response dependency, local dependency, and reliability (person separation index [PSI]). Seasoned examiners rated the content validity of each item. Test-retest reliability of the revised scale was calculated. Results. We established content and construct validity for 18 items. The resultant 18-item MAL fit the model (χ2 = 77.93; df = 72; P = .30) and targeted the population—that is, minimal floor (12.08%) or ceiling effects (0%), with acceptable reliability (PSI = 0.84) and good test-retest reliability [ICC(1, 1) = 0.86]. The hierarchy of item difficulty was independent of sex, age, affected side, diagnosis, or intervention type used, and there was local dependency in 3 pairs of items. Responses from a subsequent testing session were dependent on the responses from prior testing, indicating response dependency, for which a correction was proposed. Once response dependency was neutralized, there was a 15% greater treatment response. Conclusions. Content and construct validity are established for Rasch-based MAL-18 for chronic stages of stroke and MS. A Rasch-based conversion table enables clinical use of the MAL-18.

Evaluating Model Performance in Evolutionary Biology

Many fields of evolutionary biology now depend on stochastic mathematical models. These models are valuable for their ability to formalize predictions in the face of uncertainty and provide a quantitative framework for testing hypotheses. However, no mathematical model will fully capture biological complexity. Instead, these models attempt to capture the important features of biological systems using relatively simple mathematical principles. These simplifications can allow us to focus on differences that are meaningful, while ignoring those that are not. However, simplification also requires assumptions, and to the extent that these are wrong, so is our ability to predict or compare. Here, we discuss approaches for evaluating the performance of evolutionary models in light of their assumptions by comparing them against reality. We highlight general approaches, how they are applied, and remaining opportunities. Absolute tests of fit, even when not explicitly framed as such, are fundamental to progress in understanding evolution.

Smooth Tests of Fit for the Lindley Distribution

We consider the little-known one parameter Lindley distribution. This distribution may be of interest as it appears to be more flexible than the exponential distribution, the Lindley fitting more data than the exponential. We give smooth tests of fit for this distribution. The smooth test for the Lindley has power comparable with the Anderson-Darling test. Advantages of the smooth test are discussed. Examples that illustrate the flexibility of this distributions is given.