Optimal Tests for Combining p-Values

Combining information (p-values) obtained from individual studies to test whether there is an overall effect is an important task in statistical data analysis. Many classical statistical tests, such as chi-square tests, can be viewed as being a p-value combination approach. It remains challenging to find powerful methods to combine p-values obtained from various sources. In this paper, we study a class of p-value combination methods based on gamma distribution. We show that this class of tests is optimal under certain conditions and several existing popular methods are equivalent to its special cases. An asymptotically and uniformly most powerful p-value combination test based on constrained likelihood ratio test is then studied. Numeric results from simulation study and real data examples demonstrate that the proposed tests are robust and powerful under many conditions. They have potential broad applications in statistical inference.

Evaluation of Bedside Tests of Attention and Arousal Assessing Delirium in Parkinson’s Disease, Dementia, and Older Adults

Background: Delirium is a serious acute neuropsychiatric condition associated with altered attention and arousal. Objective: To evaluate simple bedside tests for attention and arousal to detect delirium in those with and without Parkinson’s disease (PD) and dementia. Methods: Participants from two prospective delirium studies were pooled comprising 30 with PD without cognitive impairment, 24 with Lewy body cognitive impairment (PD dementia or dementia with Lewy bodies), 16 with another dementia and 179 PD and dementia-free older adults. Participants completed standardised delirium assessments including tests of attention: digit span, Memorial Delirium Assessment Scale (MDAS) attention and months of the year backwards; and arousal: Glasgow Coma Scale (GSC), Observational Scale of Level of Arousal (OSLA), Modified Richmond Agitation Scale and MDAS consciousness. Delirium was diagnosed using the DSM-5 criteria. Results: On their first admission, 21.7%participants had prevalent delirium. Arousal measures accurately detected delirium in all participants (p < 0.01 for all), but only selected attention measures detected delirium in PD and dementia. In PD and dementia-free older adults, impaired digit span and OSLA were the optimal tests to detect delirium (area under the curve [AUC] = 0.838, p < 0.001) while in PD and dementia the optimal tests were MDAS attention and GCS LB. Conclusion: Simple bedside tests of attention and arousal at a single visit could accurately detect delirium in PD, dementia and PD and dementia-free older adults; however, the optimal tests differed between groups. Combined attention and arousal scores increased accuracy, which could have clinical utility to aid the identification of delirium neurodegenerative disorders.

On the testing hypothesis in uniform family of distributions with nuisance parameter

The problem of finding optimal tests in the family of uniform distributions is investigated. The general forms of the uniformly most powerful and generalized likelihood ratio tests are derived. Moreover, the problem of finding the uniformly most powerful unbiased test for testing two-sided hypothesis in the presence of nuisance parameter is investigated, and it is shown that such a test is equivalent to the generalized likelihood ratio test for the same problem. The simulation study is performed to evaluate the performance of power function of the tests.

Testable forecasts

Predictions about the future are commonly evaluated through statistical tests. As shown by recent literature, many known tests are subject to adverse selection problems and cannot discriminate between forecasters who are competent and forecasters who are uninformed but predict strategically. We consider a framework where forecasters' predictions must be consistent with a paradigm, a set of candidate probability laws for the stochastic process of interest. This paper presents necessary and sufficient conditions on the paradigm under which it is possible to discriminate between informed and uninformed forecasters. We show that optimal tests take the form of likelihood‐ratio tests comparing forecasters' predictions against the predictions of a hypothetical Bayesian outside observer. In addition, the paper illustrates a new connection between the problem of testing strategic forecasters and the classical Neyman–Pearson paradigm of hypothesis testing.

Optimal Detection of Bilinear Dependence in Short Panels of Regression Data

In this paper, we propose parametric and nonparametric locally andasymptotically optimal tests for regression models with superdiagonal bilinear time series errors in short panel data (large n, small T). We establish a local asymptotic normality property– with respect to intercept μ, regression coefficient β, the scale parameter σ of the error, and the parameter b of panel superdiagonal bilinear model (which is the parameter of interest)– for a given density f1 of the error terms. Rank-based versions of optimal parametric tests are provided. This result, which allows, by Hájek’s representation theorem, the construction of locally asymptotically optimal rank-based tests for the null hypothesis b = 0 (absence of panel superdiagonal bilinear model). These tests –at specified innovation densities f1– are optimal (most stringent), but remain valid under any actual underlying density. From contiguity, we obtain the limiting distribution of our test statistics under the null and local sequences of alternatives. The asymptotic relative efficiencies, with respect to the pseudo-Gaussian parametric tests, are derived. A Monte Carlo study confirms the good performance of the proposed tests.

Development of Hyperset Paging mechanism

Algorithms for page replacement play important roles in virtual memory management, especially in paging operating systems. Page substitution happens when the required page is not retained in the memory (file fault) or the free accessible file is not adequate to fulfill the requirement. It is either there are none or the amount of free sites is fewer than the required total. Two regular page replacements were hybridized as Hybrid Page replacements (HRA) in this analysis (LRU and OptimalOPT algorithms recently used). For its service, HRA is based on the principle of OPT and LRU. The HRA was determined by comparing the page failures caused with the default algorithms First InFirst Out FIFO, LRU and Optimal. Tests showed the amount of frames through to 4 and beyond the HRA outperformed FIFO, OPT and LRU.

Distributions You Can Count On …But What’s the Point?

The Poisson regression model remains an important tool in the econometric analysis of count data. In a pioneering contribution to the econometric analysis of such models, Lung-Fei Lee presented a specification test for a Poisson model against a broad class of discrete distributions sometimes called the Katz family. Two members of this alternative class are the binomial and negative binomial distributions, which are commonly used with count data to allow for under- and over-dispersion, respectively. In this paper we explore the structure of other distributions within the class and their suitability as alternatives to the Poisson model. Potential difficulties with the Katz likelihood leads us to investigate a class of point optimal tests of the Poisson assumption against the alternative of over-dispersion in both the regression and intercept only cases. In a simulation study, we compare score tests of ‘Poisson-ness’ with various point optimal tests, based on the Katz family, and conclude that it is possible to choose a point optimal test which is better in the intercept only case, although the nuisance parameters arising in the regression case are problematic. One possible cause is poor choice of the point at which to optimize. Consequently, we explore the use of Hellinger distance to aid this choice. Ultimately we conclude that score tests remain the most practical approach to testing for over-dispersion in this context.