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Asymptotic Efficiency (asymptotic + efficiency)

Distribution by Scientific Domains
Mathematics and Statistics83%

Selected Abstracts

ASYMPTOTIC EFFICIENCY OF THE BLEST-TYPE TESTS FOR INDEPENDENCE

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 3 2008
Natalia Stepanova
Summary Blest (2000, Aust. N. Z. J. Stat. 42, 101,111) proposed a new measure of rank correlation that is sensitive to discrepancies in the small ranks. This paper investigates the efficiency properties of non-parametric tests for independence based on Blest's correlation coefficient and its modifications. Pitman efficiency comparisons are made with analogous tests existing in the literature. Conditions for Pitman optimality of the Blest-type tests are established. [source]

Exploring the performance of massively multithreaded architectures

CONCURRENCY AND COMPUTATION: PRACTICE & EXPERIENCE, Issue 5 2010
Shahid Bokhari
Abstract We present a new scheme for evaluating the performance of multithreaded computers and demonstrate its application to the Cray MTA-2 and XMT supercomputers. Our scheme is based on the concept of clock cycles per element, , plotted against both problem size and the number of processors. This scheme clearly shows if an implementation has achieved its asymptotic efficiency and is more general than (but includes) the commonly used speedup metric. It permits the discovery of any imperfections in both the software as well as the hardware, and is expected to permit a unified comparison of many different parallel architectures. Measurements on a number of well-known parallel algorithms, ranging from matrix multiply to quicksort, are presented for the MTA-2 and XMT and highlight some interesting differences between these machines. The performance of sequence alignment using dynamic programming is evaluated on the MTA-2, XMT, IBM x3755 and SGI Altix 350 and provides a useful comparison of the capabilities of the Cray machines with more conventional shared memory architectures. Copyright © 2009 John Wiley & Sons, Ltd. [source]

A unified approach to regression analysis under double-sampling designs

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 3 2000
Yi-Hau Chen
We propose a unified approach to the estimation of regression parameters under double-sampling designs, in which a primary sample consisting of data on the rough or proxy measures for the response and/or explanatory variables as well as a validation subsample consisting of data on the exact measurements are available. We assume that the validation sample is a simple random subsample from the primary sample. Our proposal utilizes a specific parametric model to extract the partial information contained in the primary sample. The resulting estimator is consistent even if such a model is misspecified, and it achieves higher asymptotic efficiency than the estimator based only on the validation data. Specific cases are discussed to illustrate the application of the estimator proposed. [source]

Maximum likelihood estimation of higher-order integer-valued autoregressive processes

JOURNAL OF TIME SERIES ANALYSIS, Issue 6 2008
Ruijun Bu
Abstract., In this article, we extend the earlier work of Freeland and McCabe [Journal of time Series Analysis (2004) Vol. 25, pp. 701,722] and develop a general framework for maximum likelihood (ML) analysis of higher-order integer-valued autoregressive processes. Our exposition includes the case where the innovation sequence has a Poisson distribution and the thinning is binomial. A recursive representation of the transition probability of the model is proposed. Based on this transition probability, we derive expressions for the score function and the Fisher information matrix, which form the basis for ML estimation and inference. Similar to the results in Freeland and McCabe (2004), we show that the score function and the Fisher information matrix can be neatly represented as conditional expectations. Using the INAR(2) specification with binomial thinning and Poisson innovations, we examine both the asymptotic efficiency and finite sample properties of the ML estimator in relation to the widely used conditional least squares (CLS) and Yule,Walker (YW) estimators. We conclude that, if the Poisson assumption can be justified, there are substantial gains to be had from using ML especially when the thinning parameters are large. [source]

An affine-invariant multivariate sign test for cluster correlated data

THE CANADIAN JOURNAL OF STATISTICS, Issue 4 2003
Denis Larocque
Abstract The author presents a multivariate location model for cluster correlated observations. He proposes an affine-invariant multivariate sign statistic for testing the value of the location parameter. His statistic is an adaptation of that proposed by Randles (2000). The author shows, under very mild conditions, that his test statistic is asymptotically distributed as a chi-squared random variable under the null hypothesis. In particular, the test can be used for skewed populations. In the context of a general multivariate normal model, the author obtains values of his test's Pitman asymptotic efficiency relative to another test based on the overall average. He shows that there is an improvement in the relative performance of the new test as soon as intra-cluster correlation is present Even in the univariate case, the new test can be very competitive for Gaussian data. Furthermore, the statistic is easy to compute, even for large dimensional data. The author shows through simulations that his test performs well compared to the average-based test. He illustrates its use with real data. L'auteur présente un modèle de position multivarié pour données corrélées en grappes. Il propose une statistique du signe multivarié affine-invariant permettant de tester la valeur du vecteur de position. Sa statistique est une adaptation de celle proposée par Randles (2000). L'auteur montre que sous des conditions peu restrictives, la loi asymptotique de sa statistique sous l'hypothèse nulle est celle du khi-deux. En particulier, le test peut ,tre utilisé avec des populations asymétriques. Dans le cadre d'un modèle multinormal général, l'auteur calcule les valeurs de l'efficacité asymptotique de Pitman de son test par rapport à un autre test basé sur la moyenne globale. Ses résultats montrent que la performance du nouveau test s'améliore en présence de corrélation intra-grappe. M,me dans le cas univarié, le nouveau test s'avère très performant pour des données gaussiennes. De plus, la statistique se calcule facilement, m,me en haute dimension. L'auteur montre par simulation que son test se comporte bien par rapport à celui fondé sur la moyenne globale. Il en illustre l'emploi au moyen de données réelles. [source]

Interpreting Statistical Evidence with Empirical Likelihood Functions

BIOMETRICAL JOURNAL, Issue 4 2009
Zhiwei Zhang
Abstract There has been growing interest in the likelihood paradigm of statistics, where statistical evidence is represented by the likelihood function and its strength is measured by likelihood ratios. The available literature in this area has so far focused on parametric likelihood functions, though in some cases a parametric likelihood can be robustified. This focused discussion on parametric models, while insightful and productive, may have left the impression that the likelihood paradigm is best suited to parametric situations. This article discusses the use of empirical likelihood functions, a well-developed methodology in the frequentist paradigm, to interpret statistical evidence in nonparametric and semiparametric situations. A comparative review of literature shows that, while an empirical likelihood is not a true probability density, it has the essential properties, namely consistency and local asymptotic normality that unify and justify the various parametric likelihood methods for evidential analysis. Real examples are presented to illustrate and compare the empirical likelihood method and the parametric likelihood methods. These methods are also compared in terms of asymptotic efficiency by combining relevant results from different areas. It is seen that a parametric likelihood based on a correctly specified model is generally more efficient than an empirical likelihood for the same parameter. However, when the working model fails, a parametric likelihood either breaks down or, if a robust version exists, becomes less efficient than the corresponding empirical likelihood. [source]