Search results for "Test statistic"

Testing for homogeneity in meta-analysis I. The one-parameter case: standardized mean difference.

2010

Meta-analysis seeks to combine the results of several experiments in order to improve the accuracy of decisions. It is common to use a test for homogeneity to determine if the results of the several experiments are sufficiently similar to warrant their combination into an overall result. Cochran's Q statistic is frequently used for this homogeneity test. It is often assumed that Q follows a chi-square distribution under the null hypothesis of homogeneity, but it has long been known that this asymptotic distribution for Q is not accurate for moderate sample sizes. Here, we present an expansion for the mean of Q under the null hypothesis that is valid when the effect and the weight for each s…

Test Procedures in Configural Frequency Analysis (CFA) Controlling the Local and Multiple Level

1987

The test statistics used until now in the CFA have been developed under the assumption of the overall hypothesis of total independence. Therefore, the multiple test procedures based on these statistics are really only different tests of the overall hypothesis. If one likes to test a special cell hypothesis, one should only assume that this hypothesis is true and not the whole overall hypothesis. Such cell tests can then be used as elements of a multiple test procedure. In this paper it is shown that the usual test procedures can be very anticonservative (except of the two-dimensional, and, for some procedures, the three-dimensional case), and corrected test procedures are developed. Further…

Sign test of independence between two random vectors

2003

A new affine invariant extension of the quadrant test statistic Blomqvist (Ann. Math. Statist. 21 (1950) 593) based on spatial signs is proposed for testing the hypothesis of independence. In the elliptic case, the new test statistic is asymptotically equivalent to the interdirection test by Gieser and Randles (J. Amer. Statist. Assoc. 92 (1997) 561) but is easier to compute in practice. Limiting Pitman efficiencies and simulations are used to compare the test to the classical Wilks’ test. peerReviewed

A Modification of Stone's Test for Trend for Binary Outcome

1998

STONE (1988) suggested the first isotonic regression estimator as a tool for drawing inferences on possibly increased cancer case counts among several subregions around a putative source. He assumed the case counts to be Poisson distributed and therefore introduced a rare disease assumption into his approach. However, when analyzing cross sectional data one would rather refer to prevalence estimates among these subregions around a point risk source (for example the origin of chemical fallout). Therefore we applied antitonic regression estimation in Binomial distributions to derive a test statistic and a p value to test for a possible trend in the observed prevalence data around the putative…

2019

In the independent component model, the multivariate data are assumed to be a mixture of mutually independent latent components. The independent component analysis (ICA) then aims at estimating these latent components. In this article, we study an ICA method which combines the use of linear and quadratic autocorrelations to enable efficient estimation of various kinds of stationary time series. Statistical properties of the estimator are studied by finding its limiting distribution under general conditions, and the asymptotic variances are derived in the case of ARMA-GARCH model. We use the asymptotic results and a finite sample simulation study to compare different choices of a weight coef…

Sample-size calculation and reestimation for a semiparametric analysis of recurrent event data taking robust standard errors into account

2014

In some clinical trials, the repeated occurrence of the same type of event is of primary interest and the Andersen-Gill model has been proposed to analyze recurrent event data. Existing methods to determine the required sample size for an Andersen-Gill analysis rely on the strong assumption that all heterogeneity in the individuals' risk to experience events can be explained by known covariates. In practice, however, this assumption might be violated due to unknown or unmeasured covariates affecting the time to events. In these situations, the use of a robust variance estimate in calculating the test statistic is highly recommended to assure the type I error rate, but this will in turn decr…

Rejoinder: Bayesian Checking of the Second Levels of Hierarchical Models

2008

Rejoinder: Bayesian Checking of the Second Levels of Hierarchical Models [arXiv:0802.0743]

The “ThreePlusOne” Likelihood-Based Test Statistics: Unified Geometrical and Graphical Interpretations

2014

The presentation of the well known Likelihood Ratio, Wald and Score test statistics in textbooks appears to lack a unified graphical and geometrical interpretation. We present two simple graphical representations on a common scale for these three test statistics, and also the recently proposed Gradient test statistic. These unified graphical displays may favour better understanding of the geometrical meaning of the likelihood based statistics and provide useful insights into their connections.

Testing with a nuisance parameter present only under the alternative: a score-based approach with application to segmented modelling

2016

ABSTRACTWe introduce a score-type statistic to test for a non-zero regression coefficient when the relevant term involves a nuisance parameter present only under the alternative. Despite the non-regularity and complexity of the problem and unlike the previous approaches, the proposed test statistic does not require the nuisance to be estimated. It is simple to implement by relying on the conventional distributions, such as Normal or t, and it justified in the setting of probabilistic coherence. We focus on testing for the existence of a breakpoint in segmented regression, and illustrate the methodology with an analysis on data of DNA copy number aberrations and gene expression profiles from…