Search results for "Nuisance parameter"
showing 4 items of 4 documents
On the moments of Cochran's Q statistic under the null hypothesis, with application to the meta-analysis of risk difference.
2011
W. G. Cochran's Q statistic was introduced in 1937 to test for equality of means under heteroscedasticity. Today, the use of Q is widespread in tests for homogeneity of effects in meta-analysis, but often these effects (such as risk differences and odds ratios) are not normally distributed. It is common to assume that Q follows a chi-square distribution, but it has long been known that this asymptotic distribution for Q is not accurate for moderate sample sizes. In this paper, the effect and weight for an individual study may depend on two parameters: the effect and a nuisance parameter. We present expansions for the first two moments of Q without any normality assumptions. Our expansions w…
Multivariate equivalence tests for use in pharmaceutical development.
2014
Statistical equivalence analyses are well-established parts of many studies in the biomedical sciences. Also in pharmaceutical development and manufacturing equivalence testing methods are required in order to statistically establish similarities between machines, process components, or complete processes. This article presents a choice of multivariate equivalence testing procedures for normally distributed data as generalizations of existing univariate methods. In all derived methods, variability is interpreted as nuisance parameter. The use of the proposed methods in pharmaceutical development is demonstrated with a comparative analysis of dissolution profiles.
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…
Bayesian measures of surprise for outlier detection
2003
From a Bayesian point of view, testing whether an observation is an outlier is usually reduced to a testing problem concerning a parameter of a contaminating distribution. This requires elicitation of both (i) the contaminating distribution that generates the outlier and (ii) prior distributions on its parameters. However, very little information is typically available about how the possible outlier could have been generated. Thus easy, preliminary checks in which these assessments can often be avoided may prove useful. Several such measures of surprise are derived for outlier detection in normal models. Results are applied to several examples. Default Bayes factors, where the contaminating…