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Constructing Confidence Intervals (constructing + confidence_interval)

Distribution by Scientific Domains
Mathematics and Statistics40%

Selected Abstracts

A New Method for Constructing Confidence Intervals for the Index Cpm

QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, Issue 7 2004
Michael Perakis
Abstract In the statistical literature on the study of the capability of processes through the use of indices, Cpm appears to have been one of the most widely used capability indices and its estimation has attracted much interest. In this article, a new method for constructing approximate confidence intervals or lower confidence limits for this index is suggested. The method is based on an approximation of the non-central chi-square distribution, which was proposed by Pearson. Its coverage appears to be more satisfactory compared with that achieved by any of the two most widely used methods that were proposed by Boyles, in situations where one is interested in assessing a lower confidence limit for Cpm. This is supported by the results of an extensive simulation study. Copyright © 2004 John Wiley & Sons, Ltd. [source]

A two-step procedure for constructing confidence intervals of trait loci with application to a rheumatoid arthritis dataset

GENETIC EPIDEMIOLOGY, Issue 1 2006
Charalampos Papachristou
Abstract Preliminary genome screens are usually succeeded by fine mapping analyses focusing on the regions that signal linkage. It is advantageous to reduce the size of the regions where follow-up studies are performed, since this will help better tackle, among other things, the multiplicity adjustment issue associated with them. We describe a two-step approach that uses a confidence set inference procedure as a tool for intermediate mapping (between preliminary genome screening and fine mapping) to further localize disease loci. Apart from the usual Hardy-Weiberg and linkage equilibrium assumptions, the only other assumption of the proposed approach is that each region of interest houses at most one of the disease-contributing loci. Through a simulation study with several two-locus disease models, we demonstrate that our method can isolate the position of trait loci with high accuracy. Application of this two-step procedure to the data from the Arthritis Research Campaign National Repository also led to highly encouraging results. The method not only successfully localized a well-characterized trait contributing locus on chromosome 6, but also placed its position to narrower regions when compared to their LOD support interval counterparts based on the same data. Genet. Epidemiol. 30:18,29, 2006. © 2005 Wiley-Liss, Inc. [source]

Confidence Intervals for Unbalanced Two-factor Gauge R&R Studies

QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, Issue 8 2005
Liyun Gong
Abstract We consider methods for constructing confidence intervals in a two-factor gauge repeatability and reproducibility (R&R) study when there are unequal replicates. We consider both random and mixed models and propose a general approach using unweighted sums of squares. Computer simulation is used to determine how well confidence intervals maintain the stated confidence level. The main conclusion is that the method performs well under a variety of conditions typically encountered in gauge R&R studies. The method is simple and the intervals can be computed in a spreadsheet program. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Confidence Intervals for Relative Risks in Disease Mapping

BIOMETRICAL JOURNAL, Issue 4 2003
M.D. Ugarte
Abstract Several analysis of the geographic variation of mortality rates in space have been proposed in the literature. Poisson models allowing the incorporation of random effects to model extra-variability are widely used. The typical modelling approach uses normal random effects to accommodate local spatial autocorrelation. When spatial autocorrelation is absent but overdispersion persists, a discrete mixture model is an alternative approach. However, a technique for identifying regions which have significant high or low risk in any given area has not been developed yet when using the discrete mixture model. Taking into account the importance that this information provides to the epidemiologists to formulate hypothesis related to the potential risk factors affecting the population, different procedures for obtaining confidence intervals for relative risks are derived in this paper. These methods are the standard information-based method and other four, all based on bootstrap techniques, namely the asymptotic-bootstrap, the percentile-bootstrap, the BC-bootstrap and the modified information-based method. All of them are compared empirically by their application to mortality data due to cardiovascular diseases in women from Navarra, Spain, during the period 1988,1994. In the small area example considered here, we find that the information-based method is sensible at estimating standard errors of the component means in the discrete mixture model but it is not appropriate for providing standard errors of the estimated relative risks and hence, for constructing confidence intervals for the relative risk associated to each region. Therefore, the bootstrap-based methods are recommended for this matter. More specifically, the BC method seems to provide better coverage probabilities in the case studied, according to a small scale simulation study that has been carried out using a scenario as encountered in the analysis of the real data. [source]

Likelihood Analysis for the Ratio of Means of Two Independent Log-Normal Distributions

BIOMETRICS, Issue 2 2002
Jianrong Wu
Summary. Existing methods for comparing the means of two independent skewed log-normal distributions do not perform well in a range of small-sample settings such as a small-sample bioavailability study. In this article, we propose two likelihood-based approaches,the signed log-likelihood ratio statistic and modified signed log-likelihood ratio statistic,for inference about the ratio of means of two independent log-normal distributions. More specifically, we focus on obtaining p -values for testing the equality of means and also constructing confidence intervals for the ratio of means. The performance of the proposed methods is assessed through simulation studies that show that the modified signed log-likelihood ratio statistic is nearly an exact approach even for very small samples. The methods are also applied to two real-life examples. [source]