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Simultaneous Confidence Bands (simultaneous + confidence_bands)

Distribution by Scientific Domains
Mathematics and Statistics100%

Selected Abstracts

Construction of Exact Simultaneous Confidence Bands for a Simple Linear Regression Model

INTERNATIONAL STATISTICAL REVIEW, Issue 1 2008
Wei Liu
Summary A simultaneous confidence band provides a variety of inferences on the unknown components of a regression model. There are several recent papers using confidence bands for various inferential purposes; see for example, Sun et al. (1999), Spurrier (1999), Al-Saidy et al. (2003), Liu et al. (2004), Bhargava & Spurrier (2004), Piegorsch et al. (2005) and Liu et al. (2007). Construction of simultaneous confidence bands for a simple linear regression model has a rich history, going back to the work of Working & Hotelling (1929). The purpose of this article is to consolidate the disparate modern literature on simultaneous confidence bands in linear regression, and to provide expressions for the construction of exact 1 ,, level simultaneous confidence bands for a simple linear regression model of either one-sided or two-sided form. We center attention on the three most recognized shapes: hyperbolic, two-segment, and three-segment (which is also referred to as a trapezoidal shape and includes a constant-width band as a special case). Some of these expressions have already appeared in the statistics literature, and some are newly derived in this article. The derivations typically involve a standard bivariate t random vector and its polar coordinate transformation. Résumé Un intervalle de confiance simultanée fournit une variété d'inférences sur les composantes inconnues d'un modéle de régression. Plusieurs articles récents utilisent des intervalles de confiance dans des buts variés; voir par exemple Sun, Raz et Faraway (1999), Spurrier (1999), Al-Saidy et al. (2003), Liu, Jamshidian et Zhang (2004), Bhargava et Spurrier (2004), Piegorsch et al. (2005), Liu et al. (2007). La construction d'intervalles de confiance simultanés pour un simple modéle de régression linéaire a une histoire riche, qui remonte aux travaux de Working et hotelling (1929). L'objet de cet article est de consolider la littérature moderne disparate sur les intervalles de confiance simultanés dans la régression linéaire, de fournir des expressions pour la construction d'intervalles de confiance simultanés de niveau exact 1 ,, pour un modéle de régression linéaire simple ou pour des formes unilatérales ou bilatérales. Nous concentrons notre attention sur les trois formes les plus reconnues: hyperbolique, à deux segments et à trois segments (qui est aussi appelée forme trapézoïdale et inclut un intervalle de largeur constante comme cas spécial). Certaines de ces expressions sont déjà apparues dans la littérature statistique, d'autres sont nouvellement introduites dans cet article. Les dérivations comprennent typiquement un vecteur aléatoire standard bivarié t et sa transformation en coordonnées polaires. [source]

Functional Generalized Linear Models with Images as Predictors

BIOMETRICS, Issue 1 2010
Philip T. Reiss
Summary Functional principal component regression (FPCR) is a promising new method for regressing scalar outcomes on functional predictors. In this article, we present a theoretical justification for the use of principal components in functional regression. FPCR is then extended in two directions: from linear to the generalized linear modeling, and from univariate signal predictors to high-resolution image predictors. We show how to implement the method efficiently by adapting generalized additive model technology to the functional regression context. A technique is proposed for estimating simultaneous confidence bands for the coefficient function; in the neuroimaging setting, this yields a novel means to identify brain regions that are associated with a clinical outcome. A new application of likelihood ratio testing is described for assessing the null hypothesis of a constant coefficient function. The performance of the methodology is illustrated via simulations and real data analyses with positron emission tomography images as predictors. [source]

Confidence Bands for Low-Dose Risk Estimation with Quantal Response Data

BIOMETRICS, Issue 4 2003
Obaid M. Al-Saidy
Summary. We study the use of simultaneous confidence bands for low-dose risk estimation with quantal response data, and derive methods for estimating simultaneous upper confidence limits on predicted extra risk under a multistage model. By inverting the upper bands on extra risk, we obtain simultaneous lower bounds on the benchmark dose (BMD). Monte Carlo evaluations explore characteristics of the simultaneous limits under this setting, and a suite of actual data sets are used to compare existing methods for placing lower limits on the BMD. [source]