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Coverage Properties (coverage + property)

Distribution by Scientific Domains
Mathematics and Statistics83%

Kinds of Coverage Properties

  • good coverage property
    		•

    Selected Abstracts

    Small-sample confidence intervals for multivariate impulse response functions at long horizons

    JOURNAL OF APPLIED ECONOMETRICS, Issue 8 2006
    Elena Pesavento
    Existing methods for constructing confidence bands for multivariate impulse response functions may have poor coverage at long lead times when variables are highly persistent. The goal of this paper is to propose a simple method that is not pointwise and that is robust to the presence of highly persistent processes. We use approximations based on local-to-unity asymptotic theory, and allow the horizon to be a fixed fraction of the sample size. We show that our method has better coverage properties at long horizons than existing methods, and may provide different economic conclusions in empirical applications. We also propose a modification of this method which has good coverage properties at both short and long horizons. Copyright © 2006 John Wiley & Sons, Ltd. [source]

    Parameter estimation for differential equations: a generalized smoothing approach

    JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 5 2007
    J. O. Ramsay
    Summary., We propose a new method for estimating parameters in models that are defined by a system of non-linear differential equations. Such equations represent changes in system outputs by linking the behaviour of derivatives of a process to the behaviour of the process itself. Current methods for estimating parameters in differential equations from noisy data are computationally intensive and often poorly suited to the realization of statistical objectives such as inference and interval estimation. The paper describes a new method that uses noisy measurements on a subset of variables to estimate the parameters defining a system of non-linear differential equations. The approach is based on a modification of data smoothing methods along with a generalization of profiled estimation. We derive estimates and confidence intervals, and show that these have low bias and good coverage properties respectively for data that are simulated from models in chemical engineering and neurobiology. The performance of the method is demonstrated by using real world data from chemistry and from the progress of the autoimmune disease lupus. [source]

    Modeling multiple-response categorical data from complex surveys

    THE CANADIAN JOURNAL OF STATISTICS, Issue 4 2009
    Christopher R. Bilder
    Abstract Although "choose all that apply" questions are common in modern surveys, methods for analyzing associations among responses to such questions have only recently been developed. These methods are generally valid only for simple random sampling, but these types of questions often appear in surveys conducted under more complex sampling plans. The purpose of this article is to provide statistical analysis methods that can be applied to "choose all that apply" questions in complex survey sampling situations. Loglinear models are developed to incorporate the multiple responses inherent in these types of questions. Statistics to compare models and to measure association are proposed and their asymptotic distributions are derived. Monte Carlo simulations show that tests based on adjusted Pearson statistics generally hold their correct size when comparing models. These simulations also show that confidence intervals for odds ratios estimated from loglinear models have good coverage properties, while being shorter than those constructed using empirical estimates. Furthermore, the methods are shown to be applicable to more general problems of modeling associations between elements of two or more binary vectors. The proposed analysis methods are applied to data from the National Health and Nutrition Examination Survey. The Canadian Journal of Statistics © 2009 Statistical Society of Canada Quoique les questions du type « Sélectionner une ou plusieurs réponses » sont courantes dans les enquêtes modernes, les méthodes pour analyser les associations entre les réponses à de telles questions viennent seulement d'être développées. Ces méthodes sont habituellement valides uni-quement pour des échantillons aléatoires simples, mais ce genre de questions apparaissent souvent dans les enquêtes conduites sous des plans de sondage beaucoup plus complexes. Le but de cet article est de donner des méthodes d'analyse statistique pouvant être appliquées aux questions de type « Sélectionner une ou plusieurs réponses » dans des enquêtes utilisant des plans de sondage complexes. Des modèles loglinéaires sont développés permettant d'incorporer les réponses multiples inhérentes à ce type de questions. Des statistiques permettant de comparer les modèles et de mesu-rer l'association sont proposées et leurs distributions asymptotiques sont obtenues. Des simulations de Monte-Carlo montrent que les tests basés sur les statistiques de Pearson ajustées maintiennent généralement leur niveau lorsqu'ils sont utilisés pour comparer des modèles. Ces études montrent également que les niveaux des intervalles de confiance pour les rapports de cotes estimés à par-tir des modèles loglinéaires ont de bonnes propriétés de couverture tout en étant plus courts que ceux utilisant les estimations empiriques. De plus, il est montré que ces méthodes peuvent aussi êtres utilisées dans un contexte plus général de modélisation de l'association entre les éléments de deux ou plusieurs vecteurs binaires. Les méthodes d'analyse proposées sont appliquées à des données provenant de l'étude américaine « National Health and Nutrition Examination Survey » (NHANES). La revue canadienne de statistique © 2009 Société statistique du Canada [source]

    UPPER BOUNDS ON THE MINIMUM COVERAGE PROBABILITY OF CONFIDENCE INTERVALS IN REGRESSION AFTER MODEL SELECTION

    AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 3 2009
    Paul Kabaila
    Summary We consider a linear regression model, with the parameter of interest a specified linear combination of the components of the regression parameter vector. We suppose that, as a first step, a data-based model selection (e.g. by preliminary hypothesis tests or minimizing the Akaike information criterion , AIC) is used to select a model. It is common statistical practice to then construct a confidence interval for the parameter of interest, based on the assumption that the selected model had been given to us,a priori. This assumption is false, and it can lead to a confidence interval with poor coverage properties. We provide an easily computed finite-sample upper bound (calculated by repeated numerical evaluation of a double integral) to the minimum coverage probability of this confidence interval. This bound applies for model selection by any of the following methods: minimum AIC, minimum Bayesian information criterion (BIC), maximum adjusted,R2, minimum Mallows' CP and,t -tests. The importance of this upper bound is that it delineates general categories of design matrices and model selection procedures for which this confidence interval has poor coverage properties. This upper bound is shown to be a finite-sample analogue of an earlier large-sample upper bound due to Kabaila and Leeb. [source]

    Estimating Disease Prevalence Using Relatives of Case and Control Probands

    BIOMETRICS, Issue 1 2010
    Kristin N. Javaras
    Summary We introduce a method of estimating disease prevalence from case,control family study data. Case,control family studies are performed to investigate the familial aggregation of disease; families are sampled via either a case or a control proband, and the resulting data contain information on disease status and covariates for the probands and their relatives. Here, we introduce estimators for overall prevalence and for covariate-stratum-specific (e.g., sex-specific) prevalence. These estimators combine the proportion of affected relatives of control probands with the proportion of affected relatives of case probands and are designed to yield approximately unbiased estimates of their population counterparts under certain commonly made assumptions. We also introduce corresponding confidence intervals designed to have good coverage properties even for small prevalences. Next, we describe simulation experiments where our estimators and intervals were applied to case,control family data sampled from fictional populations with various levels of familial aggregation. At all aggregation levels, the resulting estimates varied closely and symmetrically around their population counterparts, and the resulting intervals had good coverage properties, even for small sample sizes. Finally, we discuss the assumptions required for our estimators to be approximately unbiased, highlighting situations where an alternative estimator based only on relatives of control probands may perform better. [source]

    A Semiparametric Estimate of Treatment Effects with Censored Data

    BIOMETRICS, Issue 3 2001
    Ronghui Xu
    Summary. A semiparametric estimate of an average regression effect with right-censored failure time data has recently been proposed under the Cox-type model where the regression effect ,(t) is allowed to vary with time. In this article, we derive a simple algebraic relationship between this average regression effect and a measurement of group differences in K -sample transformation models when the random error belongs to the Gp family of Harrington and Fleming (1982, Biometrika69, 553,566), the latter being equivalent to the conditional regression effect in a gamma frailty model. The models considered here are suitable for the attenuating hazard ratios that often arise in practice. The results reveal an interesting connection among the above three classes of models as alternatives to the proportional hazards assumption and add to our understanding of the behavior of the partial likelihood estimate under nonproportional hazards. The algebraic relationship provides a simple estimator under the transformation model. We develop a variance estimator based on the empirical influence function that is much easier to compute than the previously suggested resampling methods. When there is truncation in the right tail of the failure times, we propose a method of bias correction to improve the coverage properties of the confidence intervals. The estimate, its estimated variance, and the bias correction term can all be calculated with minor modifications to standard software for proportional hazards regression. [source]