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A self-normalized confidence interval for the mean of a class of nonstationary processes.

ABSTRACT: We construct an asymptotic confidence interval for the mean of a class of nonstationary processes with constant mean and time-varying variances. Due to the large number of unknown parameters, traditional approaches based on consistent estimation of the limiting variance of sample mean through moving block or non-overlapping block methods are not applicable. Under a block-wise asymptotically equal cumulative variance assumption, we propose a self-normalized confidence interval that is robust against the nonstationarity and dependence structure of the data. We also apply the same idea to construct an asymptotic confidence interval for the mean difference of nonstationary processes with piecewise constant means. The proposed methods are illustrated through simulations and an application to global temperature series.

SUBMITTER: Zhao Z

PROVIDER: S-EPMC3852676 | biostudies-literature | 2011

REPOSITORIES: biostudies-literature

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A self-normalized confidence interval for the mean of a class of nonstationary processes.

Zhao Zhibiao Z

Biometrika 20110101 1

We construct an asymptotic confidence interval for the mean of a class of nonstationary processes with constant mean and time-varying variances. Due to the large number of unknown parameters, traditional approaches based on consistent estimation of the limiting variance of sample mean through moving block or non-overlapping block methods are not applicable. Under a block-wise asymptotically equal cumulative variance assumption, we propose a self-normalized confidence interval that is robust agai ...[more]

PMID: 24319293

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Project description:BackgroundThe intraclass correlation coefficient (ICC) is widely used in biomedical research to assess the reproducibility of measurements between raters, labs, technicians, or devices. For example, in an inter-rater reliability study, a high ICC value means that noise variability (between-raters and within-raters) is small relative to variability from patient to patient. A confidence interval or Bayesian credible interval for the ICC is a commonly reported summary. Such intervals can be constructed employing either frequentist or Bayesian methodologies.MethodsThis study examines the performance of three different methods for constructing an interval in a two-way, crossed, random effects model without interaction: the Generalized Confidence Interval method (GCI), the Modified Large Sample method (MLS), and a Bayesian method based on a noninformative prior distribution (NIB). Guidance is provided on interval construction method selection based on study design, sample size, and normality of the data. We compare the coverage probabilities and widths of the different interval methods.ResultsWe show that, for the two-way, crossed, random effects model without interaction, care is needed in interval method selection because the interval estimates do not always have properties that the user expects. While different methods generally perform well when there are a large number of levels of each factor, large differences between the methods emerge when the number of one or more factors is limited. In addition, all methods are shown to lack robustness to certain hard-to-detect violations of normality when the sample size is limited.ConclusionsDecision rules and software programs for interval construction are provided for practical implementation in the two-way, crossed, random effects model without interaction. All interval methods perform similarly when the data are normal and there are sufficient numbers of levels of each factor. The MLS and GCI methods outperform the NIB when one of the factors has a limited number of levels and the data are normally distributed or nearly normally distributed. None of the methods work well if the number of levels of a factor are limited and data are markedly non-normal. The software programs are implemented in the popular R language.

Dataset Information

A self-normalized confidence interval for the mean of a class of nonstationary processes.

Publications

A self-normalized confidence interval for the mean of a class of nonstationary processes.

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