Topic
Coverage probability
About: Coverage probability is a research topic. Over the lifetime, 2479 publications have been published within this topic receiving 53259 citations.
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TL;DR: In this article, the authors proposed to approximate simultaneous confidence intervals by approximating R with the closest one-factor structure correlation matrix, which is the correlation matrix R of the estimators of Θ 1, Θ 2, Θ 3.
Abstract: Consider the general linear model (GLM) Y = Xβ + e. Suppose Θ1,…, Θk, a subset of the β's, are of interest; Θ1,…, Θk may be treatment contrasts in an ANOVA setting or regression coefficients in a response surface setting. Existing simultaneous confidence intervals for Θ1,…, Θk are relatively conservative or, in the case of the MEANS option in PROC GLM of SAS, possibly misleading. The difficulty is with the multidimensionality of the integration required to compute exact coverage probability when X does not follow a nice textbook design. Noting that such exact coverage probabilities can be computed if the correlation matrix R of the estimators of Θ1, …, Θk has a one-factor structure in the factor analytic sense, it is proposed that approximate simultaneous confidence intervals be computed by approximating R with the closest one-factor structure correlation matrix. Computer simulations of hundreds of randomly generated designs in the settings of regression, analysis of covariance, and unbalanced bl...
107 citations
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TL;DR: This letter proposes a novel approach to directly formulate the prediction intervals of wind power generation based on extreme learning machine and particle swarm optimization, where prediction intervals are generated through direct optimization of both the coverage probability and sharpness, without the prior knowledge of forecasting errors.
Abstract: This letter proposes a novel approach to directly formulate the prediction intervals of wind power generation based on extreme learning machine and particle swarm optimization, where prediction intervals are generated through direct optimization of both the coverage probability and sharpness, without the prior knowledge of forecasting errors. The proposed approach has been proved to be highly efficient and reliable through preliminary case studies using real-world wind farm data, indicating a high potential of practical application.
104 citations
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TL;DR: In this article, the authors provide an analytical framework to analyze heterogeneous downlink millimeter-wave (mm-wave) cellular networks consisting of $K$ tiers of randomly located base stations (BSs), where each tier operates in an mm-wave frequency band.
Abstract: In this paper, we provide an analytical framework to analyze heterogeneous downlink millimeter-wave (mm-wave) cellular networks consisting of $K$ tiers of randomly located base stations (BSs), where each tier operates in an mm-wave frequency band. Signal-to-interference-plus-noise ratio (SINR) coverage probability is derived for the entire network using tools from stochastic geometry. The distinguishing features of mm-wave communications, such as directional beamforming, and having different path loss laws for line-of-sight and non-line-of-sight links are incorporated into the coverage analysis by assuming averaged biased-received power association and Nakagami fading. By using the noise-limited assumption for mm-wave networks, a simpler expression requiring the computation of only one numerical integral for coverage probability is obtained. Also, the effect of beamforming alignment errors on the coverage probability analysis is investigated to get insight on the performance in practical scenarios. Downlink rate coverage probability is derived as well to get more insights on the performance of the network. Moreover, the effect of deploying low-power smaller cells and the impact of biasing factor on energy efficiency is analyzed. Finally, a hybrid cellular network operating in both mm-wave and $\mu$ -wave frequency bands is addressed.
104 citations
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TL;DR: Asymptotic confidence bands in non-parametric regression are constructed based on an undersmoothed local polynomial estimator and certain rates are derived for the error in coverage probability, which improves on existing results for methods that rely on the asymPTotic distribution of the maximum of some Gaussian process.
Abstract: In the present paper we construct asymptotic confidence bands in non-parametric regression. Our assumptions cover unequal variances of the observations and nonuni-form, possibly considerably clustered design. The confidence band is based on an undersmoothed local polynomial estimator. An appropriate quantile is obtained via the wild bootstrap. We derive certain rates (in the sample size n) for the error in coverage probability, which improves on existing results for methods that rely on the asymptotic distribution of the maximum of some Gaussian process. We propose a practicable rule for a data-dependent choice of the band-width. A small simulation study illustrates the possible gains by our approach over alternative frequently used methods.
104 citations
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TL;DR: In this paper, the conditional and overall coverage probabilities of a variable X to be predicted and the learning sample Yn that was observed have a joint distribution, which depends on an unknown parameter θ.
Abstract: Suppose that the variable X to be predicted and the learning sample Yn that was observed have a joint distribution, which depends on an unknown parameter θ. The parameter θ can be finite- or infinite-dimensional. A prediction region Dn for X is a random set, depending on Yn , that contains X with prescribed probability α. This article studies methods for controlling simultaneously the conditional coverage proability of Dn , given Yn , and the overall (unconditional) coverage probability of Dn . The basic construction yields a prediction region Dn , which has the following properties in regular models: Both the conditional and overall coverage probabilities of Dn converge to α as the size n of the learning sample increases. The convergence of the former is in probability. Moreover, the asymptotic distribution of the conditional coverage probability about α is typically normal; and the overall coverage probability tends to α at rate n −1. Can one reduce the dispersion of the conditional coverage pr...
103 citations