Large Sample Simultaneous Confidence Intervals for Multinomial Proportions

Quesenberry, C. P.; Hurst, David C.

doi:10.1080/00401706.1964.10490163

Cited by 113 publications

(47 citation statements)

References 2 publications

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“…These simultaneous intervals are based on the Bonferroni inequality and on the assumption that for large samples the ni are normally distributed with mean Nqi and variance Nqi(lq i ) . The above simultaneous confidence interval is accurate for large samples, and Quesenberry and Hurst [24] suggest that a sufficiently large N is one for which the smallest to apply. In other words, using samples sizes based loosely on the Chebyshev bound for binomial data (50,000 in our case) and, in addition, using only those estimates whose proportion estimate Qi exceeds l/(d + 1) conservatively justifies the use of the large sample statistics; that is, we use as constraints those coefficients whose proportion estimates qi exceed l/(d + 1) = 1/14 = 0.0714, and hence, estimates fi9, .…”

Section: Combining Monte Carlo Estimates and Boundsmentioning

confidence: 79%

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Combining monte carlo estimates and bounds for network reliability

Nel

Colbourn

1990

Networks

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A simplified model of a communications network is a probabilistic graph in which each edge operates with the same probability. The all-terminal reliability, or probability that all nodes are connected, can be expressed as a polynomial in the edge operation probability. The coefficients of this polynomial are obtained from an interval partitioning of the cographic matroid, and only the first few coefficients can be computed efficiently. One of the best sets of efficiently computable reliability bounds is the Ball-Provan bounds. These bounds are obtained using the efficiently computable coefficients and can be improved substantially if additional coefficients are known. In this paper, we develop a Monte Carlo method for estimating additional coefficients by randomly sampling over spanning trees of the network. Confidence intervals for all-terminal reliability are obtained by using these estimates as additional constraints in the Ball-Provan bounds. This approach has some advantages over conventional Monte Carlo point estimate methods. In particular, the computational complexity does not depend on the reliability of the network.The communication links of a large computer or communications network can be unreliable, affecting node-to-node communications. A simplified model of the topology of such a network is a probabilistic graph G = ( V , E ) consisting of a set V of n nodes, representing communication centers, and a set E of m edges, representing communication links. In addition, each edge e E E has an independent probability p e of being operational. In this paper, we consider only the case in which each edge operates with the same probability p .Since links are unreliable, a link may at any instant be operating or failed. A state of the network is a set S E of edges that represents the operating edges. The probability, P ( S ) , that the network is in state S is n e E s p rIeEE-S (1 -p ) . A state S is operational if all the nodes in the graph G' = ( V , S) are connected, that is, if G' contains at least a spanning tree. Define the binary functions r ( S ) to be 1 if state S is operational, and 0 otherwise.

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Section: Combining Monte Carlo Estimates and Boundsmentioning

confidence: 79%

“…, nk, Cf==, ni = N are the observed frequencies in N samples of a multinomial population with k classes, 1 -6. Quesenberry and Hurst [24] give the following simultaneous confidence intervals:…”

Section: Combining Monte Carlo Estimates and Boundsmentioning

confidence: 99%

Combining monte carlo estimates and bounds for network reliability

Nel

Colbourn

1990

Networks

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“…The resulting proportions for each outcome were then calculated for each chemical. Confidence intervals were then formed for each proportion using Goodman's (1965) tighter alternative to Quesenberry and Hurst's (1964) confidence intervals for simultaneous inference on multinomial probabilities. It was found that there were statistically significant (5% level) differences between northern and southern sites for each chemical except styrene.…”

Section: Methodsmentioning

confidence: 99%

Spatial analysis of volatile organic compounds in South Philadelphia using passive samplers

Mukerjee

Smith

Thoma

et al. 2016

Journal of the Air & Waste Management Association

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Select volatile organic compounds (VOCs) were measured in the vicinity of a petroleum refinery and related operations in South Philadelphia, Pennsylvania, USA, using passive air sampling and laboratory analysis methods. Two-week, time-integrated samplers were deployed at 17 sites, which were aggregated into five site groups of varying distances from the refinery. Benzene, toluene, ethylbenzene, and xylene isomers (BTEX) and styrene concentrations were higher near the refinery's fenceline than for groups at the refinery's south edge, mid-distance, and farther removed locations. The near fenceline group was significantly higher than the refinery's north edge group for benzene and toluene but not for ethylbenzene or xylene isomers; styrene was lower at the near fenceline group versus the north edge group. For BTEX and styrene, the magnitude of estimated differences generally increased when proceeding through groups ever farther away from the petroleum refining. Perchloroethylene results were not suggestive of an influence from refining. These results suggest that emissions from the refinery complex contribute to higher concentrations of BTEX species and styrene in the vicinity of the plant, with this influence declining as distance from the petroleum refining increases.Implications: Passive sampling methodology for VOCs as discussed here is employed in recently enacted U.S. Environmental Protection Agency Methods 325A/B for determination of benzene concentrations at refinery fenceline locations. Spatial gradients of VOC concentration near the refinery fenceline were discerned in an area containing traffic and other VOC-related sources. Though limited, these findings can be useful in application of the method at such facilities to ascertain source influence.PAPER HISTORY

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“…We can also obtain a simultaneous interval estimator of bi using the formula proposed by Quesenbeny and Hurst (1964).…”

Section: Multinomial Point Process On a Networkmentioning

confidence: 99%

Statistical Analysis of the Distribution of Points on a Network

Okabe

Yomono

Kitamura

1995

Geographical Analysis

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This paper shows four statistical methods that examine the distribution of points on a network (such as the distribution of retail stores along streets). The first statistical method is an extension of the nearest-neighbor distance method (the Clark-Evans statistic) defined on a plane to the method defined on a network. The second statistical method examines the efect of categorical attribute values of links (say, types of streets) on the distribution of activity points on a network. The third statistical method examines the effect of infrastructural elements (such as railway stations) on the distribution of activity points on a network. The fourth statistical method examines the compound effect of multiple kinds of infrastructural elements (say, railway stations and big parks) on the distribution of activity points on a network. These methods are discussed with empirical examples.

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Large Sample Simultaneous Confidence Intervals for Multinomial Proportions

Cited by 113 publications

References 2 publications

Combining monte carlo estimates and bounds for network reliability

Combining monte carlo estimates and bounds for network reliability

Spatial analysis of volatile organic compounds in South Philadelphia using passive samplers

Statistical Analysis of the Distribution of Points on a Network

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