A comparison of quantile estimators

Dielman, T. E.; Lowry, Cynthia A.; Pfaffenberger, Roger C.

doi:10.1080/03610919408813175

Cited by 68 publications

(37 citation statements)

References 13 publications

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“…For skewed distributions, such as the exponential, sample sizes as large as 80-100 may be required for q = 0.9 or above. The HD estimator is compared with nine different nonparametric estimators for a broad range of quantiles (from 0.02 to 0.98) in Dielman et al (1994). They analyzed the performance of the estimators using nine different distributions.…”

Section: Quantile Estimationmentioning

confidence: 99%

A quantile-based approach to system selection

Batur¹,

Choobineh²

2010

European Journal of Operational Research

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Section: Quantile Estimationmentioning

confidence: 99%

A quantile-based approach to system selection

Batur¹,

Choobineh²

2010

European Journal of Operational Research

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“…Finally, we note that the weighted-average methods described in this paper can be combined with smoothing and interpolation (see, for instance, Dielman et al 1994) and with importance sampling (Hesterberg 1993(Hesterberg , 1996 for further variance reductions. For two cutpoints, this is the same as choosing cutpoints so that the conditional probability Pr{Y°y q ÉX°b ᐉ } equals 0.25 for b 1 and 0.75 for b 2 (asymptotically, as s e r 0).…”

Section: Discussionmentioning

confidence: 99%

“…This estimator can (and often is) refined by smoothing, interpolating, etc. (see Dielman et al 1994 for a number of possibilities).…”

Section: Introductionmentioning

confidence: 99%

Control Variates for Probability and Quantile Estimation

Hesterberg¹,

Nelson

1998

Management Science

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I n stochastic systems, quantiles indicate the level of system performance that can be delivered with a specified probability, while probabilities indicate the likelihood that a specified level of system performance can be achieved. We present new estimators for use in simulation experiments designed to estimate such quantiles or probabilities of system performance. All of the estimators exploit control variates to increase their precision, which is especially important when extreme quantiles (in the tails of the distribution of system performance) or extreme probabilities (near zero or one) are of interest. Control variates are auxiliary random variables with known properties-in this case, known quantiles-and a strong stochastic association with the performance measure of interest. Since transforming a control variate can increase its effectiveness, we propose both continuous and discrete approximations to the optimal (variance-minimizing) transformation for estimating probabilities, and then invert the probability estimators to obtain corresponding quantile estimators. We also propose a direct control-variate quantile estimator that is not based on inverting a probability estimator. An empirical study using queueing, inventory and project-planning examples shows that substantial reductions in mean squared error can be obtained when estimating the 0.9, 0.95, and 0.99 quantiles.

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“…Sfakianakis and Verginis derived alternative estimators that have advantages over the HarrellDavis in some situations, but when sampling from heavy-tailed distributions, the standard error of their estimators can be substantially larger than the standard error of ˆq  . Comparisons with other quantile estimators are reported by Parrish (1990), Sheather and Marron (1990), as well as Dielman, Lowry, and Pfaffenberger (1994). The only certainty is that no single estimator dominates in terms of efficiency.…”

Section: Alternative Estimatormentioning

confidence: 99%

Comparisons of Two Quantile Regression Smoothers

Wilcox

2016

J. Mod. App. Stat. Meth.

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The small-sample properties of two non-parametric quantile regression estimators are compared. The first is based on constrained B-spline smoothing (COBS) and the other is based on a variation and slight extension of a running interval smoother. R functions for applying the methods were used in conjunction with default settings for the various optional arguments. Results indicate that the modified running interval smoother has practical value. Manipulation of the optional arguments might impact the relative merits of the two methods, but the extent to which this is the case remains unknown.

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A comparison of quantile estimators

Cited by 68 publications

References 13 publications

A quantile-based approach to system selection

A quantile-based approach to system selection

Control Variates for Probability and Quantile Estimation

Comparisons of Two Quantile Regression Smoothers

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