On quantile estimation by bootstrap

Brodin, Erik

doi:10.1016/j.csda.2005.08.004

Cited by 6 publications

(2 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As mentioned in Sheather and Marron (1990), using the link between Beta distributions and order statistics, the estimator suggested in Harrell and Davis (1982) is simply a bootstrap estimator of E(X (np) ) (cf. also Brodin 2006).…”

Section: The Explicit Estimator For Q(x P)mentioning

confidence: 94%

Beta kernel quantile estimators of heavy-tailed loss distributions

Charpentier

Oulidi

2009

Stat Comput

View full text Add to dashboard Cite

International audienceIn this paper we suggest several nonparametric quantile estimators based on Beta kernel. They are applied to transformed data by the generalized Champernowne distribution initially fitted to the data. A Monte Carlo based study has shown that those estimators improve the efficiency of the traditional ones, not only for light tailed distributions, but also for heavy tailed, when the probability level is close to 1. We also compare these estimators with the Extreme Value Theory Quantile applied to Danish data on large fire insurance losses

show abstract

Section: The Explicit Estimator For Q(x P)mentioning

confidence: 94%

Beta kernel quantile estimators of heavy-tailed loss distributions

Charpentier

Oulidi

2009

Stat Comput

View full text Add to dashboard Cite

show abstract

“…The simplest non-parametric methods are the empirical quantile estimator based on a single order statistic, or the extension based on two consecutive order statistics [23], for which the variance can be large. Quantile estimators based on L-statistics have been explored as a way to reduce estimation variance [24][25][26], and include Kernel quantile estimators [27][28][29][30][31]. However, performance of the latter can be very sensitive to the choice of bandwidth.…”

Section: Discussionmentioning

confidence: 99%

Computing Accurate Probabilistic Estimates of One-D Entropy from Equiprobable Random Samples

Gupta

Ehsani

Roy

et al. 2021

Entropy

View full text Add to dashboard Cite

We develop a simple Quantile Spacing (QS) method for accurate probabilistic estimation of one-dimensional entropy from equiprobable random samples, and compare it with the popular Bin-Counting (BC) and Kernel Density (KD) methods. In contrast to BC, which uses equal-width bins with varying probability mass, the QS method uses estimates of the quantiles that divide the support of the data generating probability density function (pdf) into equal-probability-mass intervals. And, whereas BC and KD each require optimal tuning of a hyper-parameter whose value varies with sample size and shape of the pdf, QS only requires specification of the number of quantiles to be used. Results indicate, for the class of distributions tested, that the optimal number of quantiles is a fixed fraction of the sample size (empirically determined to be ~0.25–0.35), and that this value is relatively insensitive to distributional form or sample size. This provides a clear advantage over BC and KD since hyper-parameter tuning is not required. Further, unlike KD, there is no need to select an appropriate kernel-type, and so QS is applicable to pdfs of arbitrary shape, including those with discontinuous slope and/or magnitude. Bootstrapping is used to approximate the sampling variability distribution of the resulting entropy estimate, and is shown to accurately reflect the true uncertainty. For the four distributional forms studied (Gaussian, Log-Normal, Exponential and Bimodal Gaussian Mixture), expected estimation bias is less than 1% and uncertainty is low even for samples of as few as 100 data points; in contrast, for KD the small sample bias can be as large as -10% and for BC as large as -50%. We speculate that estimating quantile locations, rather than bin-probabilities, results in more efficient use of the information in the data to approximate the underlying shape of an unknown data generating pdf.

show abstract

Monitoring Complex Segmented Streams of Data Using Bootstrap Control Charts

Hryniewicz,

Kaczmarek-Majer

2024

Advanced Statistical Methods in Process Monitoring, Finance, and Environmental Science

View full text Add to dashboard Cite

On quantile estimation by bootstrap

Cited by 6 publications

References 3 publications

Beta kernel quantile estimators of heavy-tailed loss distributions

Beta kernel quantile estimators of heavy-tailed loss distributions

Computing Accurate Probabilistic Estimates of One-D Entropy from Equiprobable Random Samples

Monitoring Complex Segmented Streams of Data Using Bootstrap Control Charts

Contact Info

Product

Resources

About