A Tutorial on Quantile Estimation via Monte Carlo

Hui, Dong; Nakayama, Marvin K.

doi:10.1007/978-3-030-43465-6_1

Cited by 12 publications

(4 citation statements)

References 39 publications

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“…where P M denote the probability measure under Monte Carlo simulation, since we approximate the online detection threshold ρ α,µ,n , ρ α,σ,n using Monte Carlo simulations. As the number of simulation increases, by the central limit theorem, the estimated value is approaching the true threshold value (Dong et al [2020]). Similarly, we estimate ρ σ+,n (α) and ρ σ−,n (α).…”

Section: Estimation Of the Thresholds For The Online Detectionmentioning

confidence: 96%

High dimensional change-point detection: a complete graph approach

Sun¹,

Papagiannouli²,

Spokoiny³

2022

Preprint

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The aim of online change-point detection is for a accurate, timely discovery of structural breaks. As data dimension outgrows the number of data in observation, online detection becomes challenging. Existing methods typically test only the change of mean, which omit the practical aspect of change of variance. We propose a complete graph-based, changepoint detection algorithm to detect change of mean and variance from low to high-dimensional online data with a variable scanning window. Inspired by complete graph structure, we introduce graph-spanning ratios to map high-dimensional data into metrics, and then test statistically if a change of mean or change of variance occurs. Theoretical study shows that our approach has the desirable pivotal property and is powerful with prescribed error probabilities. We demonstrate that this framework outperforms other methods in terms of detection power. Our approach has high detection power with small and multiple scanning window, which allows timely detection of change-point in the online setting. Finally, we applied the method to financial data to detect change-points in S&P 500 stocks.

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Section: Estimation Of the Thresholds For The Online Detectionmentioning

confidence: 96%

High dimensional change-point detection: a complete graph approach

Sun¹,

Papagiannouli²,

Spokoiny³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…This is computationally costly, especially for large-scale problems or when extreme target quantiles close to zero or one are to be determined, the number of required samples is especially high in this case [8]. Different variance reduction techniques can be employed to reduce the number of required samples [9]. Latin hypercube sampling as an instance of correlation-induction methods can perform very well for quantile estimation [10,11], with the largest benefits in high dimensions.…”

Section: Related Literaturementioning

confidence: 99%

“…Latin hypercube sampling as an instance of correlation-induction methods can perform very well for quantile estimation [10,11], with the largest benefits in high dimensions. Importance sampling is another effective approach for non-extreme quantiles [9].…”

Section: Related Literaturementioning

confidence: 99%

Unimodality of Parametric Linear Programming Solutions and Efficient Quantile Estimation

Mollaeivaneghi,

Santos,

Steinke

2023

AppliedMath

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For linear optimization problems with a parametric objective, so-called parametric linear programs (PLP), we show that the optimal decision values are, under few technical restrictions, unimodal functions of the parameter, at least in the two-degrees-of-freedom case. Assuming that the parameter is random and follows a known probability distribution, this allows for an efficient algorithm to determe the quantiles of linear combinations of the optimal decisions. The novel results are demonstrated with probabilistic economic dispatch. For an example setup with uncertain fuel costs, quantiles of the resulting inter-regional power flows are computed. The approach is compared against Monte Carlo and piecewise computation techniques, proving significantly reduced computation times for the novel procedure. This holds especially when the feasible set is complex and/or extreme quantiles are desired. This work is limited to problems with two effective degrees of freedom and a one-dimensional uncertainty. Future extensions to higher dimensions could yield a key tool for the analysis of probabilistic PLPs and, specifically, risk management in energy systems.

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“…One reason for estimating f is that an analyst may glean important features of the distribution of R from a graph of its density, arguably more easily than from a plot of its cumulative distribution function (CDF) F. Another motivation arises in quantile estimation [4]. A central limit theorem for the estimator of the q-quantile ξ = F −1 (q) for 0 < q < 1 has an asymptotic variance that includes f (ξ ), so constructing a confidence interval for ξ often entails estimating f (ξ ).…”

Section: Introductionmentioning

confidence: 99%

Density Estimators of the Cumulative Reward Up to a Hitting Time to a Rarely Visited Set of a Regenerative System

Nakayama

Tuffin

2022

2022 Winter Simulation Conference (WSC)

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For a regenerative process, we propose various estimators of the density function of the cumulative reward up to hitting a rarely visited set of states. The approaches exploit existing weak-convergence results for the hittingtime distribution, and we apply simulation (often with previously developed importance samplers for estimating the mean) to estimate parameters of the limiting distribution. We also combine these ideas with kernel methods. Numerical results from simulation experiments show the effectiveness of the estimators.

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A Tutorial on Quantile Estimation via Monte Carlo

Cited by 12 publications

References 39 publications

High dimensional change-point detection: a complete graph approach

High dimensional change-point detection: a complete graph approach

Unimodality of Parametric Linear Programming Solutions and Efficient Quantile Estimation

Density Estimators of the Cumulative Reward Up to a Hitting Time to a Rarely Visited Set of a Regenerative System

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