Improved quantile inference via fixed-smoothing asymptotics and Edgeworth expansion

Kaplan, David

doi:10.1016/j.jeconom.2014.08.011

Cited by 6 publications

(12 citation statements)

References 31 publications

(36 reference statements)

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“…Remark As noted by Goh () and Kaplan (), the distribution of mW ( m ) shares many features of a t ( m ) distribution in terms of the bell‐shaped symmetric pdf, moments and limiting normal distribution. As

m W_{false(m false)} = \frac{Z}{false{G a m false(m, 1 false) false/ m false}}

and

t false(m false) = \frac{Z}{\sqrt{false{G a m false(m false/ 2, 2 false) false/ m false}}}

where the numerators and denominators are independent in both cases, such close behaviour is to be anticipated.…”

Section: A T‐like Distributionmentioning

confidence: 63%

“…As with Hutson (), the method cannot be applied for extreme order statistics in some cases. When that happens, they recommended either dropping linear interpolation altogether and using Kaplan () instead or using prior information on the possible range of X . With a simulation study, they showed that Hutson's method performed at least as well as Beran and Hall's, in terms of confidence interval coverage and short interval widths.…”

Section: Quantile Confidence Interval Construction Methodsmentioning

confidence: 99%

“…Lemma 1 of Kaplan () provides an approximation to F m ( w ) in terms of m , ϕ and Φ. When m =1, the integral expression in can be expressed as

\frac{1}{\sqrt{2 π}} \int_{0}^{\infty} e^{- x / w} e^{- x^{2} / 2} d x = e^{1 / 2 w^{2}} \int_{0}^{\infty} \frac{1}{\sqrt{2 π}} e^{{- {(x + w^{- 1})}^{2} / 2}} d x,

where the integral on the right is the probability that an N (− w −1 ,1) rv exceeds 0.…”

Section: A T‐like Distributionmentioning

confidence: 99%

“…Remark Kaplan () developed an rv T m , n with m considered fixed that corresponds to our mW ( m ) . While he also made use of the independence property, he derived the asymptotic approximation to the distribution of T m , n , for large m whereas we derive the exact distribution here.…”

Section: A T‐like Distributionmentioning

confidence: 99%

“…Quantile estimation is critical in many fields from measuring value‐at‐risk in finance to modelling birth weights in demography (Kaplan, ). There is a wide literature on estimating population quantiles especially for extreme quantiles.…”

Section: Introductionmentioning

confidence: 99%

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Distribution‐free Approximate Methods for Constructing Confidence Intervals for Quantiles

Nagaraja

2019

Int Statistical Rev

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Summary Quantile estimation is important for a wide range of applications. While point estimates based on one or two order statistics are common, constructing confidence intervals around them, however, is a more difficult problem. This paper has two goals. First, it surveys the numerous distribution‐free methods for constructing approximate confidence intervals for quantiles. These techniques can be divided roughly into four categories: using a pivotal quantity, resampling, interpolation, and empirical likelihood methods. Second, a method based on the pivotal quantity that has received limited attention in the past is extended. Comprehensive simulation studies are used to compare performance across methods. The proposed method is simple and performs similarly to linear interpolation methods and a smoothed empirical likelihood method. While the proposed method has slightly wider interval widths, it can be calculated for more extreme quantiles even when there are few observations.

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m W_{false(m false)} = \frac{Z}{false{G a m false(m, 1 false) false/ m false}}

and

t false(m false) = \frac{Z}{\sqrt{false{G a m false(m false/ 2, 2 false) false/ m false}}}

where the numerators and denominators are independent in both cases, such close behaviour is to be anticipated.…”

Section: A T‐like Distributionmentioning

confidence: 63%

Section: Quantile Confidence Interval Construction Methodsmentioning

confidence: 99%

“…Lemma 1 of Kaplan () provides an approximation to F m ( w ) in terms of m , ϕ and Φ. When m =1, the integral expression in can be expressed as

\frac{1}{\sqrt{2 π}} \int_{0}^{\infty} e^{- x / w} e^{- x^{2} / 2} d x = e^{1 / 2 w^{2}} \int_{0}^{\infty} \frac{1}{\sqrt{2 π}} e^{{- {(x + w^{- 1})}^{2} / 2}} d x,

where the integral on the right is the probability that an N (− w −1 ,1) rv exceeds 0.…”

Section: A T‐like Distributionmentioning

confidence: 99%

Section: A T‐like Distributionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Distribution‐free Approximate Methods for Constructing Confidence Intervals for Quantiles

Nagaraja

2019

Int Statistical Rev

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Fractional order statistic approximation for nonparametric conditional quantile inference

Goldman

Kaplan

2017

Journal of Econometrics

Self Cite

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Using and extending fractional order statistic theory, we characterize the O(n −1 ) coverage probability error of the previously proposed confidence intervals for population quantiles using L-statistics as endpoints in Hutson (1999). We derive an analytic expression for the n −1 term, which may be used to calibrate the nominal coverage level to get O n −3/2 [log(n)] 3 coverage error. Asymptotic power is shown to be optimal. Using kernel smoothing, we propose a related method for nonparametric inference on conditional quantiles. This new method compares favorably with asymptotic normality and bootstrap methods in theory and in simulations. Code is provided for both unconditional and conditional inference.JEL classification: C21

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Survey of electron density changes in the daytime ionosphere over the Arecibo Observatory due to lightning and solar flares

Silva

Salazar

Brum

et al. 2021

Sci Rep

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Optical observations of transient luminous events and remote-sensing of the lower ionosphere with low-frequency radio waves have demonstrated that thunderstorms and lightning can have substantial impacts in the nighttime ionospheric D region. However, it remains a challenge to quantify such effects in the daytime lower ionosphere. The wealth of electron density data acquired over the years by the Arecibo Observatory incoherent scatter radar (ISR) with high vertical spatial resolution (300-m in the present study), combined with its tropical location in a region of high lightning activity, indicate a potentially transformative pathway to address this issue. Through a systematic survey, we show that daytime sudden electron density changes registered by Arecibo’s ISR during thunderstorm times are on average different than the ones happening during fair weather conditions (driven by other external factors). These changes typically correspond to electron density depletions in the D and E region. The survey also shows that these disturbances are different than the ones associated with solar flares, which tend to have longer duration and most often correspond to an increase in the local electron density content.

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Improved quantile inference via fixed-smoothing asymptotics and Edgeworth expansion

Cited by 6 publications

References 31 publications

Distribution‐free Approximate Methods for Constructing Confidence Intervals for Quantiles

Distribution‐free Approximate Methods for Constructing Confidence Intervals for Quantiles

Fractional order statistic approximation for nonparametric conditional quantile inference

Survey of electron density changes in the daytime ionosphere over the Arecibo Observatory due to lightning and solar flares

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