Finite sampling inequalities: An application to two-sample Kolmogorov–Smirnov statistics

Greene, Evan; Wellner, Jon A.

doi:10.1016/j.spa.2016.04.020

Cited by 4 publications

(4 citation statements)

References 30 publications

(46 reference statements)

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“…We may use this representation along with Bennett's inequality to obtain a Bennett-type exponential bound for Hypergeometric random variables (this bound was also discussed earlier in [7], though without proof). The proof of this claim is short, so we will provide it here.…”

Section: Exponential Boundsmentioning

confidence: 96%

Exponential bounds for the hypergeometric distribution

Greene¹,

Wellner²

2017

Bernoulli

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We establish exponential bounds for the hypergeometric distribution which include a finite sampling correction factor, but are otherwise analogous to bounds for the binomial distribution due to León and Perron (Statist. Probab. Lett. 62 (2003) 345–354) and Talagrand (Ann. Probab. 22 (1994) 28–76). We also extend a convex ordering of Kemperman’s (Nederl. Akad. Wetensch. Proc. Ser. A 76 = Indag. Math. 35 (1973) 149–164) for sampling without replacement from populations of real numbers between zero and one: a population of all zeros or ones (and hence yielding a hypergeometric distribution in the upper bound) gives the extreme case.

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Section: Exponential Boundsmentioning

confidence: 96%

Exponential bounds for the hypergeometric distribution

Greene¹,

Wellner²

2017

Bernoulli

Self Cite

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“…The cross-wavelet method was then used to explore the differences in the relationship between climate indices (the MEI, the ONI, and sunspots) and extreme meteorology before and after climate change. Finally, the GEV (Fisher & Tippett 1928), the generalized Pareto distribution (GPD) , and the Kolmogorov-Smirnov (K-S) test method (Greene & Wellner 2016) were selected in this study to study the influence of climate change on the frequency distribution of extreme weather elements from three perspectives: frequency distribution model parameters, reproducibility period, and model fit effect since they are well established and widely accepted in water hydrological science. Due to space constraints, only the Heuristic segmentation method is briefly introduced in this paper.…”

Section: Methodsmentioning

confidence: 99%

Climate change impact on extreme value and its frequency distribution function in a karst basin, Southwest China

Song

Ruan

et al. 2022

Journal of Water and Climate Change

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Studying extreme meteorology and its frequency under climate change is helpful to guide flood and drought control. The original achievements and objective of this study are to further contribute to the literature on how to analyze the impact of climate change on extreme rainfall and extreme temperature more reasonably and comprehensively for a karst basin. The Mann–Kendall method, Heuristic segmentation method, cross-wavelet analysis method, generalized extreme value (GEV) model, and generalized Pareto distribution (GPD) model were applied in this paper. The 55-year (1963–2017) extreme rainfall and temperature data recorded in the Chengbi River Basin were applied. The results show that extreme rainfall showed a downward trend (−0.169 and −8.735 mm/10a), while the trends of extreme temperatures were not obvious (Sen's slope estimate is 0). The mutation points range from 1981 to 2002 and the mutation point of extreme rainfall series is earlier than that of extreme temperatures. Compared with the GEV model, the parameters of the GPD model show a smaller variation before and after climate change, and the extreme meteorology values corresponding to the same recurrence period show a decreasing trend after climate change. The performance of GEV and GPD models after climate change is generally more fit than that before climate change.

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“…The sample was considered to be an aging accelerated sample if the value of aging acceleration was greater than 0, else it was considered to be a non‐aging‐accelerated sample. For each pair of cancers, the accumulated Kolmogorov–Smirnov (K‐S) statistics of every gene pair in aging‐accelerated samples and non‐aging‐accelerated samples were calculated. The formula was

KS = sup | F1 - F2 |

where F1 and F2 represented cumulative probability distributions of the same type of samples (aging accelerated or non‐aging accelerated) in the two cancers.…”

Section: Methodsmentioning

confidence: 99%

“…The sample was considered to be an aging accelerated sample if the value of aging acceleration was greater than 0, else it was considered to be a non-agingaccelerated sample. For each pair of cancers, the accumulated Kolmogorov-Smirnov (K-S) statistics [48] of every gene pair in aging-accelerated samples and non-aging-accelerated samples were calculated. The formula was KS ¼ supjF1 À F2j ð 6Þ…”

Section: Constructing An Aging Acceleration Interaction Network Acros...mentioning

confidence: 99%

Network analysis of aging acceleration reveals systematic properties of 11 types of cancers

Xia

Zhou

et al. 2019

FEBS Open Bio

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Cancers are known to be associated with accelerated aging, but to date, there has been a paucity of systematic and in‐depth studies of the correlation between aging and cancer. DNA methylation ( DNA m) profiles can be used as aging markers and utilized to construct aging predictors. In this study, we downloaded 333 paired samples of DNA m, expression and mutation profiles encompassing 11 types of tissues from The Cancer Genome Atlas public access portal. The DNA m aging scores were calculated using the Support Vector Machine regression model. The DNA m aging scores of cancers revealed significant aging acceleration compared to adjacent normal tissues. Aging acceleration‐associated mutation modules and expression modules were identified in 11 types of cancers. In addition, we constructed bipartite networks of mutations and expression, and the differential expression modules related to aging‐associated mutations were selected in 11 types of cancers using the expression quantitative trait locus method. The results of enrichment analyses also identified common functions across cancers and cancer‐specific characteristics of aging acceleration. The aging acceleration interaction network across cancers suggested a core status of thyroid carcinoma and neck squamous cell carcinoma in the aging process. In summary, we have identified correlations between aging and cancers and revealed insights into the biological functions of the modules in aging and cancers.

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Finite sampling inequalities: An application to two-sample Kolmogorov–Smirnov statistics

Cited by 4 publications

References 30 publications

Exponential bounds for the hypergeometric distribution

Exponential bounds for the hypergeometric distribution

Climate change impact on extreme value and its frequency distribution function in a karst basin, Southwest China

Network analysis of aging acceleration reveals systematic properties of 11 types of cancers

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