Strong consistency and asymptotic normality for quantities related to the Benjamini–Hochberg false discovery rate procedure

2020 ◽  
Vol 160 ◽  
pp. 108713
Author(s):  
Grant Izmirlian
Keyword(s):  
Asymptotic Normality ◽  
False Discovery Rate ◽  
Strong Consistency ◽  
False Discovery Rate Procedure ◽  
False Discovery ◽  
Consistency And Asymptotic Normality

On strong consistency and asymptotic normality of one-step Gauss-Newton estimators in ARMA time series models

Statistics ◽  
2020 ◽  
Vol 54 (5) ◽  
pp. 1030-1057
Author(s):  
Pierre Duchesne ◽  
Pierre Lafaye de Micheaux ◽  
Joseph François Tagne Tatsinkou
Keyword(s):  
Time Series ◽  
Asymptotic Normality ◽  
Strong Consistency ◽  
Time Series Models ◽  
One Step ◽  
Consistency And Asymptotic Normality

Multiple comparisons: philosophies and illustrations

2000 ◽  
Vol 279 (1) ◽  
pp. R1-R8 ◽  
Author(s):  
Douglas Curran-Everett
Keyword(s):  
False Discovery Rate ◽  
Null Hypothesis ◽  
Scientific Discovery ◽  
Multiple Comparisons ◽  
False Discovery Rate Procedure ◽  
False Discovery ◽  
Scientific Disciplines ◽  
Significant Difference ◽  
Statistical Issue ◽  
Promising Development

Statistical procedures underpin the process of scientific discovery. As researchers, one way we use these procedures is to test the validity of a null hypothesis. Often, we test the validity of more than one null hypothesis. If we fail to use an appropriate procedure to account for this multiplicity, then we are more likely to reach a wrong scientific conclusion—we are more likely to make a mistake. In physiology, experiments that involve multiple comparisons are common: of the original articles published in 1997 by the American Physiological Society, ∼40% cite a multiple comparison procedure. In this review, I demonstrate the statistical issue embedded in multiple comparisons, and I summarize the philosophies of handling this issue. I also illustrate the three procedures—Newman-Keuls, Bonferroni, least significant difference—cited most often in my literature review; each of these procedures is of limited practical value. Last, I demonstrate the false discovery rate procedure, a promising development in multiple comparisons. The false discovery rate procedure may be the best practical solution to the problems of multiple comparisons that exist within physiology and other scientific disciplines.

scholarly journals Nonparametric estimation of boundary measures and related functionals: asymptotic results

2009 ◽  
Vol 41 (2) ◽  
pp. 311-322 ◽  
Author(s):  
Inés Armendáriz ◽  
Antonio Cuevas ◽  
Ricardo Fraiman
Keyword(s):  
Asymptotic Normality ◽  
Surface Area ◽  
Nonparametric Estimation ◽  
Strong Consistency ◽  
Nonparametric Method ◽  
Asymptotic Results ◽  
Minkowski Content ◽  
Compact Body ◽  
Consistency And Asymptotic Normality ◽  
The One

We study a nonparametric method for estimating the boundary measure of a compact body G ⊂ ℝd (the boundary length when d = 2 and the surface area for d = 3) in the case when this measure agrees with the corresponding Minkowski content. The estimator we consider is closely related to the one proposed in Cuevas, Fraiman and Rodríguez-Casal (2007). Our method relies on two sets of random points, drawn inside and outside the set G, with different sampling intensities. Strong consistency and asymptotic normality are obtained under some shape hypotheses on the set G. Some applications and practical aspects are briefly discussed.

THE GLOBAL WEIGHTED LAD ESTIMATORS FOR FINITE/INFINITE VARIANCE ARMA(p,q) MODELS

2012 ◽  
Vol 28 (5) ◽  
pp. 1065-1086 ◽  
Author(s):  
Ke Zhu ◽  
Shiqing Ling
Keyword(s):  
Time Series ◽  
Asymptotic Normality ◽  
Simulation Study ◽  
Strong Consistency ◽  
Asymptotic Theory ◽  
Infinite Variance ◽  
Time Series Models ◽  
Absolute Deviation ◽  
Consistency And Asymptotic Normality ◽  
First Time

This paper investigates the global self-weighted least absolute deviation (SLAD) estimator for finite and infinite variance ARMA(p, q) models. The strong consistency and asymptotic normality of the global SLAD estimator are obtained. A simulation study is carried out to assess the performance of the global SLAD estimators. In this paper the asymptotic theory of the global LAD estimator for finite and infinite variance ARMA(p, q) models is established in the literature for the first time. The technique developed in this paper is not standard and can be used for other time series models.

scholarly journals Nonparametric estimation of boundary measures and related functionals: asymptotic results

2009 ◽  
Vol 41 (02) ◽  
pp. 311-322 ◽  
Author(s):  
Inés Armendáriz ◽  
Antonio Cuevas ◽  
Ricardo Fraiman
Keyword(s):  
Asymptotic Normality ◽  
Surface Area ◽  
Nonparametric Estimation ◽  
Strong Consistency ◽  
Nonparametric Method ◽  
Asymptotic Results ◽  
Minkowski Content ◽  
Compact Body ◽  
Consistency And Asymptotic Normality ◽  
The One

We study a nonparametric method for estimating the boundary measure of a compact body G ⊂ ℝ d (the boundary length when d = 2 and the surface area for d = 3) in the case when this measure agrees with the corresponding Minkowski content. The estimator we consider is closely related to the one proposed in Cuevas, Fraiman and Rodríguez-Casal (2007). Our method relies on two sets of random points, drawn inside and outside the set G, with different sampling intensities. Strong consistency and asymptotic normality are obtained under some shape hypotheses on the set G. Some applications and practical aspects are briefly discussed.

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