scholarly journals Conditional Quantile Estimators: A Small Sample Theory

2021 ◽  
Author(s):  
Grigory Franguridi ◽  
Bulat Gafarov ◽  
Kaspar Wuthrich
Keyword(s):  
Small Sample ◽  
Conditional Quantile ◽  
Quantile Estimators

scholarly journals Scaling of High-Quantile Estimators

2011 ◽  
Vol 48 (04) ◽  
pp. 968-983 ◽  
Author(s):  
Matthias Degen ◽  
Paul Embrechts
Keyword(s):  
Heavy Tails ◽  
Global Financial Crisis ◽  
Financial Institution ◽  
Small Sample ◽  
Accurate Estimation ◽  
Risk Capital ◽  
High Quantile ◽  
Quantile Estimators ◽  
Small Sample Sizes ◽  
The Global Financial Crisis

Enhanced by the global financial crisis, the discussion about an accurate estimation of regulatory (risk) capital a financial institution needs to hold in order to safeguard against unexpected losses has become highly relevant again. The presence of heavy tails in combination with small sample sizes turns estimation at such extreme quantile levels into an inherently difficult statistical issue. We discuss some of the problems and pitfalls that may arise. In particular, based on the framework of second-order extended regular variation, we compare different high-quantile estimators and propose methods for the improvement of standard methods by focusing on the concept of penultimate approximations.

scholarly journals On copula-based conditional quantile estimators

2017 ◽  
Vol 128 ◽  
pp. 14-20 ◽  
Author(s):  
Bruno Rémillard ◽  
Bouchra Nasri ◽  
Taoufik Bouezmarni
Keyword(s):  
Conditional Quantile ◽  
Quantile Estimators

scholarly journals Scaling of High-Quantile Estimators

2011 ◽  
Vol 48 (4) ◽  
pp. 968-983 ◽  
Author(s):  
Matthias Degen ◽  
Paul Embrechts
Keyword(s):  
Heavy Tails ◽  
Global Financial Crisis ◽  
Financial Institution ◽  
Small Sample ◽  
Accurate Estimation ◽  
Risk Capital ◽  
High Quantile ◽  
Quantile Estimators ◽  
Small Sample Sizes ◽  
The Global Financial Crisis

Enhanced by the global financial crisis, the discussion about an accurate estimation of regulatory (risk) capital a financial institution needs to hold in order to safeguard against unexpected losses has become highly relevant again. The presence of heavy tails in combination with small sample sizes turns estimation at such extreme quantile levels into an inherently difficult statistical issue. We discuss some of the problems and pitfalls that may arise. In particular, based on the framework of second-order extended regular variation, we compare different high-quantile estimators and propose methods for the improvement of standard methods by focusing on the concept of penultimate approximations.

scholarly journals Efficiency of Bayesian Approaches in Quantile Regression with Small Sample Size

2018 ◽  
pp. 1-13
Author(s):  
Neveen Sayed-Ahmed
Keyword(s):  
Variable Selection ◽  
Quantile Regression ◽  
Full Range ◽  
Small Sample ◽  
Adaptive Lasso ◽  
Sample Sizes ◽  
Bayesian Approaches ◽  
Conditional Quantile ◽  
Quantile Functions ◽  
Small Sample Sizes

Quantile regression is a statistical technique intended to estimate, and conduct inference about the conditional quantile functions. Just as the classical linear regression methods estimate model for the conditional mean function, quantile regression offers a mechanism for estimating models for the conditional median function, and the full range of other conditional quantile functions. In the Bayesian approach to variable selection prior distributions representing the subjective beliefs about the parameters are assigned to the regression coefficients. The estimation of parameters and the selection of the best subset of variables is accomplished by using adaptive lasso quantile regression. In this paper we describe, compare, and apply the two suggested Bayesian approaches. The two suggested Bayesian suggested approaches are used to select the best subset of variables and estimate the parameters of the quantile regression equation when small sample sizes are used.  Simulations show that the proposed approaches are very competitive in terms of variable selection, estimation accuracy and efficient when small sample sizes are used.   

Probing the ultrastructure of the mitotic and meiotic spindle in eggs: An expeditious approach based on semi-thin (0.25 μm) serial sections

1983 ◽  
Vol 41 ◽  
pp. 552-555
Author(s):  
Conly L. Rieder ◽  
S. Bowser ◽  
R. Nowogrodzki ◽  
K. Ross ◽  
G. Sluder
Keyword(s):  
Small Sample Size ◽  
Small Sample ◽  
Meiotic Spindle ◽  
Serial Sections ◽  
Mitotic Apparatus ◽  
Thin Sections ◽  
Cell Cycles ◽  
Ultrastructural Studies

Eggs have long been a favorite material for studying the mechanism of karyokinesis in-vivo and in-vitro. They can be obtained in great numbers and, when fertilized, divide synchronously over many cell cycles. However, they are not considered to be a practical system for ultrastructural studies on the mitotic apparatus (MA) for several reasons, the most obvious of which is that sectioning them is a formidable task: over 1000 ultra-thin sections need to be cut from a single 80-100 μm diameter egg and of these sections only a small percentage will contain the area or structure of interest. Thus it is difficult and time consuming to obtain reliable ultrastructural data concerning the MA of eggs; and when it is obtained it is necessarily based on a small sample size.We have recently developed a procedure which will facilitate many studies concerned with the ultrastructure of the MA in eggs. It is based on the availability of biological HVEM's and on the observation that 0.25 μm thick serial sections can be screened at high resolution for content (after mounting on slot grids and staining with uranyl and lead) by phase contrast light microscopy (LM; Figs 1-2).

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