scholarly journals Estimating Tukey Depth Using Incremental Quantile Estimators

2021 ◽  
pp. 108339
Author(s):  
Hugo Lewi ◽  
Anis Yazidi ◽  
Håvard Rue
Keyword(s):  
Tukey Depth ◽  
Quantile Estimators

scholarly journals Uncertainty of quantile estimators using the population index flood method

2003 ◽  
Vol 39 (8) ◽  
Author(s):  
O. G. B. Sveinsson ◽  
J. D. Salas ◽  
D. C. Boes
Keyword(s):  
Population Index ◽  
Index Flood ◽  
Quantile Estimators

ROBUST TEST BASED ON NONLINEAR REGRESSION QUANTILE ESTIMATORS

2005 ◽  
Vol 20 (1) ◽  
pp. 145-159 ◽  
Author(s):  
SEUNG-HOE CHOI ◽  
KYUNG-JOONG KIM ◽  
MYUNG-SOOK LEE
Keyword(s):  
Nonlinear Regression ◽  
Robust Test ◽  
Regression 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 New Bandwidth Selection for Kernel Quantile Estimators

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Ali Al-Kenani ◽  
Keming Yu
Keyword(s):  
Cross Validation ◽  
Kernel Smoothing ◽  
Bandwidth Selection ◽  
Unbiased Estimation ◽  
Optimal Bandwidth ◽  
Squared Error ◽  
Bandwidth Parameter ◽  
Integrated Squared Error ◽  
Selection For ◽  
Quantile Estimators

We propose a cross-validation method suitable for smoothing of kernel quantile estimators. In particular, our proposed method selects the bandwidth parameter, which is known to play a crucial role in kernel smoothing, based on unbiased estimation of a mean integrated squared error curve of which the minimising value determines an optimal bandwidth. This method is shown to lead to asymptotically optimal bandwidth choice and we also provide some general theory on the performance of optimal, data-based methods of bandwidth choice. The numerical performances of the proposed methods are compared in simulations, and the new bandwidth selection is demonstrated to work very well.

On the Tukey depth of an atomic measure

2007 ◽  
Vol 4 (2) ◽  
pp. 244-249 ◽  
Author(s):  
A. Hassairi ◽  
O. Regaieg
Keyword(s):  
Tukey Depth ◽  
Atomic Measure
Sign in / Sign up

Export Citation Format

Share Document