scholarly journals Tests Based on Simplicial Depth for AR(1) Models With Explosion

2016 ◽  
Vol 37 (6) ◽  
pp. 763-784 ◽  
Author(s):  
Christoph P. Kustosz ◽  
Anne Leucht ◽  
Christine H. MÜller
Keyword(s):  
Simplicial Depth

scholarly journals Computing Simplicial Depth by Using Importance Sampling Algorithm and Its Application

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Fanyu Meng ◽  
Wei Shao ◽  
Yuxia Su
Keyword(s):  
Importance Sampling ◽  
Testing Machine ◽  
Exact Algorithm ◽  
Real Data ◽  
Exact Algorithms ◽  
Approximate Algorithm ◽  
Sampling Algorithm ◽  
Simplicial Depth ◽  
Low Efficiency ◽  
Np Problem

Simplicial depth (SD) plays an important role in discriminant analysis, hypothesis testing, machine learning, and engineering computations. However, the computation of simplicial depth is hugely challenging because the exact algorithm is an NP problem with dimension d and sample size n as input arguments. The approximate algorithm for simplicial depth computation has extremely low efficiency, especially in high-dimensional cases. In this study, we design an importance sampling algorithm for the computation of simplicial depth. As an advanced Monte Carlo method, the proposed algorithm outperforms other approximate and exact algorithms in accuracy and efficiency, as shown by simulated and real data experiments. Furthermore, we illustrate the robustness of simplicial depth in regression analysis through a concrete physical data experiment.

scholarly journals A Combinatorial Approach to Colourful Simplicial Depth

2014 ◽  
Vol 28 (1) ◽  
pp. 306-322 ◽  
Author(s):  
Antoine Deza ◽  
Frédéric Meunier ◽  
Pauline Sarrabezolles
Keyword(s):  
Combinatorial Approach ◽  
Simplicial Depth ◽  
Colourful Simplicial Depth

scholarly journals Simplified simplicial depth for regression and autoregressive growth processes

2016 ◽  
Vol 173 ◽  
pp. 125-146 ◽  
Author(s):  
Christoph P. Kustosz ◽  
Christine H. Müller ◽  
Martin Wendler
Keyword(s):  
Growth Processes ◽  
Simplicial Depth

A note on simplicial depth function

2008 ◽  
Vol 92 (3) ◽  
pp. 235-253 ◽  
Author(s):  
Mario Romanazzi
Keyword(s):  
Simplicial Depth ◽  
Depth Function

scholarly journals Colourful Simplicial Depth

2006 ◽  
Vol 35 (4) ◽  
pp. 597-615 ◽  
Author(s):  
Antoine Deza ◽  
Sui Huang ◽  
Tamon Stephen ◽  
Tamas Terlaky
Keyword(s):  
Simplicial Depth ◽  
Colourful Simplicial Depth

scholarly journals Tests for multiple regression based on simplicial depth

2010 ◽  
Vol 101 (4) ◽  
pp. 824-838 ◽  
Author(s):  
Robin Wellmann ◽  
Christine H. Müller
Keyword(s):  
Multiple Regression ◽  
Simplicial Depth
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