scholarly journals The asymptotic distribution of cluster sizes for supercritical percolation on random split trees

2021 ◽  
Author(s):  
Gabriel Berzunza ◽  
Cecilia Holmgren
Keyword(s):  
Asymptotic Distribution ◽  
Split Trees

Properties of the beta coefficient of the global minimum variance portfolio

2020 ◽  
Vol 8 (1) ◽  
pp. 11-21
Author(s):  
S. M. Yaroshko ◽  
◽  
M. V. Zabolotskyy ◽  
T. M. Zabolotskyy ◽  
◽  
...  
Keyword(s):  
Confidence Interval ◽  
Asymptotic Distribution ◽  
Global Minimum ◽  
Asset Returns ◽  
Minimum Variance ◽  
Benchmark Portfolio ◽  
Beta Coefficient ◽  
Minimum Variance Portfolio ◽  
Global Minimum Variance Portfolio ◽  
Daily Returns

The paper is devoted to the investigation of statistical properties of the sample estimator of the beta coefficient in the case when the weights of benchmark portfolio are constant and for the target portfolio, the global minimum variance portfolio is taken. We provide the asymptotic distribution of the sample estimator of the beta coefficient assuming that the asset returns are multivariate normally distributed. Based on the asymptotic distribution we construct the confidence interval for the beta coefficient. We use the daily returns on the assets included in the DAX index for the period from 01.01.2018 to 30.09.2019 to compare empirical and asymptotic means, variances and densities of the standardized estimator for the beta coefficient. We obtain that the bias of the sample estimator converges to zero very slowly for a large number of assets in the portfolio. We present the adjusted estimator of the beta coefficient for which convergence of the empirical variances to the asymptotic ones is not significantly slower than for a sample estimator but the bias of the adjusted estimator is significantly smaller.

scholarly journals A matrix-less method to approximate the spectrum and the spectral function of Toeplitz matrices with real eigenvalues

2021 ◽  
Author(s):  
Sven-Erik Ekström ◽  
Paris Vassalos
Keyword(s):  
Distribution Function ◽  
Asymptotic Distribution ◽  
Numerical Experiments ◽  
Toeplitz Matrices ◽  
Future Research ◽  
Research Directions ◽  
Numerical Examples ◽  
Working Hypothesis ◽  
Wide Range ◽  
Future Research Directions

AbstractIt is known that the generating function f of a sequence of Toeplitz matrices {Tn(f)}n may not describe the asymptotic distribution of the eigenvalues of Tn(f) if f is not real. In this paper, we assume as a working hypothesis that, if the eigenvalues of Tn(f) are real for all n, then they admit an asymptotic expansion of the same type as considered in previous works, where the first function, called the eigenvalue symbol $\mathfrak {f}$ f , appearing in this expansion is real and describes the asymptotic distribution of the eigenvalues of Tn(f). This eigenvalue symbol $\mathfrak {f}$ f is in general not known in closed form. After validating this working hypothesis through a number of numerical experiments, we propose a matrix-less algorithm in order to approximate the eigenvalue distribution function $\mathfrak {f}$ f . The proposed algorithm, which opposed to previous versions, does not need any information about neither f nor $\mathfrak {f}$ f is tested on a wide range of numerical examples; in some cases, we are even able to find the analytical expression of $\mathfrak {f}$ f . Future research directions are outlined at the end of the paper.

scholarly journals Asymptotic distribution of the score test for detecting marks in hawkes processes

2021 ◽  
Author(s):  
Simon Clinet ◽  
William T. M. Dunsmuir ◽  
Gareth W. Peters ◽  
Kylie-Anne Richards
Keyword(s):  
Asymptotic Distribution ◽  
Score Test ◽  
Hawkes Processes

Hardware-Accelerated Dual-Split Trees

2020 ◽  
Vol 3 (2) ◽  
pp. 1-21
Author(s):  
Daqi Lin ◽  
Elena Vasiou ◽  
Cem Yuksel ◽  
Daniel Kopta ◽  
Erik Brunvand
Keyword(s):  
Ray Tracing ◽  
Hardware Acceleration ◽  
Memory Storage ◽  
Compact Representation ◽  
Space Partitioning ◽  
Data Movement ◽  
Bounding Volume ◽  
Bounding Boxes ◽  
Split Trees ◽  
Bounding Volume Hierarchies

Bounding volume hierarchies (BVH) are the most widely used acceleration structures for ray tracing due to their high construction and traversal performance. However, the bounding planes shared between parent and children bounding boxes is an inherent storage redundancy that limits further improvement in performance due to the memory cost of reading these redundant planes. Dual-split trees can create identical space partitioning as BVHs, but in a compact form using less memory by eliminating the redundancies of the BVH structure representation. This reduction in memory storage and data movement translates to faster ray traversal and better energy efficiency. Yet, the performance benefits of dual-split trees are undermined by the processing required to extract the necessary information from their compact representation. This involves bit manipulations and branching instructions which are inefficient in software. We introduce hardware acceleration for dual-split trees and show that the performance advantages over BVHs are emphasized in a hardware ray tracing context that can take advantage of such acceleration. We provide details on how the operations needed for decoding dual-split tree nodes can be implemented in hardware and present experiments in a number of scenes with different sizes using path tracing. In our experiments, we have observed up to 31% reduction in render time and 38% energy saving using dual-split trees as compared to binary BVHs representing identical space partitioning.

Consistency and asymptotic distribution of the Theil–Sen estimator

2008 ◽  
Vol 138 (6) ◽  
pp. 1836-1850 ◽  
Author(s):  
Hanxiang Peng ◽  
Shaoli Wang ◽  
Xueqin Wang
Keyword(s):  
Asymptotic Distribution

scholarly journals Asymptotic Distribution of the Distance Function to the Farey Points

1997 ◽  
Vol 65 (1) ◽  
pp. 130-149 ◽  
Author(s):  
Pavel Kargaev ◽  
Anatoly Zhigljavsky
Keyword(s):  
Asymptotic Distribution ◽  
Distance Function
Sign in / Sign up

Export Citation Format

Share Document