scholarly journals Yule–Walker Equations Using a Gini Covariance Matrix for the High-Dimensional Heavy-Tailed PVAR Model

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 614
Author(s):  
Jin Zou ◽  
Dong Han
Keyword(s):  
Granger Causality ◽  
Real Data ◽  
Vital Role ◽  
High Dimensional ◽  
Asymptotic Results ◽  
Vector Autoregressive ◽  
Matrix Estimation ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed ◽  
Gini Covariance

Gini covariance plays a vital role in analyzing the relationship between random variables with heavy-tailed distributions. In this papaer, with the existence of a finite second moment, we establish the Gini–Yule–Walker equation to estimate the transition matrix of high-dimensional periodic vector autoregressive (PVAR) processes, the asymptotic results of estimators have been established. We apply this method to study the Granger causality of the heavy-tailed PVAR process, and the results show that the robust transfer matrix estimation induces sign consistency in the value of Granger causality. Effectiveness of the proposed method is verified by both synthetic and real data.

Detecting common breaks in the means of high dimensional cross-dependent panels

2021 ◽  
Author(s):  
Lajos Horváth ◽  
Zhenya Liu ◽  
Gregory Rice ◽  
Yuqian Zhao
Keyword(s):  
Panel Data ◽  
Common Factors ◽  
Real Data ◽  
Change Points ◽  
High Dimensional ◽  
Asymptotic Results ◽  
Cross Sectional ◽  
Data Set ◽  
Monte Carlo Simulation Study ◽  
Cross Sectional Dependence

Abstract The problem of detecting change points in the mean of high dimensional panel data with potentially strong cross–sectional dependence is considered. Under the assumption that the cross–sectional dependence is captured by an unknown number of common factors, a new CUSUM type statistic is proposed. We derive its asymptotic properties under three scenarios depending on to what extent the common factors are asymptotically dominant. With panel data consisting of N cross sectional time series of length T, the asymptotic results hold under the mild assumption that min {N, T} → ∞, with an otherwise arbitrary relationship between N and T, allowing the results to apply to most panel data examples. Bootstrap procedures are proposed to approximate the sampling distribution of the test statistics. A Monte Carlo simulation study showed that our test outperforms several other existing tests in finite samples in a number of cases, particularly when N is much larger than T. The practical application of the proposed results are demonstrated with real data applications to detecting and estimating change points in the high dimensional FRED-MD macroeconomic data set.

scholarly journals Robust Mixture Modeling Based on Two-Piece Scale Mixtures of Normal Family

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 38 ◽  
Author(s):  
Mohsen Maleki ◽  
Javier Contreras-Reyes ◽  
Mohammad Mahmoudi
Keyword(s):  
Real Data ◽  
Finite Mixture ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Normal Distributions ◽  
Scale Mixtures ◽  
Robust Model ◽  
Heavy Tailed Distributions ◽  
The Family ◽  
Heavy Tailed

In this paper, we examine the finite mixture (FM) model with a flexible class of two-piece distributions based on the scale mixtures of normal (TP-SMN) family components. This family allows the development of a robust estimation of FM models. The TP-SMN is a rich class of distributions that covers symmetric/asymmetric and light/heavy tailed distributions. It represents an alternative family to the well-known scale mixtures of the skew normal (SMSN) family studied by Branco and Dey (2001). Also, the TP-SMN covers the SMN (normal, t, slash, and contaminated normal distributions) as the symmetric members and two-piece versions of them as asymmetric members. A key feature of this study is using a suitable hierarchical representation of the family to obtain maximum likelihood estimates of model parameters via an EM-type algorithm. The performances of the proposed robust model are demonstrated using simulated and real data, and then compared to other finite mixture of SMSN models.

scholarly journals Estimation of the tail-index in a conditional location-scale family of heavy-tailed distributions

2019 ◽  
Vol 7 (1) ◽  
pp. 394-417
Author(s):  
Aboubacrène Ag Ahmad ◽  
El Hadji Deme ◽  
Aliou Diop ◽  
Stéphane Girard
Keyword(s):  
Asymptotic Properties ◽  
Real Data ◽  
Scale Model ◽  
Extreme Value Index ◽  
Finite Sample ◽  
Scale Functions ◽  
Nonparametric Estimators ◽  
Heavy Tailed Distributions ◽  
Finite Sample Properties ◽  
Heavy Tailed

AbstractWe introduce a location-scale model for conditional heavy-tailed distributions when the covariate is deterministic. First, nonparametric estimators of the location and scale functions are introduced. Second, an estimator of the conditional extreme-value index is derived. The asymptotic properties of the estimators are established under mild assumptions and their finite sample properties are illustrated both on simulated and real data.

Robust feature screening for multi-response trans-elliptical regression model with ultrahigh-dimensional covariates

2019 ◽  
Vol 09 (04) ◽  
pp. 2150001
Author(s):  
Yong He ◽  
Hao Sun ◽  
Jiadong Ji ◽  
Xinsheng Zhang
Keyword(s):  
Regression Model ◽  
Canonical Correlation ◽  
Main Idea ◽  
Tail Dependence ◽  
Real Data ◽  
Feature Screening ◽  
Canonical Correlations ◽  
Heavy Tailed Distributions ◽  
Sure Screening ◽  
Heavy Tailed

In this paper, we innovatively propose an extremely flexible semi-parametric regression model called Multi-response Trans-Elliptical Regression (MTER) Model, which can capture the heavy-tail characteristic and tail dependence of both responses and covariates. We investigate the feature screening procedure for the MTER model, in which Kendall’ tau-based canonical correlation estimators are proposed to characterize the correlation between each transformed predictor and the multivariate transformed responses. The main idea is to substitute the classical canonical correlation ranking index in [X. B. Kong, Z. Liu, Y. Yao and W. Zhou, Sure screening by ranking the canonical correlations, TEST 26 (2017) 1–25] by a carefully constructed non-parametric version. The sure screening property and ranking consistency property are established for the proposed procedure. Simulation results show that the proposed method is much more powerful to distinguish the informative features from the unimportant ones than some state-of-the-art competitors, especially for heavy-tailed distributions and high-dimensional response. At last, a real data example is given to illustrate the effectiveness of the proposed procedure.

scholarly journals Two symmetric and computationally efficient Gini correlations

2020 ◽  
Vol 8 (1) ◽  
pp. 373-395
Author(s):  
Courtney Vanderford ◽  
Yongli Sang ◽  
Xin Dang
Keyword(s):  
Influence Function ◽  
Random Variables ◽  
Real Data ◽  
Computationally Efficient ◽  
Gini Correlation ◽  
Heavy Tailed Distributions ◽  
Data Application ◽  
Heavy Tailed ◽  
Log Normal ◽  
Log Normal Distribution

AbstractStandard Gini correlation plays an important role in measuring the dependence between random variables with heavy-tailed distributions. It is based on the covariance between one variable and the rank of the other. Hence for each pair of random variables, there are two Gini correlations and they are not equal in general, which brings a substantial difficulty in interpretation. Recently, Sang et al (2016) proposed a symmetric Gini correlation based on the joint spatial rank function with a computation cost of O(n2) where n is the sample size. In this paper, we study two symmetric and computationally efficient Gini correlations with the computational complexity of O(n log n). The properties of the new symmetric Gini correlations are explored. The influence function approach is utilized to study the robustness and the asymptotic behavior of these correlations. The asymptotic relative efficiencies are considered to compare several popular correlations under symmetric distributions with different tail-heaviness as well as an asymmetric log-normal distribution. Simulation and real data application are conducted to demonstrate the desirable performance of the two new symmetric Gini correlations.

scholarly journals Assessing The Relative Performance Of Heavy-Tailed Distributions: Empirical Evidence From The Johannesburg Stock Exchange

2014 ◽  
Vol 30 (4) ◽  
pp. 1263 ◽  
Author(s):  
Chun-Sung Huang ◽  
Chun-Kai Huang ◽  
Knowledge Chinhamu
Keyword(s):  
Risk Management ◽  
Value At Risk ◽  
Goodness Of Fit ◽  
Empirical Distribution ◽  
Stock Exchange ◽  
Vital Role ◽  
Financial Data ◽  
Johannesburg Stock Exchange ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed

<p>It has been well documented that the empirical distribution of daily logarithmic returns from financial market variables is characterized by excess kurtosis and skewness. In order to capture such properties in financial data, heavy-tailed and asymmetric distributions are required to overcome shortfalls of the widely exhausted classical normality assumption. In the context of financial forecasting and risk management, the accuracy in modeling the underlying returns distribution plays a vital role. For example, risk management tools such as value-at-risk (VaR) are highly dependent on the underlying distributional assumption, with particular focus being placed at the extreme tails. Hence, identifying a distribution that best captures all aspects of the given financial data may provide vast advantages to both investors and risk managers. In this paper, we investigate major financial indices on the Johannesburg Stock Exchange (JSE) and fit their associated returns to classes of heavy tailed distributions. The relative adequacy and goodness-of-fit of these distributions are then assessed through the robustness of their respective VaR estimates. Our results indicate that the best model selection is not only variant across the indices, but also across different VaR levels and the dissimilar tails of return series.</p>

scholarly journals Robust Algorithms for Change-Point Regressions Using the t-Distribution

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2394
Author(s):  
Kang-Ping Lu ◽  
Shao-Tung Chang
Keyword(s):  
Change Point ◽  
Regression Models ◽  
Degrees Of Freedom ◽  
Real Data ◽  
Fuzzy Classification ◽  
Robust Algorithms ◽  
Data Contamination ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed ◽  
T Distribution

Regression models with change-points have been widely applied in various fields. Most methodologies for change-point regressions assume Gaussian errors. For many real data having longer-than-normal tails or atypical observations, the use of normal errors may unduly affect the fit of change-point regression models. This paper proposes two robust algorithms called EMT and FCT for change-point regressions by incorporating the t-distribution with the expectation and maximization algorithm and the fuzzy classification procedure, respectively. For better resistance to high leverage outliers, we introduce a modified version of the proposed method, which fits the t change-point regression model to the data after moderately pruning high leverage points. The selection of the degrees of freedom is discussed. The robustness properties of the proposed methods are also analyzed and validated. Simulation studies show the effectiveness and resistance of the proposed methods against outliers and heavy-tailed distributions. Extensive experiments demonstrate the preference of the t-based approach over normal-based methods for better robustness and computational efficiency. EMT and FCT generally work well, and FCT always performs better for less biased estimates, especially in cases of data contamination. Real examples show the need and the practicability of the proposed method.

scholarly journals Proposing Robust LAD-Atan Penalty of Regression Model Estimation for High Dimensional Data

2020 ◽  
Vol 17 (2) ◽  
pp. 0550
Author(s):  
Ali Hameed Yousef ◽  
Omar Abdulmohsin Ali
Keyword(s):  
Variable Selection ◽  
Regression Model ◽  
High Dimensional Data ◽  
Real Data ◽  
Penalized Regression ◽  
Good Method ◽  
Superior Performance ◽  
High Dimensional ◽  
Absolute Deviation ◽  
Heavy Tailed

         The issue of penalized regression model has received considerable critical attention to variable selection. It plays an essential role in dealing with high dimensional data. Arctangent denoted by the Atan penalty has been used in both estimation and variable selection as an efficient method recently. However, the Atan penalty is very sensitive to outliers in response to variables or heavy-tailed error distribution. While the least absolute deviation is a good method to get robustness in regression estimation. The specific objective of this research is to propose a robust Atan estimator from combining these two ideas at once. Simulation experiments and real data applications show that the proposed LAD-Atan estimator has superior performance compared with other estimators.  

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