Multivariate Skew Normal Copula for Asymmetric Dependence: Estimation and Application

2019 ◽  
Vol 18 (01) ◽  
pp. 365-387 ◽  
Author(s):  
Zheng Wei ◽  
Seongyong Kim ◽  
Boseung Choi ◽  
Daeyoung Kim
Keyword(s):  
Convergence Property ◽  
Real Data ◽  
Radial Symmetry ◽  
High Dimensional ◽  
Dependence Structure ◽  
Data Set ◽  
Asymmetric Dependence ◽  
Identical Manner ◽  
Normal Copula ◽  
Skew Normal

The exchangeability and radial symmetry assumptions on the dependence structure of the multivariate data are restrictive in practical situations where the variables of interest are not likely to be associated to each other in an identical manner. In this paper, we propose a flexible class of multivariate skew normal copulas to model high-dimensional asymmetric dependence patterns. The proposed copulas have two sets of parameters capturing asymmetric dependence, one for association between the variables and the other for skewness of the variables. In order to efficiently estimate the two sets of parameters, we introduce the block coordinate ascent algorithm and discuss its convergence property. The proposed class of multivariate skew normal copulas is illustrated using a real data set.

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 Weighted proportional mean inactivity time model

2021 ◽  
Vol 7 (3) ◽  
pp. 4038-4060
Author(s):  
Mohamed Kayid ◽  
◽  
Adel Alrasheedi
Keyword(s):  
Frailty Model ◽  
Real Data ◽  
Survival Models ◽  
Dependence Structure ◽  
Time Model ◽  
Data Set ◽  
Population Variable ◽  
Inactivity Time ◽  
Mean Inactivity Time ◽  
Special Case

<abstract><p>In this paper, a mean inactivity time frailty model is considered. Examples are given to calculate the mean inactivity time for several reputable survival models. The dependence structure between the population variable and the frailty variable is characterized. The classical weighted proportional mean inactivity time model is considered as a special case. We prove that several well-known stochastic orderings between two frailties are preserved for the response variables under the weighted proportional mean inactivity time model. We apply this model on a real data set and also perform a simulation study to examine the accuracy of the model.</p></abstract>

scholarly journals On Properties of the Bimodal Skew-Normal Distribution and an Application

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 703
Author(s):  
David Elal-Olivero ◽  
Juan F. Olivares-Pacheco ◽  
Osvaldo Venegas ◽  
Heleno Bolfarine ◽  
Héctor W. Gómez
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Skew Normal Distribution ◽  
Data Set ◽  
Normal Distributions ◽  
Stochastic Representations ◽  
Skew Normal

The main object of this paper is to develop an alternative construction for the bimodal skew-normal distribution. The construction is based upon a study of the mixture of skew-normal distributions. We study some basic properties of this family, its stochastic representations and expressions for its moments. Parameters are estimated using the maximum likelihood estimation method. A simulation study is carried out to observe the performance of the maximum likelihood estimators. Finally, we compare the efficiency of the new distribution with other distributions in the literature using a real data set. The study shows that the proposed approach presents satisfactory results.

Empirical likelihood for high-dimensional partially functional linear model

2019 ◽  
Vol 09 (04) ◽  
pp. 2050017
Author(s):  
Zhiqiang Jiang ◽  
Zhensheng Huang ◽  
Guoliang Fan
Keyword(s):  
Linear Model ◽  
Empirical Likelihood ◽  
Likelihood Ratio Statistic ◽  
Real Data ◽  
Regression Coefficients ◽  
High Dimensional ◽  
Regularity Conditions ◽  
Functional Linear Model ◽  
Data Set ◽  
Functional Predictors

This paper considers empirical likelihood inference for a high-dimensional partially functional linear model. An empirical log-likelihood ratio statistic is constructed for the regression coefficients of non-functional predictors and proved to be asymptotically normally distributed under some regularity conditions. Moreover, maximum empirical likelihood estimators of the regression coefficients of non-functional predictors are proposed and their asymptotic properties are obtained. Simulation studies are conducted to demonstrate the performance of the proposed procedure and a real data set is analyzed for illustration.

scholarly journals -Plot for Testing Spherical Symmetry for High-Dimensional Data with a Small Sample Size

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Jiajuan Liang
Keyword(s):  
Sample Size ◽  
Spherical Symmetry ◽  
Graphical Method ◽  
Small Sample Size ◽  
High Dimensional Data ◽  
Monte Carlo Study ◽  
Real Data ◽  
Small Sample ◽  
High Dimensional ◽  
Data Set

High-dimensional data with a small sample size, such as microarray data and image data, are commonly encountered in some practical problems for which many variables have to be measured but it is too costly or time consuming to repeat the measurements for many times. Analysis of this kind of data poses a great challenge for statisticians. In this paper, we develop a new graphical method for testing spherical symmetry that is especially suitable for high-dimensional data with small sample size. The new graphical method associated with the local acceptance regions can provide a quick visual perception on the assumption of spherical symmetry. The performance of the new graphical method is demonstrated by a Monte Carlo study and illustrated by a real data set.

scholarly journals Small sample sizes: A big data problem in high-dimensional data analysis

2020 ◽  
pp. 096228022097022
Author(s):  
Frank Konietschke ◽  
Karima Schwab ◽  
Markus Pauly
Keyword(s):  
Repeated Measures ◽  
Real Data ◽  
Small Sample ◽  
High Dimensional ◽  
Data Sets ◽  
Sample Sizes ◽  
Preclinical Research ◽  
Data Set ◽  
Data Problem ◽  
Small Sample Sizes

In many experiments and especially in translational and preclinical research, sample sizes are (very) small. In addition, data designs are often high dimensional, i.e. more dependent than independent replications of the trial are observed. The present paper discusses the applicability of max t-test-type statistics (multiple contrast tests) in high-dimensional designs (repeated measures or multivariate) with small sample sizes. A randomization-based approach is developed to approximate the distribution of the maximum statistic. Extensive simulation studies confirm that the new method is particularly suitable for analyzing data sets with small sample sizes. A real data set illustrates the application of the methods.

INTRINSIC DIMENSIONALITY ESTIMATION WITHIN NEIGHBORHOOD CONVEX HULL

2009 ◽  
Vol 23 (01) ◽  
pp. 31-44 ◽  
Author(s):  
CHUN-GUANG LI ◽  
JUN GUO ◽  
BO XIAO
Keyword(s):  
Convex Hull ◽  
General Framework ◽  
Data Distribution ◽  
Real Data ◽  
High Dimensional ◽  
Data Sets ◽  
Data Set ◽  
Novel Method ◽  
Linear Reconstruction ◽  
Intrinsic Dimensionality

In this paper, a novel method to estimate the intrinsic dimensionality of high-dimensional data set is proposed. Based on neighborhood information, our method calculates the non-negative locally linear reconstruction coefficients from its neighbors for each data point, and the numbers of those dominant positive reconstruction coefficients are regarded as a faithful guide to the intrinsic dimensionality of data set. The proposed method requires no parametric assumption on data distribution and is easy to implement in the general framework of manifold learning. Experimental results on several synthesized data sets and real data sets have shown the benefits of the proposed method.

USING A VARIABLE WEIGHTING k-MEANS METHOD TO BUILD A DECISION CLUSTER CLASSIFICATION MODEL

2012 ◽  
Vol 26 (02) ◽  
pp. 1250003 ◽  
Author(s):  
YAN LI ◽  
EDWARD HUNG ◽  
KORRIS CHUNG ◽  
JOSHUA HUANG
Keyword(s):  
High Dimensional Data ◽  
Real Data ◽  
Training Data ◽  
Classification Model ◽  
Classification Method ◽  
High Dimensional ◽  
New Classification ◽  
Data Set ◽  
Variable Weighting ◽  
Anderson Darling

In this paper, a new classification method (ADCC) for high-dimensional data is proposed. In this method, a decision cluster classification (DCC) model consists of a set of disjoint decision clusters, each labeled with a dominant class that determines the class of new objects falling in the cluster. A cluster tree is first generated from a training data set by recursively calling a variable weighting k-means algorithm. Then, the DCC model is extracted from the tree. Various tests including Anderson–Darling test are used to determine the stopping condition of the tree growing. A series of experiments on both synthetic and real data sets have been conducted. Their results show that the new classification method (ADCC) performed better in accuracy and scalability than existing methods like k-NN, decision tree and SVM. ADCC is particularly suitable for large, high-dimensional data with many classes.

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