Max-sum tests for cross-sectional dependence of high-demensional panel data

by   Long Feng, et al.

We consider a testing problem for cross-sectional dependence for high-dimensional panel data, where the number of cross-sectional units is potentially much larger than the number of observations. The cross-sectional dependence is described through a linear regression model. We study three tests named the sum test, the max test and the max-sum test, where the latter two are new. The sum test is initially proposed by Breusch and Pagan (1980). We design the max and sum tests for sparse and non-sparse residuals in the linear regressions, respectively.And the max-sum test is devised to compromise both situations on the residuals. Indeed, our simulation shows that the max-sum test outperforms the previous two tests. This makes the max-sum test very useful in practice where sparsity or not for a set of data is usually vague. Towards the theoretical analysis of the three tests, we have settled two conjectures regarding the sum of squares of sample correlation coefficients asked by Pesaran (2004 and 2008). In addition, we establish the asymptotic theory for maxima of sample correlations coefficients appeared in the linear regression model for panel data, which is also the first successful attempt to our knowledge. To study the max-sum test, we create a novel method to show asymptotic independence between maxima and sums of dependent random variables. We expect the method itself is useful for other problems of this nature. Finally, an extensive simulation study as well as a case study are carried out. They demonstrate advantages of our proposed methods in terms of both empirical powers and robustness for residuals regardless of sparsity or not.


page 1

page 2

page 3

page 4


Asymptotic Independence of the Sum and Maximum of Dependent Random Variables with Applications to High-Dimensional Tests

For a set of dependent random variables, without stationary or the stron...

Asymptotic Independence of the Quadratic form and Maximum of Independent Random Variables with Applications to High-Dimensional Tests

This paper establishes the asymptotic independence between the quadratic...

Model-Free Tests for Series Correlation in Multivariate Linear Regression

Testing for series correlation among error terms is a basic problem in l...

A DFA-based bivariate regression model for estimating the dependence of PM2.5 among neighbouring cities

On the basis of detrended fluctuation analysis (DFA), we propose a new b...

Improving Sparse Associative Memories by Escaping from Bogus Fixed Points

The Gripon-Berrou neural network (GBNN) is a recently invented recurrent...

Extension of the Lagrange multiplier test for error cross-section independence to large panels with non normal errors

This paper reexamines the seminal Lagrange multiplier test for cross-sec...

Censored pairwise likelihood-based tests for mixing coefficient of spatial max-mixture models

Max-mixture processes are defined as Z = max(aX, (1 -- a)Y) with X an as...