English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider a testing problem for cross-sectional dependence forhigh-dimensional panel data, where the number of cross-sectional units ispotentially much larger than the number of observations. The cross-sectionaldependence is described through a linear regression model. We study three testsnamed the sum test, the max test and the max-sum test, where the latter two arenew. The sum test is initially proposed by Breusch and Pagan (1980). We designthe max and sum tests for sparse and non-sparse residuals in the linearregressions, respectively.And the max-sum test is devised to compromise bothsituations on the residuals. Indeed, our simulation shows that the max-sum testoutperforms the previous two tests. This makes the max-sum test very useful inpractice where sparsity or not for a set of data is usually vague. Towards thetheoretical analysis of the three tests, we have settled two conjecturesregarding the sum of squares of sample correlation coefficients asked byPesaran (2004 and 2008). In addition, we establish the asymptotic theory formaxima of sample correlations coefficients appeared in the linear regressionmodel for panel data, which is also the first successful attempt to ourknowledge. To study the max-sum test, we create a novel method to showasymptotic 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 empiricalpowers and robustness for residuals regardless of sparsity or not.

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