Abstract: A new test statistic based on Pearson correlation coefficient (rn) for cross-sectional correlation in panel data is studied. The limiting distribution of rn is presented. A simulation study shows that rn is useful in general situations. Computing rn on the residuals from models for panel data motivates the study of a new class of statistics, namely weighted degenerate U-statistics with estimated parameters . The limiting distributions of and weighted degenerate V-statistics with estimated parameters are established. Whether their limiting distributions are affected by using estimates of the parameters depends on whether or not a certain mean function has zero derivative. Applications to testing correlation in panel data and to testing for goodness-of-fit are presented.
Key words and phrases: Asymptotics, correlation, residuals, U-statistics.