Statistica Sinica
7(1997), 1021-1038
WEIGHTED DEGENERATE U- AND V-STATISTICS
WITH ESTIMATED PARAMETERS
Grace S. Shieh
Academia Sinica
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.