Some Further Results on Nonuniform Rates of Convergence to Normality in Finite Population with Applications

Abstract

Rates of convergence in CLT are studied while sampling from a finite population under suitable moment assumptions on super population. We assume that all the moments for variate values exist in super population, having specific types of moment bound; but variate values are not necessarily bounded. Consequently probabilities of deviations, nonuniform L _p version of the Berry–Esseen theorem and moment type convergences are proved for standardised sample sum from finite population. In cross-sectional growth data, for each value of time t, the growth observations y _i  = y _i (t) may be considered as sample arising from a finite population. Average of observations falling in a small window of time may then be considered as an estimate of growth to be assigned at the average of time points in that interval. Convergence rates in CLT for sample mean in a finite population are compared with optimal rates in iid set-up, in order to assess performance of growth estimates. Growth data of a bulb crop onion is analysed. Derivative and proliferation rate of growth curve of the bulb crop are estimated to find appropriate time for harvesting the crop.