Growth Curve of Elephant Foot Yam, One Sided Estimation and Confidence Band

Abstract

Almost sure convergence of an estimator to a real valued parameter from a particular side (above/below), termed one sided estimation, is of interest in conservative estimation. Such estimator converges to the parameter from a particular direction almost surely (a.s.) for all large sample size n. We consider one sided estimation of growth curve for Elephant foot yam from experimental data and examine the resultant confidence band of the curve. Almost sure upper and lower bounds for yield over time may be used as conservative estimates of crop yield with probability 1. Deviation probabilities and convergence rates in central limit theorem for proposed estimators are studied under the set-up of U-statistics. Probability bounds of tail events concerning error in approximation are shown to be exponentially decaying. Some special types of L statistics relevant to one sided convergence are also considered for computing rates in CLT. Implications of results are discussed in the context of Yam growth curve estimation with live data. Associated a.s. confidence band for estimated growth curve may be narrow even for a widely dispersed data, as the goal of constructing confidence band here is different from including all data points inside the band. Upper and lower estimate of the growth curve of yam are seen to cover the mean response curve in general. Confidence band for variance of yam yield over time exhibits similar coverage properties. Presence of an upward spike is observed in the growth curve of yam yield towards the end of yam plant lifetime. The spike is prominent when yam is harvested at the end of second season in a 2-year study, instead of harvesting the crop after first year.