Topic: Contributed on Statistical methods for imperfect data Title: Nonparametric estimation of emergence curves in weed science Authors:  Ricardo Cao - University of Coruna (Spain) [presenting]
Miguel Reyes - Universidade da Coruna (Spain)
Mario Francisco-Fernandez - Universidade da Coruna (Spain)
Abstract: The aim is to study nonparametric distribution function estimation when the data are grouped. Grouped data appear whether continuous random variables are measured or used in binned or rounded form or in systems in which the observation time is periodic. The motivational problem comes from a branch of agriculture called weed science. In this area, random variables based on humidity or temperature (or both) are very important for predicting weed emergence. In some weed science experiments the observation time is periodic, so researchers are unable to observe the exact values of those variables; instead, they obtain a data set consisting in counts between variable consecutive monitoring times. Moreover, sometimes, only data expressed as proportions of emerged seedlings are available. The problem of estimating the distribution function, $F$, with grouped data based on non-equidistant inspection times is addressed. A cumulative distribution function estimator is derived, which by construction, is already adapted for grouped data. Its asymptotic properties are derived, and its performance in different grouping scenarios is analyzed through simulation studies. Also, a brief study on bandwidth selection in this context is included. The proposed method is applied to analyze three seedling emergence datasets. It is also compared with nonlinear regression fits, which are the standard methods to address this problem in the weed science literature.