SFB 303 Discussion Paper No. A - 150

Author: Scott, David, and Heinz-Peter Schmitz
Title: Calibrating Histograms with Application to Economic Data
Abstract: Semiparametric methods in economics have provided a novel and powerful tool for modeling real economic data that are not easily fit by usual parametric models. The simplest semiparametric tool is the classical histogram. A practical consideration to successful semiparametric modeling is choosing calibration or smoothing parameters that essentially determine the optimal noise suppression level. The smoothing parameter for the histogram is the bin width. While experienced economists and statisticians can often twiddle these parameters close to optimal values, automatic or data-based algorithms are of extreme practical value. With large data sets often encountered in economics, twiddling may not be successful since alternative choices of smoothing parameters may give pictures that "look good" while supporting opposing hypotheses. Automatic procedures hold the most promise in this situation. In this paper the problem of automatic calibration of histograms by crossvalidation is considered, assuming the true underlying density is continuous with continuous first derivative. Alternative philosophies and approaches of crossvalidation for histograms are presented. Understanding their performance in this relatively simple setting should prove valuable when cross-validating other more complex semiparametric procedures.
Keywords: Histogram; Bin width; Cross-validation; Automatic bin width selection
Creation-Date: January 1988
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