Calibrating Histograms with Application to Economic Data

In this paper the problem of automatic calibration of histograms by cross-validation is considered, assuming the true underlying density is continuous with continuous first derivative. The histogram is one of the simpliest semiparametric estimators used by economists, but it is surprisingly difficult to construct histograms with small estimation errors. Cross-validation algorithms attempt, to automatically determine histogram bin widths that are nearly optimal with respect to mean integrated squared error. Alternative philosophies and approaches of cross-validation for histograms are presented. It is shown that the classical Sturges’ rule performs poorly and that cross-validation is a relatively difficult task. Understanding the performance of cross-validation algorithms in this simple setting should prove valuable when cross-validating other more complex semiparametric procedures.