The Selection of Terms in an Orthogonal Series Density Estimator
Peter John Diggle, Peter M. Hall · Journal of the American Statistical Association · 1986
We show that Kronmal and Tarter's well-known rule for selecting the terms in an orthogonal series density estimator can lead to poor performance and even inconsistency in certain cases. These difficulties arise when the underlying density has a nonmonotone sequence of Fourier coefficients, as is likely to be the case with sharply peaked or multimodal distributions. We suggest a way of overcoming these shortcomings.