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.
- Kronmal and tarter
- Nonparametric density estimation
- Number of terms
- Trigonometric series
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty