Interval-censored unimodal kernel density estimation via data sharpening

ABSTRACT

In this paper, we extend Choi and Hall's [Data sharpening as a prelude to density estimation. Biometrika. 1999;86(4):941–947] data sharpening algorithm for kernel density estimation to interval-censored data. Data sharpening has several advantages, including bias and mean integrated squared error (MISE) reduction as well as increased robustness to bandwidth misspecification. Several interval metrics are explored for use with the kernel function in the data sharpening transformation. A simulation study based on randomly generated data is conducted to assess and compare the performance of each interval metric. It is found that the bias is reduced by sharpening, often with little effect on the variance, thus maintaining or reducing overall MISE. Applications involving time to onset of HIV and running distances subject to measurement error are used for illustration.

KEYWORDS:

• Nonparametric estimation
• shape constraints
• mean-shift algorithm

Acknowledgments

The authors gratefully acknowledge the helpful comments of an anonymous reviewer.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

WJB's research is supported by an NSERC Operating Grant.