arXiv 2 Jun 2020 · Econometrics · publishedEconometric Theory (2021) · 3 citations (OpenAlex)
arXiv:2006.01328 · PDF · DOI · OpenAlex · Extracted main text
We estimate the density and its derivatives using a local polynomial approximation to the logarithm of an unknown density $f$. The estimator is guaranteed to be nonnegative and achieves the same optimal rate of convergence in the interior as well as the boundary of the support of $f$. The estimator is therefore well-suited to applications in which nonnegative density estimates are required, such as in semiparametric maximum likelihood estimation. In addition, we show that our estimator compares favorably with other kernel-based methods, both in terms of asymptotic performance and computational ease. Simulation results confirm that our method can perform similarly in finite samples to these alternative methods when they are used with optimal inputs, i.e. an Epanechnikov kernel and optimally chosen bandwidth sequence. Further simulation evidence demonstrates that, if the researcher modifies the inputs and chooses a larger bandwidth, our approach can even improve upon these optimized alternatives, asymptotically. We provide code in several languages.
appendix boundary found by appendix_command · 77% of the source is main text. Read the extracted text to check this.
The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Cattaneo, M. D., Jansson, M., and Ma, X (2019) Simple local polynomial density estimators | 1.000 | 7 | 4 | 100% |
| 2 | Lejeune, M. and Sarda, P (1992) Smooth Estimators of Distribution and Density Functions | 1.000 | 6 | 4 | 100% |
| 3 | Loader, C. R (1996) Local likelihood density estimation | 1.000 | 6 | 4 | 100% |
| 4 | Karunamuni, R. J. and Zhang, S (2008) Some improvements on a boundary corrected kernel density estimator | 0.843 | 3 | 3 | 100% |
| 5 | Zhang, S. and Karunamuni, R. J (1998) On kernel density estimation near endpoints | 0.811 | 4 | 2 | 100% |
| 6 | Klein, R. W. and Spady, R. H (1993) An efficient semiparametric estimator for binary response models | 0.737 | 3 | 2 | 100% |
| 7 | Karunamuni, R. J. and Alberts, T (2005) On boundary correction in kernel density estimation | 0.644 | 2 | 2 | 100% |
| 8 | Cheng, M.-Y., Fan, J., and Marron, J. S (1997) On automatic boundary corrections | 0.511 | 2 | 1 | 100% |
| 9 | Hjort, N. L. and Jones, M. C (1996) Locally nonparametric density estimation | 0.511 | 2 | 1 | 100% |
| 10 | Epanechnikov, V. A (1969) Nonparametric estimation of a multidimensional probability density | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 20 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Identification of Causal Effects with a Bunching Design | 0.874 | 6 | 2 |
| 2 | Semiparametric Estimation of Treatment Effects in Randomized Experiments | 0.644 | 2 | 2 |
| 3 | Tweedie Calculus | 0.405 | 1 | 1 |