EconBase
← All papers

Estimates of derivatives of (log) densities and related objects

Joris Pinkse, Karl Schurter

arXiv 2 Jun 2020 · Econometrics · publishedEconometric Theory (2021) · 3 citations (OpenAlex)

arXiv:2006.01328 · PDF · DOI · OpenAlex · Extracted main text

Abstract

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.

Citation extraction

20
references
47
in-text mentions
20
distinct cited
1
self-citations
9,061
main-text words

appendix boundary found by appendix_command · 77% of the source is main text. Read the extracted text to check this.

Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Cattaneo, M. D., Jansson, M., and Ma, X (2019) Simple local polynomial density estimators1.00074100%
2Lejeune, M. and Sarda, P (1992) Smooth Estimators of Distribution and Density Functions1.00064100%
3Loader, C. R (1996) Local likelihood density estimation1.00064100%
4Karunamuni, R. J. and Zhang, S (2008) Some improvements on a boundary corrected kernel density estimator0.84333100%
5Zhang, S. and Karunamuni, R. J (1998) On kernel density estimation near endpoints0.81142100%
6Klein, R. W. and Spady, R. H (1993) An efficient semiparametric estimator for binary response models0.73732100%
7Karunamuni, R. J. and Alberts, T (2005) On boundary correction in kernel density estimation0.64422100%
8Cheng, M.-Y., Fan, J., and Marron, J. S (1997) On automatic boundary corrections0.51121100%
9Hjort, N. L. and Jones, M. C (1996) Locally nonparametric density estimation0.51121100%
10Epanechnikov, V. A (1969) Nonparametric estimation of a multidimensional probability density0.40511100%

Showing the top 10 of 20 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Identification of Causal Effects with a Bunching Design0.87462
2Semiparametric Estimation of Treatment Effects in Randomized Experiments0.64422
3Tweedie Calculus0.40511