On integral functionals of a density

Nadaraya, É. A.; Sokhadze, Grigol

doi:10.1080/03610926.2014.974825

Cited by 2 publications

(4 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Therefore, a thorough understanding of the Bhattacharya estimator is of practical importance. In [2], [9] and [10], the authors focused on the asymptotic regime but did not consider the finite sample size case. More specifically, there are inexplicit constants in their bounds.…”

Section: Available Estimatorsmentioning

confidence: 99%

“…where the inequality in (94) follows from the assumptions in (10), and the last bound follows from the triangle inequality together with the definition of ρ max . Now consider the integral in the first term in (95)…”

Section: Appendix Cmentioning

confidence: 99%

“…where the inequalities in (103) follows from the assumptions in (10) and (83), and the bound in (107) follows by using similar step leading to the bound in (102).…”

Section: Appendix Cmentioning

confidence: 99%

“…The work of [9] was also the first to consider the problem of entropy estimation. The techniques of [2] and [9] have been generalized by Nadaraya and Sokhadze in [10] to functionals that depend on the first mth derivatives of the density. In this work, we will recover the rates of [10] with less restrictive assumptions.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Nonparametric Estimation of the Fisher Information and Its Applications

Cao,

Dytso,

Fauß

et al. 2020

Preprint

View full text Add to dashboard Cite

This paper considers the problem of estimation of the Fisher information for location from a random sample of size n. First, an estimator proposed by Bhattacharya is revisited and improved convergence rates are derived. Second, a new estimator, termed a clipped estimator, is proposed. Superior upper bounds on the rates of convergence can be shown for the new estimator compared to the Bhattacharya estimator, albeit with different regularity conditions. Third, both of the estimators are evaluated for the practically relevant case of a random variable contaminated by Gaussian noise. Moreover, using Brown's identity, which relates the Fisher information and the minimum mean squared error (MMSE) in Gaussian noise, two corresponding consistent estimators for the MMSE are proposed. Simulation examples for the Bhattacharya estimator and the clipped estimator as well as the MMSE estimators are presented. The examples demonstrate that the clipped estimator can significantly reduce the required sample size to guarantee a specific confidence interval compared to the Bhattacharya estimator.

show abstract

Section: Available Estimatorsmentioning

confidence: 99%

Section: Appendix Cmentioning

confidence: 99%

“…where the inequalities in (103) follows from the assumptions in (10) and (83), and the bound in (107) follows by using similar step leading to the bound in (102).…”

Section: Appendix Cmentioning

confidence: 99%