A class of Birnbaum–Saunders type kernel density estimators for nonnegative data

Kakizawa, Yoshihide

doi:10.1016/j.csda.2021.107249

Cited by 6 publications

(10 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We tried to conduct the LSCV smoothing parameter selection 5 . Unlike the direct sample (Kakizawa (2018(Kakizawa ( ,2021), the present LB setting, for small sample size n = 100 (not being reported here), produced multiple local minima for the LSCV score (in many cases, it was rather unstable numerically), whereas such an undesirable behavior seemed to be fixed when n = 300. A further issue of considering a plug-in selection with a pilot estimator is left in future.…”

Section: Simulation Studiesmentioning

confidence: 77%

“…The analysts can now choose what they like, among many options available for the kernel with support [0, ∞). According to Igarashi and Kakizawa (2020) (see also Kakizawa (2021)), let us choose k(•; β, x) in the following form:…”

Section: Boundary Bias Problem and Asymmetric Kernel Methodsmentioning

confidence: 99%

“…In some numerical studies of Section 5, we will put q = 1/2 (symmetrical-based BS kernel) or q = 0 (log-symmetrical (LS) kernel), with (θ, c) = (0, 1), for simplicity, and use the power exponential (PE) generator; g PE[p] (y) = exp(−λ p y p ), p ≥ 1/2, where the particular choice λ p = {Γ(3/(2p))/Γ(1/(2p))} p ensures that the PE density has the variance 1, like the standard normal density. Other generators (Kotz-type, generalized Pearson-type VII, and generalized logistic-type III) are found in Kakizawa (2018Kakizawa ( ,2021. A symmetrical-based central qBS kernel belongs to a family of symmetrical-based qMIG kernels (MIG is an abbreviation of a mixture of IG and RIG), which is enlarged, linking to a class of skew-BS type kernels.…”

Section: Boundary Bias Problem and Asymmetric Kernel Methodsmentioning

confidence: 99%

“…A symmetrical-based central qBS kernel belongs to a family of symmetrical-based qMIG kernels (MIG is an abbreviation of a mixture of IG and RIG), which is enlarged, linking to a class of skew-BS type kernels. See Kakizawa (2018Kakizawa ( ,2021.…”

Section: Boundary Bias Problem and Asymmetric Kernel Methodsmentioning

confidence: 99%

“…The asymptotic bias and variance of f β,ǫ (x) when x is near the origin; x/β → κ, where κ ≥ 0 is finite, can be obtained, as in Kakizawa (2018Kakizawa ( ,2021. The details are omitted.…”

mentioning

confidence: 99%

See 4 more Smart Citations

Asymmetric Kernel Density Estimation for Biased Data

Kakizawa¹

2023

Preprint

View full text Add to dashboard Cite

Nonparametric density estimation for nonnegative data is considered in a situation where a random sample is not directly available but the data are instead observed from the length-biased sampling. Due to the boundary bias problem of the location-scale kernel, the approach in this paper is an application of asymmetric kernel. Two nonparametric density estimators are proposed. The mean integrated squared error, strong consistency, and asymptotic normality of the estimators are investigated. Some simulations illustrate the finite sample performance of the estimators.

show abstract

Section: Simulation Studiesmentioning

confidence: 77%

Section: Boundary Bias Problem and Asymmetric Kernel Methodsmentioning

confidence: 99%

Section: Boundary Bias Problem and Asymmetric Kernel Methodsmentioning

confidence: 99%

Section: Boundary Bias Problem and Asymmetric Kernel Methodsmentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

Asymmetric Kernel Density Estimation for Biased Data

Kakizawa¹

2023

Preprint

View full text Add to dashboard Cite

show abstract

Asymmetric kernel density estimation for biased data

Kakizawa

2024

J. Korean Stat. Soc.

View full text Add to dashboard Cite

Asymptotic properties of Dirichlet kernel density estimators

Ouimet

Tolosana‐Delgado

2022

Journal of Multivariate Analysis

View full text Add to dashboard Cite

In this paper, we introduce Dirichlet kernels for the estimation of multivariate densities supported on the d-dimensional simplex. These kernels generalize the beta kernels from Brown & Chen (1999); Chen (1999, 2000a); Bouezmarni & Rolin (2003), originally studied in the context of smoothing for regression curves. We prove various asymptotic properties for the estimator : bias, variance, mean squared error, mean integrated squared error, asymptotic normality and uniform strong consistency. In particular, the asymptotic normality and uniform strong consistency results are completely new, even for the case d = 1 (beta kernels). These new kernel smoothers can be used for density estimation of compositional data. The estimator is simple to use, free of boundary bias, allocates non-negative weights everywhere on the simplex, and achieves the optimal convergence rate of n −4/(d+4) for the mean integrated squared error.

show abstract

A class of Birnbaum–Saunders type kernel density estimators for nonnegative data

Cited by 6 publications

References 42 publications

Asymmetric Kernel Density Estimation for Biased Data

Asymmetric Kernel Density Estimation for Biased Data

Asymmetric kernel density estimation for biased data

Asymptotic properties of Dirichlet kernel density estimators

Contact Info

Product

Resources

About