Family of the generalised gamma kernels: a generator of asymmetric kernels for nonnegative data

Hirukawa, Masayuki; Sakudo, Mari

doi:10.1080/10485252.2014.998669

Cited by 39 publications

(17 citation statements)

References 31 publications

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“…At the boundary the decreased amount of the data suggest concavity of the density in the vicinity of the origin. As a consequence, these kernels tend to misinterpret the local concavity as an indication of a mode over the strictly positive region, (Hirukawa & Sakudo, 2015). This is a condition where a given density, say m , has a shoulder at 0, i.e.…”

Section: The Bias Of Data-reflected Estimation Technique In Regressionmentioning

confidence: 99%

A Boundary Corrected Non-Parametric Regression Estimator for Finite Population Total

Cheruiyot¹,

Otieno²,

Orwa³

2019

IJSP

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This study explores the estimation of finite population total. For many years design-based approach dominated the scene in statistical inference in sample surveys. The scenario has since changed with emergence of the other approaches (Model-Based, Model-Assisted and the Randomization-Assisted), which have proved to rival the conventional approach. This paper focuses on a model based approach. Within this framework a nonparametric regression estimator for finite population total is developed. The nonparametric technique has been found from previous studies to be advantageous than its parametric counterpart in terms of robustness and flexibility.  Kernel smoother has been used in construction of the estimator. The challenge of the boundary problem encountered with the Nadaraya-Watson estimator has been addressed by modifying it using reflection technique. The performance of the proposed estimator has been compared to the design-based Horvitz Thompson estimator and the model –based nonparametric regression estimator proposed by (Dorfman, 1992) and the ratio estimator using simulated data.

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Section: The Bias Of Data-reflected Estimation Technique In Regressionmentioning

confidence: 99%

A Boundary Corrected Non-Parametric Regression Estimator for Finite Population Total

Cheruiyot¹,

Otieno²,

Orwa³

2019

IJSP

View full text Add to dashboard Cite

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“…This property is particularly advantageous to estimating the distributions that have long tails with sparse data. 1 Hirukawa and Sakudo [32] present the Weibull kernel as yet another special case. However, it is not confirmed that this kernel satisfies Lemma 1 below, and thus the kernel is not investigated throughout.…”

Section: Condition 3 M B (X)mentioning

confidence: 99%

“…The aim of this paper is to ameliorate the SSST further through combining it with the generalized gamma ("GG") kernels, a new class of asymmetric kernels with support on [0, ∞) that have been proposed recently by Hirukawa and Sakudo [32]. Our particular focus is on two special cases of the GG kernels, namely, the modified gamma ("MG") and Nakagami-m ("NM") kernels.…”

Section: Introductionmentioning

confidence: 99%

Testing Symmetry of Unknown Densities via Smoothing with the Generalized Gamma Kernels

Hirukawa

Sakudo

2016

Econometrics

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This paper improves a kernel-smoothed test of symmetry through combining it with a new class of asymmetric kernels called the generalized gamma kernels. It is demonstrated that the improved test statistic has a normal limit under the null of symmetry and is consistent under the alternative. A test-oriented smoothing parameter selection method is also proposed to implement the test. Monte Carlo simulations indicate superior finite-sample performance of the test statistic. It is worth emphasizing that the performance is grounded on the first-order normal limit and a small number of observations, despite a nonparametric convergence rate and a sample-splitting procedure of the test.

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“…α,β,γ (s) = |γ|s αγ−1 e −(s/β) γ β αγ Γ(α) (see Hirukawa and Sakudo (2015) for an application of Stacy (1962)'s generalized gamma density with parameters α, β, γ > 0). Here, if αγ ≥ 1, then, K…”

Section: Asymmetric Kernel Density Estimationmentioning

confidence: 99%

Limiting bias-reduced Amoroso kernel density estimators for non-negative data

Igarashi

Kakizawa

2017

Communications in Statistics - Theory and Methods

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The Amoroso kernel density estimator ) for nonnegative data is boundary-bias-free and has the mean integrated squared error (MISE) of order O(n −4/5 ), where n is the sample size. In this paper, we construct a linear combination of the Amoroso kernel density estimator and its derivative with respect to the smoothing parameter. Also, we propose a related multiplicative estimator. We show that the MISEs of these bias-reduced estimators achieve the convergence rates n −8/9 , if the underlying density is four times continuously differentiable. We illustrate the finite sample performance of the proposed estimators, through the simulations.

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Family of the generalised gamma kernels: a generator of asymmetric kernels for nonnegative data

Cited by 39 publications

References 31 publications

A Boundary Corrected Non-Parametric Regression Estimator for Finite Population Total

A Boundary Corrected Non-Parametric Regression Estimator for Finite Population Total

Testing Symmetry of Unknown Densities via Smoothing with the Generalized Gamma Kernels

Limiting bias-reduced Amoroso kernel density estimators for non-negative data

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