Nonparametric estimation of the derivatives of a density by the method of wavelet for mixing sequences

Hosseinioun, Nargess; Doosti, Hassan; Nirumand, Hossein Ali

doi:10.1007/s00362-010-0328-3

Cited by 7 publications

(2 citation statements)

References 5 publications

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“…For example, Hall et al (2004), Fan and Yim (2004), De Gooijer and Zerom (2003), and so on. By the way, estimation of density has been studied by many authors, such as Emura and Konno (2012), Hosseinioun et al (2012), Liu and Lu (2011), and Wied and Weiβbach (2012). In these papers, it is assumed that the observations are complete.…”

Section: Introductionmentioning

confidence: 98%

Asymptotic normality of conditional density estimation with left-truncated and dependent data

Liang

Baek

2014

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Based on the idea of the local polynomial smoother, we construct the Nadaraya-Watson type and local linear estimators of conditional density function for a left-truncation model. Asymptotic normality of the estimators is established under the lifetime observations are assumed to be a sequence of stationary α-mixing random variables. Finite sample behavior of the estimators is investigated via simulations too.

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Section: Introductionmentioning

confidence: 98%

Asymptotic normality of conditional density estimation with left-truncated and dependent data

Liang

Baek

2014

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“…Chaubey et al [16] consider the upper bound over L p -loss for wavelet estimators of density derivative functions. A convergence rate over the mean integrated error of a derivative estimator for mixing sequences is proved by [17]. For the estimation problem (1), the derivatives estimation of the variance function via the wavelet method is proved by [18].…”

Section: Introductionmentioning

confidence: 99%

Partial Derivatives Estimation of Multivariate Variance Function in Heteroscedastic Model via Wavelet Method

Kou,

Zhang

2024

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For derivative function estimation, conventional research only focuses on the derivative estimation of one-dimensional functions. This paper considers partial derivatives estimation of a multivariate variance function in a heteroscedastic model. A wavelet estimator of partial derivatives of a multivariate variance function is proposed. The convergence rates of a wavelet estimator under different estimation errors are discussed. It turns out that the strong convergence rate of the wavelet estimator is the same as the optimal uniform almost sure convergence rate of nonparametric function problems.

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On Bahadur representation for sample quantiles under α-mixing sequence

Zhang

Yang

2012

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Nonparametric estimation of the derivatives of a density by the method of wavelet for mixing sequences

Cited by 7 publications

References 5 publications

Asymptotic normality of conditional density estimation with left-truncated and dependent data

Asymptotic normality of conditional density estimation with left-truncated and dependent data

Partial Derivatives Estimation of Multivariate Variance Function in Heteroscedastic Model via Wavelet Method

On Bahadur representation for sample quantiles under α-mixing sequence

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