Optimal variance estimation based on lagged second-order difference in nonparametric regression

Wang, Wenwu; Li, Lin; Yu, Lie

doi:10.1007/s00180-016-0666-2

Cited by 8 publications

(3 citation statements)

References 30 publications

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“…More recently, and close to our work, optimal variance difference-based estimators have been proposed in the standard partial linear model under homoscedasticity of the errors, e.g. Wang et al (2017) and Zhou et al (2018), among others. To the best of our knowledge the ACF estimation problem via difference schemes in the general partial linear regression with dependent errors model, (1.2), has not been considered.…”

Section: Introductionsupporting

confidence: 63%

ACF estimation via difference schemes for a semiparametric model with $m$-dependent errors

Levine¹,

Tecuapetla-Gómez²

2019

Preprint

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We discuss a class of difference-based estimators of the autocovariance function in a semiparametric regression model where the signal consists of the sum of an identifiable smooth function and another function with jumps (change points) and the errors are m-dependent. We establish that the influence of the smooth part of the signal over the bias of our estimators is negligible; this result does not depend on any distributional assumption. Under Gaussianity of the errors, we show that the mean squared error of the proposed estimators does not depend on either the unknown smooth function or on the values of the difference sequence coefficients; our finite sample studies suggest that the latter feature holds true regardless of the Gaussianity assumption. We also allow that both the number of change points and the magnitude of the largest jump grow with the sample size. In this case, we provide conditions on the interplay between the growth rate of these two quantities in order to ensure √ n consistency of our estimators.

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Section: Introductionsupporting

confidence: 63%

ACF estimation via difference schemes for a semiparametric model with $m$-dependent errors

Levine¹,

Tecuapetla-Gómez²

2019

Preprint

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“…When choosing blocks of length n = 2 , the estimator ̂ 2 Mean results in a differencebased estimator which considers ⌊N∕2⌋ consecutive non-overlapping differences: Difference-based estimators have been considered in many papers, see Von Neumann et al (1941), Rice (1984), Gasser et al (1986), Hall et al (1990), Dette et al (1998), Munk et al (2005), Tong et al (2013), among many others. Dai and Tong (2014) discussed estimation approaches based on differences in nonparametric regression context, Wang et al (2017) considered an estimation technique which involves differences of second order, while Tecuapetla-Gómez and Munk (2017) proposed a difference-based estimator for m-dependent data. An ordinary differencebased estimator of first order, which considers all N − 1 consecutive differences, is [see, e.g., Von Neumann et al (1941)]:…”

Section: Choice Of the Block Sizementioning

confidence: 99%

On variance estimation under shifts in the mean

Axt

Fried

2020

AStA Adv Stat Anal

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In many situations, it is crucial to estimate the variance properly. Ordinary variance estimators perform poorly in the presence of shifts in the mean. We investigate an approach based on non-overlapping blocks, which yields good results in change-point scenarios. We show the strong consistency and the asymptotic normality of such blocks-estimators of the variance under independence. Weak consistency is shown for short-range dependent strictly stationary data. We provide recommendations on the appropriate choice of the block size and compare this blocks-approach with difference-based estimators. If level shifts occur frequently and are rather large, the best results can be obtained by adaptive trimming of the blocks.

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“…The trade‐off is that, as pointed out by Dette, Munk & Wagner (1998), these earlier proposals of difference‐based estimators cannot achieve the optimal rate of MSE given in (2). More recent proposals of difference‐based estimators (Tong & Wang 2005; Wang, Lin & Yu 2017) can achieve the optimal rate (2) at the cost of a more complicated procedure and the selection of some difference order which plays a similar role as the smoothing parameter used in a residual‐based estimator. The precise magnitude of the higher order term o ( n −1 ) in (2) varies across these proposals.…”

Section: Introductionmentioning

confidence: 99%

Efficient error variance estimation in non‐parametric regression

Lin

2020

Aus NZ J of Statistics

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Summary Error variance estimation plays a key role in the analysis of homogeneous non‐parametric regression models. For a random design model, most methods in the literature for error variance estimation assume the independence between the predictor variable X and the error ε. In this work, we derive the optimal semi‐parametric efficiency bound for the error variance σ2=varfalse(ϵfalse) without such an independence assumption. A residual‐based efficient estimator for σ2 is proposed and its asymptotic normality is established. An extensive simulation study is conducted, which shows that our proposed estimator works very favourably against competitors. A simple real‐data example is also presented.

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Optimal variance estimation based on lagged second-order difference in nonparametric regression

Cited by 8 publications

References 30 publications

ACF estimation via difference schemes for a semiparametric model with $m$-dependent errors

ACF estimation via difference schemes for a semiparametric model with $m$-dependent errors

On variance estimation under shifts in the mean

Efficient error variance estimation in non‐parametric regression

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