Composite Estimation: An Asymptotically Weighted Least Squares Approach

Lin, Lu; Feng, Li; Wang, Kangning; Zhu, Lixing

doi:10.5705/ss.202016.0399

Cited by 3 publications

(4 citation statements)

References 21 publications

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“…Remark 2 In the existing works, e.g., Sun et al (2013); Lin et al (2019); Jiang et al (2016), the condition C m2 is fulfilled empirically by replacing the unknown function…”

Section: Model-based Weight Selectionsmentioning

confidence: 99%

“…Remark 3 As stated in Remark 2, to fulfill C m2 , the existing methods in Sun et al (2013); Lin et al (2019); Jiang et al (2016) rely on the estimation of the inverse of the CDF of ε, which is unavailable directly from the sample set of (X, Y ). Instead of directly related to the distribution of the error, the condition C ′ m2 only relies on the two expectations in ( 22), which can be directly estimated by the sample of (X, Y ), and the estimation has the convergence rate of parametric estimation.…”

Section: Model-based Weight Selectionsmentioning

confidence: 99%

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Renewable Composite Quantile Method and Algorithm for Nonparametric Models with Streaming Data

Chen

Fang

Lü

2022

Preprint

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We are interested in renewable estimations and algorithms for nonparametric models with streaming data. In our method, the nonparametric function of interest is expressed through a functional depending on a weight function and a conditional distribution function (CDF). The CDF is estimated by renewable kernel estimations combined with function interpolations, based on which we propose the method of renewable weighted composite quantile regression (WCQR). Then we fully use the model structure and obtain new selectors for the weight function, such that the WCQR can achieve asymptotic unbiasness when estimating specific functions in the model. We also propose practical bandwidth selectors for streaming data and find the optimal weight function minimizing the asymptotic variance. The asymptotical results show that our estimator is almost equivalent to the oracle estimator obtained from the entire data together. Besides, our method also enjoys adaptiveness to error distributions, robustness to outliers, and efficiency in both estimation and computation. Simulation studies and real data analyses further confirm our theoretical findings.

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“…Remark 2 In the existing works, e.g., Sun et al (2013); Lin et al (2019); Jiang et al (2016), the condition C m2 is fulfilled empirically by replacing the unknown function…”

Section: Model-based Weight Selectionsmentioning

confidence: 99%

Section: Model-based Weight Selectionsmentioning

confidence: 99%

Renewable Composite Quantile Method and Algorithm for Nonparametric Models with Streaming Data

Chen

Fang

Lü

2022

Preprint

Self Cite

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“…For instance, in quantile regression and nonparametric regression, statisticians have achieved the optimal estimation efficiency via optimizing the composite estimation covariance, see Zou and Yuan (2008); Kai, Li, and Zou (2010); Sun, Gai, and Lin (2013); Kai, Li, and Zou (2011);Bradic, Fan, and Wang (2011) and among others. Recently, the composition idea has also been utilized to reduce the estimation bias for various statistical models, see Lin et al (2019); Cheng et al (2018); Lin and Li (2008) for further reading.…”

Section: Introductionmentioning

confidence: 99%

A race-DC in Big Data

Li¹

2019

Preprint

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The strategy of divide-and-combine (DC) has been widely used in the area of big data. Bias-correction is crucial in the DC procedure for validly aggregating the locally biased estimators, especial for the case when the number of batches of data is large. This paper establishes a race-DC through a residualadjustment composition estimate (race). The race-DC applies to various types of biased estimators, which include but are not limited to Lasso estimator, Ridge estimator and principal component estimator in linear regression, and least squares estimator in nonlinear regression. The resulting global estimator is strictly unbiased under linear model, and is acceleratingly bias-reduced in nonlinear model, and can achieve the theoretical optimality, for the case when the number of batches of data is large. Moreover, the race-DC is computationally simple because it is a least squares estimator in a pro forma linear regression. Detailed simulation studies demonstrate that the resulting global estimator is significantly bias-corrected, and the behavior is comparable with the oracle estimation and is much better than the competitors.

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“…Recently, bias-reduction by composition has attained much attention as well in the literature. Based on the asymptotic or approximate representation of the initial estimator, Lin et al (2019), and Lin and Li (2008) introduced composite least squares to realize the targets of reducing estimation bias and optimizing estimation covariance, simultaneously. Moreover, the relevant composition methods were suggested by , Dai et al (2016 and, Wang and Lin (2015), and Tong and Wang (2005) for constructing the composite estimators of the derivative and variance in nonparametric regression.…”

Section: Introductionmentioning

confidence: 99%

A Global Bias-Correction DC Method for Biased Estimation under Memory Constraint

Li¹,

Li²

2019

Preprint

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This paper establishes a global bias-correction divide-and-conquer (GBC-DC) rule for biased estimation under the case of memory constraint. In order to introduce the new estimation, a closed representation of the local estimators obtained by the data in each batch is adopted, aiming to formulate a pro forma linear regression between the local estimators and the true parameter of interest. Least square method is then used within this framework to composite a global estimator of the parameter. Thus, the main advantage over the classical DC method is that the new GBC-DC method can absorb the information hidden in the statistical structure and the variables in each batch of data. Consequently, the resulting global estimator is strictly unbiased even if the local estimator has a non-negligible bias. Moreover, the global estimator is consistent, and even can achieve root-n consistency, without the constraint on the number of batches. Another attractive feature of the new method is computationally simple and efficient, without use of any iterative algorithm and local bias-correction. Specifically, the proposed GBC-DC method applies to various biased estimations such as shrinkage-type estimation and nonparametric regression estimation. Detailed simulation studies demonstrate that the proposed GBC-DC approach is significantly bias-corrected, and the behavior is comparable with the full data estimation and is much better than the competitors.

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Composite Estimation: An Asymptotically Weighted Least Squares Approach

Cited by 3 publications

References 21 publications

Renewable Composite Quantile Method and Algorithm for Nonparametric Models with Streaming Data

Renewable Composite Quantile Method and Algorithm for Nonparametric Models with Streaming Data

A race-DC in Big Data

A Global Bias-Correction DC Method for Biased Estimation under Memory Constraint

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