Nonparametric estimation in a regression model with additive and multiplicative noise

Chesneau, Christophe; Kolei, Salima El; Kou, Junke; Navarro, Fabien

doi:10.1016/j.cam.2020.112971

Cited by 11 publications

(15 citation statements)

References 34 publications

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“…, where the last step above follows by repeated application of the Cauchy-Schwarz inequality. Finally, using inequality (7) in inequality ( 5), we get…”

Section: Bounding the Mean Deviation Termmentioning

confidence: 99%

“…εi n (x) that may be easier to verify in some contexts. By slightly changing some of the steps leading to inequality (7), the third term on the r.h.s. of inequality ( 8) can be replaced with the term…”

Section: Bounding the Mean Deviation Termmentioning

confidence: 99%

“…Finally, Fan et al [12] present a quasi-maximum likelihood approach for estimating the parameters of GARCH models and investigate their asymptotic properties. Next, consider the nonparametric setup in Example 2, and suppose the function Q * and its regression estimate Qn are (asymptotically) a.s. uniformly invertible 7 . We have…”

Section: Example 2 [Nonparametric Model] the Model Class Ismentioning

confidence: 99%

“…Section 3 of Zhou et al [30] presents robust estimators of Q * when f * is linear and notes that these estimators Qn possess asymptotic and finite sample guarantees in the form of Assumptions 7, 8, and 9. Finally, Theorem 3.1 of Chesneau et al [7] can be used to derive asymptotic guarantees for wavelet estimators of Q * .…”

Section: Example 2 [Nonparametric Model] the Model Class Ismentioning

confidence: 99%

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Heteroscedasticity-aware residuals-based contextual stochastic optimization

Kannan¹,

Bayraksan²,

Luedtke³

2021

Preprint

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We explore generalizations of some integrated learning and optimization frameworks for datadriven contextual stochastic optimization that can adapt to heteroscedasticity. We identify conditions on the stochastic program, data generation process, and the prediction setup under which these generalizations possess asymptotic and finite sample guarantees for a class of stochastic programs, including two-stage stochastic mixed-integer programs with continuous recourse. We verify that our assumptions hold for popular parametric and nonparametric regression methods.

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“…, where the last step above follows by repeated application of the Cauchy-Schwarz inequality. Finally, using inequality (7) in inequality ( 5), we get…”

Section: Bounding the Mean Deviation Termmentioning

confidence: 99%

Section: Bounding the Mean Deviation Termmentioning

confidence: 99%

Section: Example 2 [Nonparametric Model] the Model Class Ismentioning

confidence: 99%

Section: Example 2 [Nonparametric Model] the Model Class Ismentioning

confidence: 99%

See 2 more Smart Citations

Heteroscedasticity-aware residuals-based contextual stochastic optimization

Kannan¹,

Bayraksan²,

Luedtke³

2021

Preprint

View full text Add to dashboard Cite

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“…Most recently, Chesneau, El Kolei, Kou and Navarro (2020) considered the problem in a multivariate setting and proposed a wavelet thresholding approach to solve it. This problem has a great deal of applications, for instance, in Global Positioning System (GPS) signal propagation modeling where there is empirical evidence that in heavy multi-path urban areas, the GPS signal encounters both additive and multiplicative noise (see Huang et al (2013)), or in finance where one is interested in estimating the variance from the returns of an asset and the interested reader may refer to Chesneau et al (2020) for more. Almost all of these articles assume that the error terms are white noise processes or i.i.d.…”

Section: Introductionmentioning

confidence: 99%

Estimation in nonparametric regression model with additive and multiplicative noise via Laguerre series

Benhaddou¹

2020

Preprint

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We look into the nonparametric regression estimation with additive and multiplicative noise and construct adaptive thresholding estimators based on Laguerre series. The proposed approach achieves asymptotically near-optimal convergence rates when the unknown function belongs to Laguerre-Sobolev space. We consider the problem under two noise structures; (1) i.i.d. Gaussian errors and (2) long-memory Gaussian errors. In the i.i.d. case, our convergence rates are similar to those found in the literature. In the long-memory case, the convergence rates depend on the long-memory parameters only when long-memory is strong enough in either noise source, otherwise, the rates are identical to those under i.i.d. noise.

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