Asymptotic properties of one-step <i>M</i>-estimators

Linke, Yuliana

doi:10.1080/03610926.2018.1487982

Cited by 14 publications

(7 citation statements)

References 42 publications

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“…The second relation in (35) directly follows from (42). Moreover, the above-mentioned arguments and the representations ( 40) and ( 42) imply (36). Further, the first estimator in (37) is obvious by the above remark about the domain of summation in the definition of functions w nj (t), and the relations sup…”

Section: Proofsmentioning

confidence: 82%

“…Proof. Let us prove (35) and (36). First of all, note that, due to the Cauchy-Bunyakovsky-Schwartz inequality, w 0 (t)w 2 (t) − w 2 1 (t) ≥ 0 for all t ∈ [0, 1] and this difference is continuous in t.…”

Section: Proofsmentioning

confidence: 97%

“…4). Similar conditions for design elements were also used in [37] and [40] in nonparametric regression, and in [36]- [38] -in nonlinear regression.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Universal local linear kernel estimators in nonparametric regression

Linke¹,

Borisov²,

Ruzankin³

et al. 2022

Preprint

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New local linear estimators are proposed for a wide class of nonparametric regression models. The estimators are uniformly consistent regardless of satisfying traditional conditions of dependence of design elements. The estimators are the solutions of a specially weighted least-squares method. The design can be fixed or random and does not need to meet classical regularity or independence conditions. As an application, several estimators are constructed for the mean of dense functional data. The theoretical results of the study are illustrated by simulations. An example of processing real medical data from the epidemiological crosssectional study ESSE-RF is included. We compare the new estimators with the estimators best known for such studies.

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Section: Proofsmentioning

confidence: 82%

Section: Proofsmentioning

confidence: 97%

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Universal local linear kernel estimators in nonparametric regression

Linke¹,

Borisov²,

Ruzankin³

et al. 2022

Preprint

Self Cite

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“…The conditions provide uniform consistency of the estimators, but guarantee only pointwise consistency of the Nadarya-Watson ones. Besides, similar restrictions on the design elements were used before in Linke and Borisov (2017), and Linke (2019 in estimation of the parameters of several nonlinear regression models.…”

Section: Introductionmentioning

confidence: 99%

“…Previously, similar ideas were implemented in [50] for slightly different evaluations (in detail, see Section 4). Similar conditions for design elements were also used in [51,52] in nonparametric regression, and in [53][54][55]-in nonlinear regression.…”

Section: Introductionmentioning

confidence: 99%

Universal Local Linear Kernel Estimators in Nonparametric Regression

et al. 2022

Self Cite

View full text Add to dashboard Cite

New local linear estimators are proposed for a wide class of nonparametric regression models. The estimators are uniformly consistent regardless of satisfying traditional conditions of dependence of design elements. The estimators are the solutions of a specially weighted least-squares method. The design can be fixed or random and does not need to meet classical regularity or independence conditions. As an application, several estimators are constructed for the mean of dense functional data. The theoretical results of the study are illustrated by simulations. An example of processing real medical data from the epidemiological cross-sectional study ESSE-RF is included. We compare the new estimators with the estimators best known for such studies.

show abstract