Least product relative error estimation for identification in multiplicative additive models

Ming, Hao; Liu, Huilan; Yang, Hu

doi:10.1016/j.cam.2021.113886

Cited by 6 publications

(2 citation statements)

References 19 publications

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“…However, the asymptotic theory becomes troublesome. Furthermore, as in [16], how to identify which set of covariates lies in the linear part or the nonlinear part is interesting. Additionally, when the dimension of covariates is high, how to effectively select the true important variables deserves to be studied thoroughly.…”

Section: Discussionmentioning

confidence: 99%

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SIMEX Estimation of Partially Linear Multiplicative Regression Model with Mismeasured Covariates

Chen,

Wan

2023

Symmetry

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In many practical applications, such as the studies of financial and biomedical data, the response variable usually is positive, and the commonly used criteria are based on absolute errors, which is not desirable. Rather, the relative errors are more of concern. We consider statistical inference for a partially linear multiplicative regression model when covariates in the linear part are measured with error. The simulation–extrapolation (SIMEX) estimators of parameters of interest are proposed based on the least product relative error criterion and B-spline approximation, where two kinds of relative errors are both introduced and the symmetry emerges in the loss function. Extensive simulation studies are conducted and the results show that the proposed method can effectively eliminate the bias caused by the measurement errors. Under some mild conditions, the asymptotic normality of the proposed estimator is established. Finally, a real example is analyzed to illustrate the practical use of our proposed method.

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Section: Discussionmentioning

confidence: 99%

“…Recently, Ref. [16] proposed multiplicative additive models based on the least product relative error criterion (LPRE), where the B-spline basis functions are used to estimate the nonparametric functions. Simulation studies have demonstrated that their approach performs well.…”

Section: Introductionmentioning

confidence: 99%

SIMEX Estimation of Partially Linear Multiplicative Regression Model with Mismeasured Covariates

Chen,

Wan

2023

Symmetry

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Credibility Theory Under the Least Squared Relative Loss Function

Yong,

Zhang,

Zhu

2024

Appl Stoch Models Bus & Ind

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The classical Bühlmann model employs a least squared loss criterion that penalizes pricing errors equally across all risk classes. In contrast, this paper develops a new credibility theory based on the least squared relative loss (LSRL) function to address scenarios where the classical approach may fall short. We derive explicit expressions of LSRL‐based credibility estimators, including non‐parametric versions and Bühlmann–Straub extensions. Through a comparative study, we illustrate the real‐world applicability of the LSRL estimator across different scenarios, highlighting its advantages and limitations in comparison to the classical model. Additionally, we explore different LSRL formulations to provide deeper insights into their practical viability.

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Efficient variable selection for high-dimensional multiplicative models: a novel LPRE-based approach

Chen,

Ming,

Yang

2024

Stat Papers

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Least product relative error estimation for identification in multiplicative additive models

Cited by 6 publications

References 19 publications

SIMEX Estimation of Partially Linear Multiplicative Regression Model with Mismeasured Covariates

SIMEX Estimation of Partially Linear Multiplicative Regression Model with Mismeasured Covariates

Credibility Theory Under the Least Squared Relative Loss Function

Efficient variable selection for high-dimensional multiplicative models: a novel LPRE-based approach

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