Inference for biased models: A quasi-instrumental variable approach

Lin, Lu; Zhu, Lixing; Gai, Yujie

doi:10.1016/j.jmva.2015.11.011

Cited by 2 publications

(13 citation statements)

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“…Because of the remodelling in (5), the model becomes linear and the methodology in Lin et al (2016) can be employed although the linearity is just pro forma. Note that P (Î = I) → 1.…”

Section: Bias-correctionmentioning

confidence: 99%

“…The linear transformation model is an example as the function H(•) is nonparametric. Lin et al (2016) investigated this issue for linear models. They proposed a bias correction method to achieve estimation consistency vias a semiparametric remodeling.…”

Section: Introductionmentioning

confidence: 99%

“…They proposed a bias correction method to achieve estimation consistency vias a semiparametric remodeling. Their method highly relies on the linear model structure, and the two methods proposed by Lin et al (2016), which select quasi-instrumental variables for the semiparametric remodeling, would be complex to implement and theoretically do not have the consistency of the estimated number of quasi-instrumental variables. For the linear transformation model under study, the problem is more difficult.…”

Section: Introductionmentioning

confidence: 99%

“…It is worth mentioning that unlike the classical liner model, given the selected predictors, the conditional expectation of the error in this pro forma 'linear' model is not centered, while it just has a zero expectation of the product of the error and the predictors. An idea in spirit similarly as that of Lin et al (2016) is used to construct some 'new' predictors such that a semiparametric re-modelling is possible to remove bias. However, as the linearity is just pro forma, the bias correction is more delicate than that in Lin et al (2016).…”

Section: Introductionmentioning

confidence: 99%

“…An idea in spirit similarly as that of Lin et al (2016) is used to construct some 'new' predictors such that a semiparametric re-modelling is possible to remove bias. However, as the linearity is just pro forma, the bias correction is more delicate than that in Lin et al (2016). The detail will be elaborated in Section 3.…”

Section: Introductionmentioning

confidence: 99%

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Inference for biased transformation models

Zhu

Wang

Zhao

et al. 2017

Computational Statistics & Data Analysis

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Working regression models are often parsimonious for practical use and however may be biased. This is because either some strong signals to the response are not included in working models or too many weak signals are excluded in the modelling stage, which make cumulative bias. Thus, estimating consistently the parameters of interest in biased working models is then a challenge. This paper investigates the estimation problem for linear transformation models with three aims. First, to identify strong signals in the original full models, a sufficient dimension reduction approach is applied to transferring linear transformation models to pro forma linear models. This method can efficiently avoid high-dimensional nonparametric estimation for the unknown model transformation. Second, after identifying strong signals, a semiparametric re-modeling with some artificially constructed predictors is performed to correct model bias in working models. The construction procedure is introduced and a ridge ratio estimation is proposed to determine the

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“…Because of the remodelling in (5), the model becomes linear and the methodology in Lin et al (2016) can be employed although the linearity is just pro forma. Note that P (Î = I) → 1.…”

Section: Bias-correctionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations