Estimation for biased partial linear single index models

Lü, Jun; Zhu, Xuehu; Lin, Lu; Zhu, Lixing

doi:10.1016/j.csda.2019.03.006

Cited by 3 publications

(3 citation statements)

References 12 publications

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“…Together with the results under Case (I), we can conclude that there would be some important covariates inṼ 2 = (V 1 , V 5 , V 6 , V 7 , V 9 , V 13 , V 14 ) and thus some further selection is necessary. Note that Lu et al (2019) also found this phenomenon that the reduced model determined by LASSO has a large bias, then constructed an artificial variable into the regression model to reduce bias. Therefore, we should takeṼ 2 into the consideration to predict the price of automobiles.…”

Section: F I G U R Ementioning

confidence: 95%

“…We now analyze an automobile data of 205 records with 25 attributes, including the logarithm of price of automobiles as the response Y and the other 24 covariates. Lu et al (2019) gave a brief overview to provide more information about these variables. After dropping off those samples…”

Section: Automobile Datamentioning

confidence: 99%

“…10 , V 13 , and V 14 marginally have significant dependence with the response. However, Lu et al (2019) built a partial linear single-index model to describe the dependence of the response on the covariates, and adapted the LASSO method (Tibshirani, 1996) to select four continuous covariatesṼ 1 = (V 2 , V 3 , V 4 , V 10 ) as important ones. To check whether there exist some more important covariates…”

Section: Ta B L Ementioning

confidence: 99%

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Testing for conditional independence: A groupwise dimension reduction‐based adaptive‐to‐model approach

Zhu

Lü

Zhang

et al. 2021

Scandinavian J Statistics

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In this article, we propose an adaptive-to-model test for conditional independence through groupwise dimension reduction developed in sufficient dimension reduction field. The test statistic under the null hypothesis is asymptotically normally distributed. Although it is also based on nonparametric estimation like any local smoothing tests for conditional independence, its behavior is similar to existing local smoothing tests with only the number of covariates under the null hypothesis. Furthermore, it can detect local alternatives distinct from the null at the rate that is also only related to the number of covariates under the null hypothesis. Therefore, the curse of dimensionality is largely alleviated. To achieve the above goal, we also suggest a groupwise least squares estimation for the groupwise central subspace in sufficient dimension reduction. It is of its own importance in estimation theory though it is as a by-product for the model adaptation of test statistic described herewith. Numerical studies and analyses for two real data sets are then conducted to examine the finite sample performance of the proposed test.

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Section: F I G U R Ementioning

confidence: 95%

Section: Automobile Datamentioning

confidence: 99%