Instrumental Variable Method for Regularized Estimation in Generalized Linear Measurement Error Models
Regularized regression methods have attracted much attention in the literature, mainly due to its application in high-dimensional variable selection problems. Most existing regularization methods assume that the predictors are directly observed and precisely measured. It is well known that in a low-...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-07-01
|
| Series: | Econometrics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2225-1146/12/3/21 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850261094316113920 |
|---|---|
| author | Lin Xue Liqun Wang |
| author_facet | Lin Xue Liqun Wang |
| author_sort | Lin Xue |
| collection | DOAJ |
| description | Regularized regression methods have attracted much attention in the literature, mainly due to its application in high-dimensional variable selection problems. Most existing regularization methods assume that the predictors are directly observed and precisely measured. It is well known that in a low-dimensional regression model if some covariates are measured with error, then the naive estimators that ignore the measurement error are biased and inconsistent. However, the impact of measurement error in regularized estimation procedures is not clear. For example, it is known that the ordinary least squares estimate of the regression coefficient in a linear model is attenuated towards zero and, on the other hand, the variance of the observed surrogate predictor is inflated. Therefore, it is unclear how the interaction of these two factors affects the selection outcome. To correct for the measurement error effects, some researchers assume that the measurement error covariance matrix is known or can be estimated using external data. In this paper, we propose the regularized instrumental variable method for generalized linear measurement error models. We show that the proposed approach yields a consistent variable selection procedure and root-n consistent parameter estimators. Extensive finite sample simulation studies show that the proposed method performs satisfactorily in both linear and generalized linear models. A real data example is provided to further demonstrate the usage of the method. |
| format | Article |
| id | doaj-art-e8c2607c28124205a6d90450c01e980c |
| institution | OA Journals |
| issn | 2225-1146 |
| language | English |
| publishDate | 2024-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Econometrics |
| spelling | doaj-art-e8c2607c28124205a6d90450c01e980c2025-08-20T01:55:30ZengMDPI AGEconometrics2225-11462024-07-011232110.3390/econometrics12030021Instrumental Variable Method for Regularized Estimation in Generalized Linear Measurement Error ModelsLin Xue0Liqun Wang1Department of Statistics, University of Manitoba, Winnipeg, MB R3T 2N2, CanadaDepartment of Statistics, University of Manitoba, Winnipeg, MB R3T 2N2, CanadaRegularized regression methods have attracted much attention in the literature, mainly due to its application in high-dimensional variable selection problems. Most existing regularization methods assume that the predictors are directly observed and precisely measured. It is well known that in a low-dimensional regression model if some covariates are measured with error, then the naive estimators that ignore the measurement error are biased and inconsistent. However, the impact of measurement error in regularized estimation procedures is not clear. For example, it is known that the ordinary least squares estimate of the regression coefficient in a linear model is attenuated towards zero and, on the other hand, the variance of the observed surrogate predictor is inflated. Therefore, it is unclear how the interaction of these two factors affects the selection outcome. To correct for the measurement error effects, some researchers assume that the measurement error covariance matrix is known or can be estimated using external data. In this paper, we propose the regularized instrumental variable method for generalized linear measurement error models. We show that the proposed approach yields a consistent variable selection procedure and root-n consistent parameter estimators. Extensive finite sample simulation studies show that the proposed method performs satisfactorily in both linear and generalized linear models. A real data example is provided to further demonstrate the usage of the method.https://www.mdpi.com/2225-1146/12/3/21regularization methodpenalized estimationmeasurement errorinstrumental variablegeneralized linear modelvariable selection |
| spellingShingle | Lin Xue Liqun Wang Instrumental Variable Method for Regularized Estimation in Generalized Linear Measurement Error Models Econometrics regularization method penalized estimation measurement error instrumental variable generalized linear model variable selection |
| title | Instrumental Variable Method for Regularized Estimation in Generalized Linear Measurement Error Models |
| title_full | Instrumental Variable Method for Regularized Estimation in Generalized Linear Measurement Error Models |
| title_fullStr | Instrumental Variable Method for Regularized Estimation in Generalized Linear Measurement Error Models |
| title_full_unstemmed | Instrumental Variable Method for Regularized Estimation in Generalized Linear Measurement Error Models |
| title_short | Instrumental Variable Method for Regularized Estimation in Generalized Linear Measurement Error Models |
| title_sort | instrumental variable method for regularized estimation in generalized linear measurement error models |
| topic | regularization method penalized estimation measurement error instrumental variable generalized linear model variable selection |
| url | https://www.mdpi.com/2225-1146/12/3/21 |
| work_keys_str_mv | AT linxue instrumentalvariablemethodforregularizedestimationingeneralizedlinearmeasurementerrormodels AT liqunwang instrumentalvariablemethodforregularizedestimationingeneralizedlinearmeasurementerrormodels |