Direction estimation in a general regression model with discrete predictors. (English) Zbl 1366.62081
Jin, Zhezhen (ed.) et al., New developments in statistical modeling, inference and application. Selected papers from the 2014 ICSA/KISS joint applied statistics symposium in Portland, OR, USA, June 15–18, 2014. Cham: Springer (ISBN 978-3-319-42570-2/hbk; 978-3-319-42571-9/ebook). ICSA Book Series in Statistics, 77-88 (2016).
Summary: Consider a general regression model, where the response \(Y\) depends on discrete predictors \({\mathbf X}\) only through the index \( \boldsymbol{\beta }^{T}\mathbf{X} \). It is well-known that the ordinary least squares (OLS) estimator can recover the underlying direction \( \boldsymbol{\beta } \) exactly if the link function between \(Y\) and \(X\) is linear. K.-C. Li and N. Duan [Ann. Stat. 17, No. 3, 1009–1052 (1989; Zbl 0753.62041)] showed that the OLS estimator can recover \( \boldsymbol{\beta} \) proportionally if the predictors satisfy the linear conditional mean (LCM) condition. For discrete predictors, we demonstrate that the LCM condition generally does not hold. To improve the OLS estimator in the presence of discrete predictors, we model the conditional mean \( \mathrm{E}(\mathbf{X}|\boldsymbol{\beta }^{T}\mathbf{X}) \) as a polynomial function of \(\boldsymbol{\beta}^{T}\mathbf{X} \) and use the central solution space (CSS) estimator. The superior performances of the CSS estimators are confirmed through numerical studies.
For the entire collection see [Zbl 1357.62013].
For the entire collection see [Zbl 1357.62013].
MSC:
| 62G08 | Nonparametric regression and quantile regression |
| 62F12 | Asymptotic properties of parametric estimators |
| 62J05 | Linear regression; mixed models |
| 62J12 | Generalized linear models (logistic models) |
Keywords:
general regression model; discrete predictors; linear conditional mean (LCM); central solution space (CSS); numerical studiesCitations:
Zbl 0753.62041References:
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