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Bradic, Jelena; Guo, Jiaqi

Generalized M-estimators for high-dimensional Tobit I models. (English) Zbl 1417.62342

Electron. J. Stat. 13, No. 1, 582-645 (2019).
Consider the design of statistical methods in case of censored data which may occur e.g. if the measurement device in physical sciences has a certain value limit. For coping with censored data, robust methods are discussed here, especially for high-dimensional left-censored linear models: \[ y_t = \max \{0,\beta^Tx_t + \epsilon_t, t=1,2,\dots,n \}, \] where \(x_t, y_t\), \(t=1,\dots,n\), are the input \(p\)-vectors, scalar output variables, resp., \(\epsilon_t\), \(t=1,\dots,n\), denote independent error vectors, and \(\beta\) is the unknown parameter \(p\)-vector to be estimated. For high-dimensional data, robust estimation methods and confidence intervals are presented for left-censored regression problems. Furthermore, consistency and asymptotic normality results are derived. Numerical results on simulated data sets are shown.
Reviewer: Kurt Marti (München)

MSC:

62P20 Applications of statistics to economics
62J05 Linear regression; mixed models
62N01 Censored data models
62G35 Nonparametric robustness
62G15 Nonparametric tolerance and confidence regions
62H12 Estimation in multivariate analysis

Keywords:

left-censored linear models; left-censored regression; estimation methods; Tobit I models; design; robust methods; confidence intervals
PDFBibTeX XMLCite
\textit{J. Bradic} and \textit{J. Guo}, Electron. J. Stat. 13, No. 1, 582--645 (2019; Zbl 1417.62342)
Full Text: DOI Euclid

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