HIGHER ORDER ESTIMATING EQUATIONS FOR HIGH-DIMENSIONAL MODELS
By James Robins, Lingling Li, Rajarshi Mukherjee, E. T. Tchetgen Tchetgen, A. van der Vaart. 2017
11 citations recorded by the source corpus.
We introduce a new method of estimation of parameters in semi-parametric and nonparametric models. The method is based on estimating equations that are U-statistics in the observations. The U-statistics are based on higher order influence functions that extend ordinary linear influence functions of the parameter of interest, and represent higher derivatives of this parameter. For parameters for which the representation cannot be perfect the method leads to a bias-variance trade-off, and results in estimators that converge at a slower than n-rate. In a number of examples the resulting rate can be shown to be optimal. We are particularly interested in estimating parameters in models with a nuisance parameter of high dimension or low regularity, where the parameter of interest cannot be estimated at n-rate, but we also consider efficient n-estimation using novel nonlinear estimators. The general approach is applied in detail to the example of estimating a mean response when the response is not always observed.
Subfields: Artificial Intelligence, Statistics and Probability
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In Artificial Intelligence
In Statistics and Probability
- Robert P. Lieli
- Stefan Wager
- Xinkun Nie
- Yu‐Chin Hsu
- Qingliang Fan
- Yichong Zhang
- Susan Athey
- Edward H. Kennedy
Citations in the corpus
- Quasi-oracle estimation of heterogeneous treatment effects (2017, methodology): “Our approach is motivated by the transformation of Robinson (1988), and draws more broadly from the literature on semiparametric inference and constructions of orthogonal moments (Athey and Wager, 2017; Belloni et al., 2017; Bickel et al., 1998; Luedtke and van der Laan, 2016; Newey, 1994; Robins, 2”
- Estimation of Conditional Average Treatment Effects With High-Dimensional Data (2019, background): “…and Robins (2003), Hirano, Imbens, and Ridder (2003), van der Laan and Rubin (2006), Firpo (2007), Tsiatis (2007), van der Laan and Rose (2011), Belloni et al. (2017), Farrell (2015), Kennedy et al. (2017), Robins et al. (2017), Wager and Athey (2018), and Su, Ura, and Zhang (2019), among others.”