On automatic boundary corrections

By Ming-Yen Cheng, Jianqing Fan, James Stephen Marron. 1997

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Citations in the corpus

Local Linear Forests (2018, background): “Cheng, Fan, and Marron (1997) used local polynomials to estimate the value of a function at the boundary of its domain.”
Simple Local Polynomial Density Estimators (2018, methodology): “The most closely related approaches currently available in the literature are the local polynomial density estimators of Cheng et al. (1997) and Zhang and Karunamuni (1998), which require knowledge of the boundary location and pre-binning of the data (or, more generally, pre-estimation of the densit”
Does Head Start Improve Children's Life Chances? Evidence from a Regression Discontinuity Design (2005, unknown): “We use the triangle kernel K(z)=(1-|z|)I [0] [1] (|z|), which is boundary optimal [Cheng et al., 1997], although consistent with previous research we find our results are not very sensitive to choice of kernel [Fan and Gijbels, 1996].”
Causal Inference with Observational Data (2007, background): “Fan and Gijbels 1996, Stone 1974, 1977), and the triangle kernel has good properties in the RD context, due to being boundary optimal (Cheng et al. 1997). There are several rule-of-thumb bandwidth choosers and cross-validation techniques for automating bandwidth choice, but none is foolproof. McCrar”
Probit Transformation for Kernel Density Estimation on the Unit Interval (2013, background): “problem has attracted a lot of attention in the literature, see, inter alia, Schuster (1985), Muller (1991), Lejeune and Sarda (1992), Jones (1993), Jones and Foster (1996), Cowling and Hall (1996), Cheng et al (1997), Zhang and Karunamuni (1998, 2000), Zhang et al (1999), Chen (2000), Hall and Park”
Regression discontinuity designs with unknown discontinuity points: Testing and estimation (2015, background): “Cheng et al (1997) shows that the optimal kernel for the boundary point is the triangular or Bartlett kernel max f0; (1 juj)g. 48 It is easy to see that smaller bandwidth in estimating will not a¤ect the asymptotic argument in Theorem 5.”
Regression discontinuity design with many thresholds (2017, unknown): “Authors have previously analyzed minimax optimality of non-parametric estimators of a regression function at a boundary point, for example, Cheng et al. (1997) and Sun (2005). Theorem 3 is novel because it combines boundary points to estimate averages of non-parametric regression functions.”
Coverage error optimal confidence intervals for local polynomial regression (2018, methodology): “The asymptotic variance of a local polynomial point estimator at a boundary or interior point is minimized by employing the uniform kernel [13].”
Estimation in the Regression Discontinuity Model (2003, background): “Conditional mean boundary estimation is considered in Cheng, Fan, and Marron (1997).”
Robust Data-Driven Inference in the Regression-Discontinuity Design (2014, methodology): “These regression estimators are particularly well-suited for inference in the RD design because of their good properties at the boundary of the support of the regression function; see Fan and Gijbels (1996) and Cheng et al. (1997) for more details.”
Capturing the Zero: A New Class of Zero-Augmented Distributions and Multiplicative Error Processes (2010, unknown): “This is in contrast to boundary correction methods for fixed kernels such as boundary kernels (Jones, 1993) or local-linear estimation (Cheng et al., 1997).”
Manipulation of the Running Variable in the Regression Discontinuity Design: A Density Test (2007, unknown): “The estimator, which is a simple extension of the local linear density estimator (Cheng et al., 1997), proceeds in two steps.”
Simple and honest confidence intervals in nonparametric regression (2016, methodology): “In particular, known kernel efficiency results under the RMSE criterion such as those in Fan (1993), Cheng et al. (1997), and Fan et al.”
On nonparametric density estimation at the boundary (2000, methodology): “During the preparation of this paper, we learned that a more general result of Zhang and Karunamuni (1998), similar to the present paper, has been proved in Cheng et al. (1997), where they not only proved the optimality of the above stated order (0,2) boundary kernel, but also obtained the optimal k”