Twicing Kernels and a Small Bias Property of Semiparametric Estimators

By Whitney K. Newey, F. Hsieh, James M. Robins. 2004

100 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Finance, Statistics and Probability

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Finance

In Statistics and Probability

Citations in the corpus

Double/De-Biased Machine Learning of Global and Local Parameters Using Regularized Riesz Representers (2018, background): “Newey et al. (1998, 2004) further develop theory in this vein, in a low-dimensional nonparametric setting.”
Double/Debiased Machine Learning for Treatment and Causal Parameters (2016, background): “ (1982), Robinson (1988), Newey (1990), van der Vaart (1991), Andrews (1994a), Newey (1994), Newey et al. (1998), Robins and Rotnitzky (1995), Linton (1996), Bickel et al. (1998), Chen et al. (2003), Newey et al. (2004), van der Laan and Rose (2011), and Ai and Chen (2012). Neyman orthogonality (1.8”
Semiparametric Estimation and Inference Using Doubly Robust Moment Conditions (2013, unknown): “In very different contexts, Newey, Hsieh, and Robins (2004) and Klein and Shen (2010) propose methods that do not exploit higher order differentiability conditions to reduce the impact of the first stage smoothing bias on the properties of certain two-step estimators.”
SMALL BANDWIDTH ASYMPTOTICS FOR DENSITY-WEIGHTED AVERAGE DERIVATIVES (2013, unknown): “We also explored other choices of kernel functions, such as a twiced Gaussian kernel (e.g., Newey et al., 2004), but the results were qualitatively similar and therefore we omit them to conserve space.”
Characterization of parameters with a mixed bias property (2019, background): “The first class, described in Robins et al. (2008) is comprised of parameters with influence function of the form χ(1)η = Saba (Z) b (Z) + Saa (Z) + Sbb (Z) + S0 − χ (η) where Sa and Sb are statistics. The second class, described in Chernozhukov et al. (2018b) (see also Hirshberg and Wager (2017) an”
Synthetic Difference In Differences (2018, unknown): “istency of ^˝[Athey, Imbens, and Wager, 2018, Belloni, Chernozhukov, and Hansen, 2014, Chernozhukov, Escanciano, Ichimura, Newey, and Robins, 2018b, Hirshberg and Wager, 2018, Imbens and Rubin, 2015, Newey, Hsieh, and Robins, 2004, Scharfstein, Rotnitzky, and Robins, 1999]. Before discussing our cho”
Locally Robust Semiparametric Estimation (2016, background): “These results are distinguished from Newey, Hsieh, and Robins (1998, 2004) and Robins et al. (2008, 2009) in the conclusion of Theorem 2 and in providing, for any first step key regularity conditions used in the asymptotic theory of Section 6.”
Double/debiased machine learning for treatment and structural parameters (2017, unknown): “Newey et al. (1998, 2004) showed that n−1/2 ∑n i=1 ψ(Wi; θ0, η̂0) from equation (2.30) will have a second order remainder in η̂0, which is the key asymptotic property of orthogonal scores.”
Cross-fitting and fast remainder rates for semiparametric estimation (2017, background): “1) is min{1, sγ}+min{1, sα} > 1, which requires both sα > 0 and sγ > 0 and so is slightly stronger than the Robins et al.(2009) condition sγ + sα > 1.”
Kernel-Based Semiparametric Estimators: Small Bandwidth Asymptotics and Bootstrap Consistency (2018, background): “An exception to this rule might occur when the moment function g(z θ γ) is “locally robust” in the sense of Chernozhukov et al. (2016), as θ̂n then has the “small bias property” discussed by Newey, Hsieh, and Robins (2004); that is, the magnitude of BSn is smaller than that of γn − γ0.”
Robust Data-Driven Inference for Density-Weighted Average Derivatives (2010, unknown): “…derivatives by deriving valid Edgeworth expansions for the estimator considered in this paper (see also Robinson 1995), while Härdle and Tsybakov (1993) and Powell and Stoker (1996) provide second-order mean squared error expansions for this estimator (see also Newey, Hsieh, and Robins 2004).”
Adaptive Bayesian density estimation with location-scale mixtures (2010, methodology): “The construction of the sequence { f i } i ∈ N is related to the use of superkernels in kernel density estimation (see e.g. [30] and [4]), or to the twicing kernels used in econometrics (see [24]).”
A unifying approach for doubly-robust $\ell_1$ regularized estimation of causal contrasts (2019, background): “One such assumption is the often referred to as the ultra sparsity condition that s = o ( √ n) (Ostrovskii and Bach (2018), van de Geer and Müller (2012)).”