Nonparametric estimators which can be "plugged-in"

By Peter J. Bickel, Yaacov Ritov. 2003

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In Statistics and Probability

Citations in the corpus

On the optimal estimation of probability measures in weak and strong topologies (2013, background): “Several recent works [6, 26, 16, 17, 18, 19] have shown that many popular density estimators on X = R, such as maximum likelihood estimator, kernel density estimator and wavelet estimator satisfy (2) if F is P-Donsker—the Donsker classes that were considered in these works are: functions of bounded ”
A Bernstein–von Mises theorem for smooth functionals in semiparametric models (2013, methodology): “We study this as an application of the main theorem in the important case of estimation of the squared L2norm of an unknown regression function in the case where the convergence rate for the functional is still parametric but where the “plug-in” property in the sense of Bickel and Ritov [5] is not n”
Uniform limit theorems for wavelet density estimators (2008, unknown): “These results again parallel limit theorems for the classical Rosenblatt–Parzen estimator [see Bickel and Ritov (2003), Giné and Nickl (2008, 2009)].”
Uniform in Bandwidth Estimation of Integral Functionals of the Density Function (2008, methodology): “…sample with Xi deleted; then, since this CDF and the empirical CDF are asymptotically equivalent under the conditions of the theorems below (e.g. Bickel & Ritov, 2003, p. 1036), they would © Board of the Foundation of the Scandinavian Journal of Statistics 2008. also hold with this choice of…”
Locally Robust Semiparametric Estimation (2016, methodology): “that is continuous in the norm R [γ1(u)− γ10(u)]2du 1/2 ,and iii) γ20(xi) = θ′pK(x i)for some θthen E[m(zi,β0,pK′λ∗)] = 0. The orthogonal series estimators of linear functionals of a pdf discussed in Bickel and Ritov (2003) are examples. Those estimators are special cases of the estimator above wher”
Quarticity and other functionals of volatility: Efficient estimation (2012, background): “, [2, 3]), and with an asymptotic variance always smaller than if one uses the first method.”
√n-consistent parameter estimation for systems of ordinary differential equations : bypassing numerical integration via smoothing (2010, unknown): “Note that undersmoothing is a different approach than the one in [5], where it is assumed that nonparametric estimators attain the minimax rate of convergence and the √ n-rate for estimation of a functional in concrete examples, if possible, is achieved by different means exploiting extra smoothness”
An exponential inequality for the distribution function of the kernel density estimator, with applications to adaptive estimation (2009, background): “Bickel and Ritov [2] label this the “plug-in property” of an estimator, which is useful, e.”
Adaptation on the space of finite signed measures (2008, background): “More generally, Theorem 1 below shows that optimally rate-adaptive estimators possessing the plugin property of Bickel and Ritov [1] exist.”
Nonparametric Bernstein–von Mises theorems in Gaussian white noise (2012, background): “A key point in these applications is related to the notion of the “plug-in property” coined by Bickel and Ritov [3].”
Predicting the Conditional Probability of Discovering a New Class (2004, methodology): “The validity of Û(0) = n1s−1 has been widely accepted (Esty 1983; Chao and Lee 1992; Chao, Hwang, Chen, and Kuo 2000), and a thorough investigation was done by Mao and Lindsay (2002). In contrast, the general situation with t > 0 has received little investigation after Good and Toulmin (1956) and Ha”
Donsker-type theorems for nonparametric maximum likelihood estimators (2007, background): “Bickel and Ritov [3] already gave a number of statistical examples where one can take advantage of density estimators possessing the plug-in property.”
Optimal rate of direct estimators in systems of ordinary differential equations linear in functions of the parameters (2013, methodology): “This is an example of the use of nonparametric “plug-in” or substitution estimators (see [19] and [4]).”
Uniform central limit theorems for kernel density estimators (2008, background): “In particular, the choice hn n−1/(2t+1) is admissible if the kernel is of order r > t +1/2, so the theorem implies that classical kernel density estimators can possess Bickel and Ritov’s [3] ‘plug-in property’ for pregaussian classes of functions that are not Donsker.”
INFERENCE FOR SEMIPARAMETRIC MODELS: SOME QUESTIONS AND AN ANSWER (2001, background): “Some initial discussion is in Bickel and Ritov (2000b).”