On Some Global Measures of the Deviations of Density Function Estimates

By Richard A. Davis, K. Lii, Dimitris Nicolas Politis. 2011

304 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/43178477ed3956a7bc98b23765355df15e6e1898

How researchers see this paper

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

In Statistics and Probability

Citations in the corpus

Asymptotic theory for stationary processes (2011, result): “Liu and Wu’s theorem substantially generalize earlier results which were obtained under independence (Bickel and Rosenblatt, 1973) or restrictive beta mixing assumptions (Neumann, 1998).”
Testing functional inequalities (2011, methodology): “See, e.g., Bickel and Rosenblatt (1973), Härdle and Mammen (1993), Stute (1997), Delgado and González Manteiga (2000), Horowitz and Spokoiny (2001), and Khmaladze and Koul (2004) among many others.”
Uniform convergence rates for nonparametric regression and principal component analysis in functional/longitudinal data (2010, background): “Those include Bickel and Rosenblatt (1973), Härdle, Janssen and Serfling (1988) and Härdle (1989). More recently, Claeskens and Van Keilegom (2003) extended some of those results to local likelihood estimators and local estimating equations. However, as remarked in Yao, Müller and Wang (2005a), whet”
Local and global asymptotic inference in smoothing spline models (2012, methodology): “By incorporating the reproducing kernel Hilbert space (RKHS) theory into [2], we obtain an SCB applicable to general nonparametric regression models, and we demonstrate its theoretical validity based on strong approximation techniques.”
Simultaneous inference of linear models with time varying coefficients (2010, background): “Assuming that the observations are independent, we can construct simultaneous confidence bands that have asymptotically correct coverage probabilities; see Bickel and Rosenblatt (1973), Eubank and Speckman (1993), Johnston (1982), Neumann and Polzehl (1998) and Fan and Zhang (2000) among others.”
An updated review of Goodness-of-Fit tests for regression models (2013, methodology): “This alternative route for GoF is related to the seminal paper by Bickel and Rosenblatt (1973), whose ideas were extended to the p-dimensional setting in the 1990s.”
Supremum Norm Posterior Contraction and Credible Sets for Nonparametric Multivariate Regression (2014, background): “Nonparametric confidence bands for an unknown function were considered by [1, 30] and more recently by [5, 6, 13].”
On asymptotic constants in the theory of extremes for Gaussian processes (2012, background): “It is known that H1 = 1 and that H2 = 1/√π (Bickel and Rosenblatt [10], Piterbarg [30]), and that Hα is continuous as a function of α (Dȩbicki [16]).”
POLYNOMIAL SPLINE CONFIDENCE BANDS FOR REGRESSION CURVES (2009, methodology): “This transformation had been used in, for instance, Bickel and Rosenblatt (1973), Härdle (1989). Substituting the vector t =(t1,t2) in Theorem 3.”
Simultaneous Confidence Bands for Penalized Spline Estimators (2010, unknown): “The approach of Bickel and Rosenblatt (1973) relates this to a study of the distribution of supa≤x≤b |Z(x)|, with Z(x) a (standardized) Gaussian process satisfying certain conditions, which they showed to have an”
A Confidence Corridor for Expectile Functions (2011, unknown): “(18) Drawing upon the result of Bickel and Rosenblatt (1973), we finally obtain asymptotically the Gumbel distribution.”
Gaussian approximation of suprema of empirical processes (2012, background): “Limit theorems for Wn are developed in [2, 17, 21, 36, 40, 51], among others.”
CONFIDENCE BANDS IN DENSITY ESTIMATION (2010, methodology): “2(log 2)l and B(l) = A(l) − log l + log(π log 2) − log √ 1 +Dr A(l) , r = 3, 4, D3 = ∑ k(a (3) k −a (3) k−2) 2/M with M as in Lemma 1, and D4 = 9 ∑ k(a (4) k −a (4) k−2) 2/C with C as in (4.”
Functional Data Analysis (2016, methodology): “In summary, the construction of simultaneous conﬁdence bands for functional data requires diﬀerent methods for ultra-dense, dense, and sparse functional data, where in the latter case one does not have tightness and the rescaling approach of Bickel & Rosenblatt (1973) may be applied.”
Bayes Hilbert Spaces (2014, background): “Typical examples are goodness-of-fit tests (Bickel & Rosenblatt 1973; Durbin 1973), kernel estimation of densities (Rosenblatt 1956; Parzen 1962; Silverman 1986; Bowman & Azzalini 1997), or information theory (Kullback & Leibler *Author to whom correspondence should be addressed.”
On adaptive inference and confidence bands (2011, background): “bands, dating back to Bickel and Rosenblatt [2].”
Multivariate goodness-of-fit tests based on Wasserstein distance (2020, background): “Among them, distances between densities (after kernel smoothing) have attracted much interest, starting with Bickel and Rosenblatt (1973) in the univariate case.”
Efficient and fast spline-backfitted kernel smoothing of additive models (2009, background): “J. Wang (B) Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, IL 60607, USA e-mail: wangjing@math.uic.edu L. Yang Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, USA e-mail: yang@stt.msu.edu”
CONFIDENCE BANDS IN QUANTILE REGRESSION (2009, methodology): “The leading linear term will then be approximated in a similar way as in Johnston (1982) and Bickel and Rosenblatt (1973).”