$U$-Processes: Rates of Convergence

Nolan, Deborah; Pollard, David

doi:10.1214/aos/1176350374

Cited by 359 publications

(307 citation statements)

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“…Rescale by C 1 , then the conditions of theorem 9 of Nolan and Pollard (1987) are satisfied, and therefore…”

Section: A4 Convergence Of R H 1nmentioning

confidence: 97%

“…A detailed proof of convergence of the last remainder term is given at the end. This particular remainder term arises in the linearization of H n − H. Whereas the lemmas of Gørgens and Horowitz employ empirical process theory, the proof of convergence of the last remainder term uses U-process theory developed by Nolan and Pollard (1987).…”

Section: A Proof Of Theoremsmentioning

confidence: 99%

“…The U-Process P n ⊗ P nρn : Convergence will follow from theorem 9 of Nolan and Pollard (1987). Symmetrize the U-process by defining…”

Section: A4 Convergence Of R H 1nmentioning

confidence: 99%

“…The class F = f : (t, z) ∈ S 2 , 0 < κ zn < 1 is Euclidean for a constant envelope by lemmas 2.13 and 2.14 of Pakes and Pollard (1989) and lemma 22 of Nolan and Pollard (1987)…”

Section: A4 Convergence Of R H 1nmentioning

confidence: 99%

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Semiparametric estimation of censored transformation models

Gorgens

2003

Journal of Nonparametric Statistics

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Many widely used models, including proportional hazards models with unobserved heterogeneity, can be written in the form Λ(Y ) = min[β X + U, C], where Λ is an unknown increasing function, the error term U has unknown distribution function Ψ and is independent of X, C is a random censoring threshold, and U and C are conditionally independent given X. This paper develops new n 1/2 -consistent and asymptotically normal semiparametric estimators of Λ and Ψ which are easier to use than existing estimators. Moreover, Monte Carlo results suggest that the mean integrated squared error of predictions based on the new estimators is lower than for existing estimators.

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“…Rescale by C 1 , then the conditions of theorem 9 of Nolan and Pollard (1987) are satisfied, and therefore…”

Section: A4 Convergence Of R H 1nmentioning

confidence: 97%

Section: A Proof Of Theoremsmentioning

confidence: 99%

“…The U-Process P n ⊗ P nρn : Convergence will follow from theorem 9 of Nolan and Pollard (1987). Symmetrize the U-process by defining…”

Section: A4 Convergence Of R H 1nmentioning

confidence: 99%

“…The class F = f : (t, z) ∈ S 2 , 0 < κ zn < 1 is Euclidean for a constant envelope by lemmas 2.13 and 2.14 of Pakes and Pollard (1989) and lemma 22 of Nolan and Pollard (1987)…”

Section: A4 Convergence Of R H 1nmentioning

confidence: 99%

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Semiparametric estimation of censored transformation models

Gorgens

2003

Journal of Nonparametric Statistics

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“…Finally as Assumption E.1 (e) is identical to Assumption 2.1 (f) the result is proven from Theorem 2.1. Notice that sgn θ (ξ − w 0 δ) and E[x(θ − F ξ (w 0 δ|x)] are functions of bounded variation and thus are Euclidean by Lemma 22, p.797, of Nolan and Pollard (1987). Also x is Euclidean due to the fact that E[x] is finite and Lemmata II.28 and II.25 of Pollard (1984).…”

Section: (C) Assumption 22 (C) Is Immediate Formentioning

confidence: 98%

Gel Methods for Nonsmooth Moment Indicators

Parente

Smith

2010

Econom. Theory

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This paper considers the first order large sample properties of the GEL class of estimators for models specified by non-smooth indicators. The GEL class includes a number of estimators recently introduced as alternatives to the efficient GMM estimator which may suffer from substantial biases in finite samples. These include EL, ET and the CUE. This paper also establishes the validity of tests suggested in the smooth moment indicators case for over-identifying restrictions and specification. In particular, a number of these tests avoid the necessity of providing an estimator for the Jacobian matrix which may be problematic for the sample sizes typically encountered in practice.JEL Classification: C13, C30

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U‐Statistics

Serfling¹

2004

Encyclopedia of Statistical Sciences

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$U$-Processes: Rates of Convergence

Cited by 359 publications

References 0 publications

Semiparametric estimation of censored transformation models

Semiparametric estimation of censored transformation models

Gel Methods for Nonsmooth Moment Indicators

U‐Statistics

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