Introduction to Empirical Processes and Semiparametric Inference

Kosorok, Michael R.

doi:10.1007/978-0-387-74978-5

Cited by 830 publications

(1,099 citation statements)

References 51 publications

Supporting

Mentioning

1,083

Contrasting

Unclassified

Order By: Relevance

“…. , X n are independent identically distributed distributed according to the cdf C. Next, note that Theorem 2.6 in Kosorok (2008) yields…”

Section: Introductionmentioning

confidence: 97%

“…For a precise statement of the asymptotic properties of this process we denote by P W weak convergence conditional on the data in probability as defined by Kosorok (2008), that is α res…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, C n = Φ(F n ) and C = Φ(C), and consequently the functional delta method [see Kosorok (2008)…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A note on bootstrap approximations for the empirical copula process

Bücher

Dette

2010

Statistics & Probability Letters

View full text Add to dashboard Cite

It is well known that the empirical copula process converges weakly to a centered Gaussian field. Because the covariance structure of the limiting process depends on the partial derivatives of the unknown copula several bootstrap approximations for the empirical copula process have been proposed in the literature. We present a brief review of these procedures.Because some of these procedures also require the estimation of the derivatives of the unknown copula we propose an alternative approach which circumvents this problem. Finally a simulation study is presented in order to compare the different bootstrap approximations for the empirical copula process.

show abstract

“…. , X n are independent identically distributed distributed according to the cdf C. Next, note that Theorem 2.6 in Kosorok (2008) yields…”

Section: Introductionmentioning

confidence: 97%

“…For a precise statement of the asymptotic properties of this process we denote by P W weak convergence conditional on the data in probability as defined by Kosorok (2008), that is α res…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A note on bootstrap approximations for the empirical copula process

Bücher

Dette

2010

Statistics & Probability Letters

View full text Add to dashboard Cite

show abstract

“…(6.19) can be obtained with similar steps as in the first part of the proof of Theorem 2.3 in using Theorem 11.16 in Kosorok (2008) which is a central limit theorem for triangular arrays of row-wise i.i.d. data.…”

Section: Proof Of Theorem 31mentioning

confidence: 99%

Nonparametric inference of gradual changes in the jump behaviour of time-continuous processes

Hoffmann

Vetter

Dette

2018

Stochastic Processes and their Applications

View full text Add to dashboard Cite

In applications changes of the properties of a stochastic feature occur often gradually rather than abruptly, that is: after a constant phase for some time they slowly start to change. Efficient analysis for change points should address the specific features of such a smooth change. In this paper we discuss statistical inference for localizing and detecting gradual changes in the jump characteristic of a discretely observed Itō semimartingale. We propose a new measure of time variation for the jump behaviour of the process. The statistical uncertainty of a corresponding estimate is analyzed deriving new results on the weak convergence of a sequential empirical tail integral process and a corresponding multiplier bootstrap procedure.

show abstract

“…Because log(#G δ ) ≤ H δ/2,∞ (G) for any function class G and any norm dominated by the sup-norm (see, e.g., Lemma 9.22 in [10]), one can use (3.2) to obtain…”

Section: Functional Spaces Meeting the Assumptionsmentioning

confidence: 99%

On a dense minimizer of empirical risk in inverse problems

Podlewski¹,

Szkutnik²

2016

OpMath

View full text Add to dashboard Cite

Abstract. Properties of estimators of a functional parameter in an inverse problem setup are studied. We focus on estimators obtained through dense minimization (as opposed to minimization over δ-nets) of suitably defined empirical risk. At the cost of imposition of a sort of local finite-dimensionality assumption, we fill some gaps in the proofs of results published by Klemelä and Mammen [Ann. Statist. 38 (2010), 482-511]. We also give examples of functional classes that satisfy the modified assumptions.

show abstract

Introduction to Empirical Processes and Semiparametric Inference

Cited by 830 publications

References 51 publications

A note on bootstrap approximations for the empirical copula process

A note on bootstrap approximations for the empirical copula process

Nonparametric inference of gradual changes in the jump behaviour of time-continuous processes

On a dense minimizer of empirical risk in inverse problems

Contact Info

Product

Resources

About