Notes on the Asymptotic Linearity Theorems

1995 ◽  
Vol 18 (2) ◽  
pp. 169-177 ◽  
Author(s):  
Shigeru Arimoto ◽  
Mark Spivakovsky ◽  
Keith F. Taylor
Keyword(s):  
Asymptotic Linearity

scholarly journals On Quadratic Expansions of Log-Likelihoods and a General Asymptotic Linearity Result

2013 ◽  
Author(s):  
Marc Hallin ◽  
Ramon Van den Akker ◽  
Bas J. M. Werker
Keyword(s):  
Asymptotic Linearity

scholarly journals On the asymptotic linearity of Castelnuovo–Mumford regularity

2005 ◽  
Vol 201 (1-3) ◽  
pp. 42-48 ◽  
Author(s):  
Ngô Viêt Trung ◽  
Hsin-Ju Wang
Keyword(s):  
Asymptotic Linearity

scholarly journals BOOTSTRAPPING DENSITY-WEIGHTED AVERAGE DERIVATIVES

2014 ◽  
Vol 30 (6) ◽  
pp. 1135-1164 ◽  
Author(s):  
Matias D. Cattaneo ◽  
Richard K. Crump ◽  
Michael Jansson
Keyword(s):  
Theoretical Approach ◽  
Traditional Approach ◽  
Weighted Average ◽  
Statistical Properties ◽  
Independent Interest ◽  
Inference Procedure ◽  
Edgeworth Expansions ◽  
Semiparametric Inference ◽  
Key Innovation ◽  
Asymptotic Linearity

We investigate the properties of several bootstrap-based inference procedures for semiparametric density-weighted average derivatives. The key innovation in this paper is to employ an alternative asymptotic framework to assess the properties of these inference procedures. This theoretical approach is conceptually distinct from the traditional approach (based on asymptotic linearity of the estimator and Edgeworth expansions), and leads to different theoretical prescriptions for bootstrap-based semiparametric inference. First, we show that the conventional bootstrap-based approximations to the distribution of the estimator and its classical studentized version are both invalid in general. This result shows a fundamental lack of “robustness” of the associated, classical bootstrap-based inference procedures with respect to the bandwidth choice. Second, we present a new bootstrap-based inference procedure for density-weighted average derivatives that is more “robust” to perturbations of the bandwidth choice, and hence exhibits demonstrable superior theoretical statistical properties over the traditional bootstrap-based inference procedures. Finally, we also examine the validity and invalidity of related bootstrap-based inference procedures and discuss additional results that may be of independent interest. Some simulation evidence is also presented.

Rank estimates and asymptotic linearity in regression parameters

1999 ◽  
pp. 358-382
Author(s):  
Jaroslav Hájek ◽  
Zbyněk Šidák ◽  
Pranab K. Sen
Keyword(s):  
Regression Parameters ◽  
Asymptotic Linearity ◽  
Rank Estimates
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