Journal ArticleDOI
Effect of the initial estimator on the asymptotic behavior of one-step M-estimator
Jana Jurečková,Pranab Kumar Sen +1 more
TLDR
In this paper, the asymptotic distribution of n(Mn(1)-Mn) is studied; it is typically non-normal and reveals the role of the initial estimator Mn(0).Abstract:
For a general (real) parameter, let Mnbe the M-estimator and Mn(1) be its one-step version (based on a suitable initial estimator Mn(0)). It is known that, under certain regularity conditions, n(Mn(1)-Mn)=Op(1). The asymptotic distribution of n(Mn(1)-Mn) is studied; it is typically non-normal and it reveals the role of the initial estimator Mn(0).read more
Citations
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Journal ArticleDOI
Convergence of Probability Measures
TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
Journal ArticleDOI
A journey in single steps: robust one-step M-estimation in linear regression
Alan H. Welsh,Elvezio Ronchetti +1 more
TL;DR: In this paper, the authors present a unified treatment of different types of one-step M-estimation in regression models which incorporates the Newton-Raphson, method of scoring and iteratively reweighted least squares forms of one step estimator.
Reference EntryDOI
Journal De La Société Française De Statistique
TL;DR: The history of the Journal of the Statistical Society of Paris (1860-1998) can be found in this paper, where the journal was referred to as the journal of the French Statistical Society.
Journal ArticleDOI
One-step M-estimators: Jones and Faddy's skewed t-distribution
TL;DR: In this paper, the authors proposed to use new initial estimates for the calculation of the OSM-estimator, where the distribution of the error terms is Jones and Faddy's skewed t. The Monte-Carlo simulation study showed that the estimator(s) based on the proposed initial estimates is/are more efficient than the traditional initial estimates especially for the skewed cases.
Journal ArticleDOI
Trimming and likelihood: Robust location and dispersion estimation in the elliptical model
TL;DR: In this paper, the authors proposed different models for truncated or censored likelihoods, as well as a likelihood based on an only outliers gross errors model, based on a subsample obtained with such a procedure.
References
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Book
Convergence of Probability Measures
TL;DR: Weak Convergence in Metric Spaces as discussed by the authors is one of the most common modes of convergence in metric spaces, and it can be seen as a form of weak convergence in metric space.
Journal ArticleDOI
Convergence of Probability Measures
TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
The behavior of maximum likelihood estimates under nonstandard conditions
TL;DR: In this paper, the authors prove consistency and asymptotic normality of maximum likelihood estimators under weaker conditions than usual, such that the true distribution underlying the observations belongs to the parametric family defining the estimator, and the regularity conditions do not involve the second and higher derivatives of the likelihood function.
Book
Theory of point estimation
TL;DR: In this paper, the authors present an approach for estimating the average risk of a risk-optimal risk maximization algorithm for a set of risk-maximization objectives, including maximalaxity and admissibility.