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Displaying similar documents to “ M -estimators of structural parameters in pseudolinear models”

Rank theory approach to ridge, LASSO, preliminary test and Stein-type estimators: Comparative study

A. K. Md. Ehsanes Saleh, Radim Navrátil (2018)

Kybernetika

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In the development of efficient predictive models, the key is to identify suitable predictors for a given linear model. For the first time, this paper provides a comparative study of ridge regression, LASSO, preliminary test and Stein-type estimators based on the theory of rank statistics. Under the orthonormal design matrix of a given linear model, we find that the rank based ridge estimator outperforms the usual rank estimator, restricted R-estimator, rank-based LASSO, preliminary...

Existence, Consistency and computer simulation for selected variants of minimum distance estimators

Václav Kůs, Domingo Morales, Jitka Hrabáková, Iva Frýdlová (2018)

Kybernetika

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The paper deals with sufficient conditions for the existence of general approximate minimum distance estimator (AMDE) of a probability density function f 0 on the real line. It shows that the AMDE always exists when the bounded φ -divergence, Kolmogorov, Lévy, Cramér, or discrepancy distance is used. Consequently, n - 1 / 2 consistency rate in any bounded φ -divergence is established for Kolmogorov, Lévy, and discrepancy estimators under the condition that the degree of variations of the corresponding...

Instrumental weighted variables under heteroscedasticity. Part I – Consistency

Jan Ámos Víšek (2017)

Kybernetika

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The proof of consistency instrumental weighted variables, the robust version of the classical instrumental variables is given. It is proved that all solutions of the corresponding normal equations are contained, with high probability, in a ball, the radius of which can be selected - asymptotically - arbitrarily small. Then also n -consistency is proved. An extended numerical study (the Part II of the paper) offers a picture of behavior of the estimator for finite samples under various...

Estimator selection in the gaussian setting

Yannick Baraud, Christophe Giraud, Sylvie Huet (2014)

Annales de l'I.H.P. Probabilités et statistiques

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We consider the problem of estimating the mean f of a Gaussian vector Y with independent components of common unknown variance σ 2 . Our estimation procedure is based on estimator selection. More precisely, we start with an arbitrary and possibly infinite collection 𝔽 of estimators of f based on Y and, with the same data Y , aim at selecting an estimator among 𝔽 with the smallest Euclidean risk. No assumptions on the estimators are made and their dependencies with respect to Y may be unknown....

Compact hypothesis and extremal set estimators

João Tiago Mexia, Pedro Corte Real (2003)

Discussiones Mathematicae Probability and Statistics

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In extremal estimation theory the estimators are local or absolute extremes of functions defined on the cartesian product of the parameter by the sample space. Assuming that these functions converge uniformly, in a convenient stochastic way, to a limit function g, set estimators for the set ∇ of absolute maxima (minima) of g are obtained under the compactness assumption that ∇ is contained in a known compact U. A strongly consistent test is presented for this assumption. Moreover, when...

Locally and uniformly best estimators in replicated regression model

Júlia Volaufová, Lubomír Kubáček (1983)

Aplikace matematiky

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The aim of the paper is to estimate a function γ = t r ( D β β ' ) + t r ( C ∑ ) (with d , C known matrices) in a regression model ( Y , X β , ∑ ) with an unknown parameter β and covariance matrix ∑ . Stochastically independent replications Y 1 , ... , Y m of the stochastic vector Y are considered, where the estimators of X β and ∑ are Y ¯ = 1 m ∑ i = 1 m Y i and ∑ ^ = ( m - 1 ) - 1 ∑ i = 1 m ( Y i - Y ¯ ) ( Y i - Y ¯ ) ' , respectively. Locally and uniformly best inbiased estimators of the function γ , based on Y ¯ and ∑ ^ , are given.

An estimator for parameters of a nonlinear nonnegative multidimensional AR(1) process

Jiří Anděl (1998)

Applications of Mathematics

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Let 𝕖 t = ( e t 1 , ⋯ , e t p ) ' be a p -dimensional nonnegative strict white noise with finite second moments. Let h i j ( x ) be nondecreasing functions from [ 0 , ∞ ) onto [ 0 , ∞ ) such that h i j ( x ) ≤ x for i , j = 1 , ⋯ , p . Let 𝕌 = ( u i j ) be a p × p matrix with nonnegative elements having all its roots inside the unit circle. Define a process 𝕏 t = ( X t 1 , ⋯ , X t p ) ' by X t j = u j 1 h 1 j ( X t - 1 , 1 ) + ⋯ + u j p h p j ( X t - 1 , p ) + e t j for j = 1 , ⋯ , p . A method for estimating 𝕌 from a realization 𝕏 1 , ⋯ , 𝕏 n is proposed. It is proved that the estimators are strongly consistent.