$M$-estimators of structural parameters in pseudolinear models

Friedrich Liese; Igor Vajda

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

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 $\sqrt{n}$ -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 $γ = t r (D β β^{'}) + t r (C \sum)$ (with $d, C$ known matrices) in a regression model $(Y, X β, \sum)$ with an unknown parameter $β$ and covariance matrix $\sum$ . Stochastically independent replications $Y_{1}, ..., Y_{m}$ of the stochastic vector $Y$ are considered, where the estimators of $X β$ and $\sum$ are $\bar{Y} = \frac{1}{m} \sum_{i = 1}^{m} Y_{i}$ and $\sum^{^} = {(m - 1)}^{- 1} \sum_{i = 1}^{m} (Y_{i} - \bar{Y}) {(Y_{i} - \bar{Y})}^{'}$ , respectively. Locally and uniformly best inbiased estimators of the function $γ$ , based on $\bar{Y}$ and $\sum^{^}$ , 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 $𝕖_{t} = {(e_{t 1}, \dots, e_{t p})}^{'}$ be a $p$ -dimensional nonnegative strict white noise with finite second moments. Let $h_{i j} (x)$ be nondecreasing functions from $[0, \infty)$ onto $[0, \infty)$ such that $h_{i j} (x) \leq x$ for $i, j = 1, \dots, p$ . Let $𝕌 = (u_{i j})$ be a $p \times p$ matrix with nonnegative elements having all its roots inside the unit circle. Define a process $𝕏_{t} = {(X_{t 1}, \dots, X_{t p})}^{'}$ by $X_{t j} = u_{j 1} h_{1 j} (X_{t - 1, 1}) + \dots + u_{j p} h_{p j} (X_{t - 1, p}) + e_{t j}$ for $j = 1, \dots, p$ . A method for estimating $𝕌$ from a realization $𝕏_{1}, \dots, 𝕏_{n}$ is proposed. It is proved that the estimators are strongly consistent.

Orthogonal series regression estimation under long-range dependent errors

Waldemar Popiński (2001)

Applicationes Mathematicae

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This paper is concerned with general conditions for convergence rates of nonparametric orthogonal series estimators of the regression function. The estimators are obtained by the least squares method on the basis of an observation sample $Y_{i} = f (X_{i}) + η_{i}$ , i=1,...,n, where $X_{i} \in A \subset ℝ^{d}$ are independently chosen from a distribution with density ϱ ∈ L¹(A) and $η_{i}$ are zero mean stationary errors with long-range dependence. Convergence rates of the error $n^{- 1} \sum_{i = 1}^{n} (f (X_{i}) - f ̂_{N} (X_{i})) ²$ for the estimator $f ̂_{N} (x) = \sum_{k = 1}^{N} c ̂_{k} e_{k} (x)$ , constructed using an orthonormal system...

More general credibility models

Virginia Atanasiu (2009)

Mathematica Bohemica

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This communication gives some extensions of the original Bühlmann model. The paper is devoted to semi-linear credibility, where one examines functions of the random variables representing claim amounts, rather than the claim amounts themselves. The main purpose of semi-linear credibility theory is the estimation of $μ_{0} (θ) = E [f_{0} (X_{t + 1}) | θ]$ (the net premium for a contract with risk parameter $θ$ ) by a linear combination of given functions of the observable variables: ${\underset{̲}{X}}^{'} = (X_{1}, X_{2}, ..., X_{t})$ . So the estimators mainly considered here...

Orthogonal series estimation of band-limited regression functions

Waldemar Popiński (2014)

Applicationes Mathematicae

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The problem of nonparametric function fitting using the complete orthogonal system of Whittaker cardinal functions $s_{k}$ , k = 0,±1,..., for the observation model $y_{j} = f (u_{j}) + η_{j}$ , j = 1,...,n, is considered, where f ∈ L²(ℝ) ∩ BL(Ω) for Ω > 0 is a band-limited function, $u_{j}$ are independent random variables uniformly distributed in the observation interval [-T,T], $η_{j}$ are uncorrelated or correlated random variables with zero mean value and finite variance, independent of the observation points. Conditions...

Variance components estimation in generalized orthogonal models

Célia Fernandes, Paulo Ramos, Sandra Saraiva Ferreira, João Tiago Mexia (2007)

Discussiones Mathematicae Probability and Statistics

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The model $y = \sum_{j = 1}^{w} X_{j} β ̲_{j} + e ̲$ is generalized orthogonal if the orthogonal projection matrices on the range spaces of matrices $X_{j}$ , j = 1, ..., w, commute. Unbiased estimators are obtained for the variance components of such models with cross-nesting.

$L_{1}$ -penalization in functional linear regression with subgaussian design

Vladimir Koltchinskii, Stanislav Minsker (2014)

Journal de l’École polytechnique — Mathématiques

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We study functional regression with random subgaussian design and real-valued response. The focus is on the problems in which the regression function can be well approximated by a functional linear model with the slope function being “sparse” in the sense that it can be represented as a sum of a small number of well separated “spikes”. This can be viewed as an extension of now classical sparse estimation problems to the case of infinite dictionaries. We study an estimator of the regression...

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

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