One Bootstrap suffices to generate sharp uniform bounds in functional estimation

Paul Deheuvels

Displaying similar documents to “One Bootstrap suffices to generate sharp uniform bounds in functional estimation”

Estimation of nuisance parameters for inference based on least absolute deviations

Wojciech Niemiro (1995)

Applicationes Mathematicae

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Statistical inference procedures based on least absolute deviations involve estimates of a matrix which plays the role of a multivariate nuisance parameter. To estimate this matrix, we use kernel smoothing. We show consistency and obtain bounds on the rate of convergence.

Estimation and prediction in regression models with random explanatory variables

Nguyen Bac-Van

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The regression model X(t),Y(t);t=1,...,n with random explanatory variable X is transformed by prescribing a partition $S_{1}, . . ., S_{k}$ of the given domain S of X-values and specifying $X (1), . . ., X (n) \cap S_{i} = X_{i 1}, . . ., X_{i α (i)}, i = 1, . . ., k .$ Through the conditioning $α (i) = a (i), i = 1, . . ., k, X_{i 1}, . . ., X_{i α (i)}; i = 1, . . ., k = x_{11}, . . ., x_{k a (k)}$ the initial model with i.i.d. pairs (X(t),Y(t)),t=1,...,n, becomes a conditional fixed-design $(x_{11}, . . ., x_{k a (k)})$ model $Y_{i j}, i = 1, . . ., k; j = 1, . . ., a (i)$ where the response variables $Y_{i j}$ are independent and distributed according to the mixed conditional distribution $Q (\cdot, x_{i j})$ of Y given X at the observed value $x_{i j}$ .Afterwards, we investigate the case $(Q) E (Y^{'} | x) = \sum_{i = 1}^{k} b_{i} (x) θ_{i} I_{S_{i}} (x), (Q) D (Y | x) = \sum_{i = 1}^{k} d_{i} (x) Σ_{i} I_{S_{i}} (x)$ which...

Robust median estimator for generalized linear models with binary responses

Tomáš Hobza, Leandro Pardo, Igor Vajda (2012)

Kybernetika

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The paper investigates generalized linear models (GLM's) with binary responses such as the logistic, probit, log-log, complementary log-log, scobit and power logit models. It introduces a median estimator of the underlying structural parameters of these models based on statistically smoothed binary responses. Consistency and asymptotic normality of this estimator are proved. Examples of derivation of the asymptotic covariance matrix under the above mentioned models are presented. Finally...

Bayesian nonparametric estimation of hazard rate in monotone Aalen model

Jana Timková (2014)

Kybernetika

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This text describes a method of estimating the hazard rate of survival data following monotone Aalen regression model. The proposed approach is based on techniques which were introduced by Arjas and Gasbarra [4]. The unknown functional parameters are assumed to be a priori piecewise constant on intervals of varying count and size. The estimates are obtained with the aid of the Gibbs sampler and its variants. The performance of the method is explored by simulations. The results indicate...

Robust estimation in capital asset pricing model.

Wong, Wing-Keung, Bian, Guorui (2000)

Journal of Applied Mathematics and Decision Sciences

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A central limit theorem for random fields.

Fazekas, István, Chuprunov, Alexey (2004)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

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An efficient estimator for Gibbs random fields

Martin Janžura (2014)

Kybernetika

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An efficient estimator for the expectation $\int f P ̣$ is constructed, where $P$ is a Gibbs random field, and $f$ is a local statistic, i. e. a functional depending on a finite number of coordinates. The estimator coincides with the empirical estimator under the conditions stated in Greenwood and Wefelmeyer [6], and covers the known special cases, namely the von Mises statistic for the i.i.d. underlying fields and the case of one-dimensional Markov chains.