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Kybernetika

### A survey of limit laws for bootstrapped sums.

International Journal of Mathematics and Mathematical Sciences

### Adaptive non-asymptotic confidence balls in density estimation

ESAIM: Probability and Statistics

We build confidence balls for the common density s of a real valued sample X1,...,Xn. We use resampling methods to estimate the projection of s onto finite dimensional linear spaces and a model selection procedure to choose an optimal approximation space. The covering property is ensured for all n ≥ 2 and the balls are adaptive over a collection of linear spaces.

### Adaptive non-asymptotic confidence balls in density estimation

ESAIM: Probability and Statistics

We build confidence balls for the common density s of a real valued sample X1,...,Xn. We use resampling methods to estimate the projection of s onto finite dimensional linear spaces and a model selection procedure to choose an optimal approximation space. The covering property is ensured for all n ≥ 2 and the balls are adaptive over a collection of linear spaces.

### Additions and correction to “The bootstrap of the mean with arbitrary bootstrap sample”

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

### An approximate necessary condition for the optimal bandwidth selector in kernel density estimation

Applicationes Mathematicae

An approximate necessary condition for the optimal bandwidth choice is derived. This condition is used to construct an iterative bandwidth selector. The algorithm is based on resampling and step-wise fitting the bandwidth to the density estimator from the previous iteration. Examples show fast convergence of the algorithm to the bandwidth value which is surprisingly close to the optimal one no matter what is the initial knowledge on the unknown density.

### Análisis de duración mediante un modelo lineal generalizado semiparamétrico.

Qüestiió

Aitkin y Clayton (1980) proponen el análisis de modelos de duración mediante modelos lineales generalizados. En este trabajo extendemos esta metodología permitiendo que el efecto de alguna de las variables explicativas pueda no ser especificado. Así, el modelo propuesto es un modelo lineal generalizado semiparamétrico, con una componente paramétrica donde se especifica la forma funcional concreta del efecto de las variables explicativas sobre la duración, y una componente no paramétrica donde recogemos...

### Analytical bootstrap methods for censored data.

Journal of Applied Mathematics and Decision Sciences

### Applications of intentionally biased bootstrap methods.

Documenta Mathematica

### Bootstrap in nonstationary autoregression

Kybernetika

The first-order autoregression model with heteroskedastic innovations is considered and it is shown that the classical bootstrap procedure based on estimated residuals fails for the least-squares estimator of the autoregression coefficient. A different procedure called wild bootstrap, respectively its modification is considered and its consistency in the strong sense is established under very mild moment conditions.

Metrika

### Bootstraping of M-smoothers

Acta Universitatis Carolinae. Mathematica et Physica

Metrika

### Bootstrapping the shorth for regression

ESAIM: Probability and Statistics

The paper is concerned with the asymptotic distributions of estimators for the length and the centre of the so-called η-shorth interval in a nonparametric regression framework. It is shown that the estimator of the length converges at the n1/2-rate to a Gaussian law and that the estimator of the centre converges at the n1/3-rate to the location of the maximum of a Brownian motion with parabolic drift. Bootstrap procedures are proposed and shown to be consistent. They are compared with the plug-in...

### Complete convergence theorems for normed row sums from an array of rowwise pairwise negative quadrant dependent random variables with application to the dependent bootstrap

Applications of Mathematics

Let $\left\{{X}_{n,j},1\le j\le m\left(n\right),n\ge 1\right\}$ be an array of rowwise pairwise negative quadrant dependent mean 0 random variables and let $0<{b}_{n}\to \infty$. Conditions are given for ${\sum }_{j=1}^{m\left(n\right)}{X}_{n,j}/{b}_{n}\to 0$ completely and for ${max}_{1\le k\le m\left(n\right)}|{\sum }_{j=1}^{k}{X}_{n,j}|/{b}_{n}\to 0$ completely. As an application of these results, we obtain a complete convergence theorem for the row sums ${\sum }_{j=1}^{m\left(n\right)}{X}_{n,j}^{*}$ of the dependent bootstrap samples $\left\{\left\{{X}_{n,j}^{*},1\le j\le m\left(n\right)\right\},n\ge 1\right\}$ arising from a sequence of i.i.d. random variables $\left\{{X}_{n},n\ge 1\right\}$.

### Computational intensive methods for prediction and imputation in time series analysis

Discussiones Mathematicae Probability and Statistics

One of the main goals in times series analysis is to forecast future values. Many forecasting methods have been developed and the most successful are based on the concept of exponential smoothing, based on the principle of obtaining forecasts as weighted combinations of past observations. Classical procedures to obtain forecast intervals assume a known distribution for the error process, what is not true in many situations. A bootstrap methodology can be used to compute distribution free forecast...

### ¿Cuántos clusters hay en una población?

Qüestiió

Sea una población cerrada formada por un número desconocido K y finito de clusters. El método bootstrap es utilizado para estimar el número de clusters que constituyen una población. Se propone un estimador para K, el cual es ajustado y corregido por su sesgo estimado mediante el método bootstrap de Efron (1979). La varianza del "estimador bootstrap" se calcula por el método jackknife agrupado. Mediante simulación, el estimador es comparado con el de Bickel y Yavah (1985).

### Dependent Lindeberg central limit theorem and some applications

ESAIM: Probability and Statistics

In this paper, a very useful lemma (in two versions) is proved: it simplifies notably the essential step to establish a Lindeberg central limit theorem for dependent processes. Then, applying this lemma to weakly dependent processes introduced in Doukhan and Louhichi (1999), a new central limit theorem is obtained for sample mean or kernel density estimator. Moreover, by using the subsampling, extensions under weaker assumptions of these central limit theorems are provided. All the usual causal...

### Detecting atypical data in air pollution studies by using shorth intervals for regression

ESAIM: Probability and Statistics

To validate pollution data, subject-matter experts in Airpl (an organization that maintains a network of air pollution monitoring stations in western France) daily perform visual examinations of the data and check their consistency. In this paper, we describe these visual examinations and propose a formalization for this problem. The examinations consist in comparisons of so-called shorth intervals so we build a statistical test that compares such intervals in a nonparametric regression model. This...

### Detecting atypical data in air pollution studies by using shorth intervals for regression

ESAIM: Probability and Statistics

To validate pollution data, subject-matter experts in Airpl (an organization that maintains a network of air pollution monitoring stations in western France) daily perform visual examinations of the data and check their consistency. In this paper, we describe these visual examinations and propose a formalization for this problem. The examinations consist in comparisons of so-called shorth intervals so we build a statistical test that compares such intervals in a nonparametric regression model. This...

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