Fehlerabschätzung für eine Klasse von nichtparametrischen Schätzfolgen.
Finite-sample comparison of -estimators of location
Forward estimation for ergodic time series
Gamma minimax nonparametric estimation
Let Y be a random vector taking its values in a measurable space and let z be a vector-valued function defined on that space. We consider gamma minimax estimation of the unknown expected value p of the random vector z(Y). We assume a weighted squared error loss function.
Gaussian semiparametric estimation in seasonal/cyclical long memory time series
Gaussian semiparametric or local Whittle estimation of the memory parameter in standard long memory processes was proposed by Robinson [18]. This technique shows several advantages over the popular log- periodogram regression introduced by Geweke and Porter–Hudak [7]. In particular under milder assumptions than those needed in the log periodogram regression it is asymptotically more efficient. We analyse the asymptotic behaviour of the Gaussian semiparametric estimate of the memory parameter in...
Generalized jackknife semi-parametric estimators of the tail index.
Hazard rate model and statistical analysis of a compound point process
A stochastic process cumulating random increments at random moments is studied. We model it as a two-dimensional random point process and study advantages of such an approach. First, a rather general model allowing for the dependence of both components mutually as well as on covariates is formulated, then the case where the increments depend on time is analyzed with the aid of the multiplicative hazard regression model. Special attention is devoted to the problem of prediction of process behaviour....
Hermite Series Estimators for Probability Densities.
Histogram selection in non Gaussian regression
We deal with the problem of choosing a piecewise constant estimator of a regression function s mapping into . We consider a non Gaussian regression framework with deterministic design points, and we adopt the non asymptotic approach of model selection via penalization developed by Birgé and Massart. Given a collection of partitions of , with possibly exponential complexity, and the corresponding collection of piecewise constant estimators, we propose a penalized least squares criterion which...
How many bins should be put in a regular histogram
Given an n-sample from some unknown density f on [0,1], it is easy to construct an histogram of the data based on some given partition of [0,1], but not so much is known about an optimal choice of the partition, especially when the data set is not large, even if one restricts to partitions into intervals of equal length. Existing methods are either rules of thumbs or based on asymptotic considerations and often involve some smoothness properties of f. Our purpose in this paper is to give an automatic,...
How to get Central Limit Theorems for global errors of estimates
The asymptotic behavior of global errors of functional estimates plays a key role in hypothesis testing and confidence interval building. Whereas for pointwise errors asymptotic normality often easily follows from standard Central Limit Theorems, global errors asymptotics involve some additional techniques such as strong approximation, martingale theory and Poissonization. We review these techniques in the framework of density estimation from independent identically distributed random variables,...
Improving feature selection process resistance to failures caused by curse-of-dimensionality effects
The purpose of feature selection in machine learning is at least two-fold - saving measurement acquisition costs and reducing the negative effects of the curse of dimensionality with the aim to improve the accuracy of the models and the classification rate of classifiers with respect to previously unknown data. Yet it has been shown recently that the process of feature selection itself can be negatively affected by the very same curse of dimensionality - feature selection methods may easily over-fit...
Inefficient estimators of the bivariate survival function for three models
Inferring the residual waiting time for binary stationary time series
For a binary stationary time series define to be the number of consecutive ones up to the first zero encountered after time , and consider the problem of estimating the conditional distribution and conditional expectation of after one has observed the first outputs. We present a sequence of stopping times and universal estimators for these quantities which are pointwise consistent for all ergodic binary stationary processes. In case the process is a renewal process with zero the renewal state...
Intermittent estimation for finite alphabet finitarily Markovian processes with exponential tails
We give some estimation schemes for the conditional distribution and conditional expectation of the the next output following the observation of the first outputs of a stationary process where the random variables may take finitely many possible values. Our schemes are universal in the class of finitarily Markovian processes that have an exponential rate for the tail of the look back time distribution. In addition explicit rates are given. A necessary restriction is that the scheme proposes an...
Intervalles de confiance pour les estimations des courbes de survie à partir du modèle de Cox
Invariant Density Estimation.
Kernel Estimation of a Smooth Distribution Function Based on Censored Data.
-penalization in functional linear regression with subgaussian design
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 function...
-type contraction for systems of conservation laws
The semi-group associated with the Cauchy problem for a scalar conservation law is known to be a contraction in . However it is not a contraction in for any . Leger showed in [20] that for a convex flux, it is however a contraction in up to a suitable shift. We investigate in this paper whether such a contraction may happen for systems. The method is based on the relative entropy method. Our general analysis leads us to the new geometrical notion of Genuinely non-Temple systems. We treat in...