Wyniki wyszukiwania - Biblioteka Nauki

Nowa wersja platformy, zawierająca wyłącznie zasoby pełnotekstowe, jest już dostępna.
Przejdź na https://bibliotekanauki.pl

Ograniczanie wyników

Znaleziono wyników: 5

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: weak dependence

Sortuj według:

Ogranicz wyniki do:

On non-uniform Berry-Esseen bounds for time series

100%

Jirak M.

Probability and Mathematical Statistics

2015

tom Vol. 35, Fasc. 1

1--14

Given a stationary sequence {Xk}k ϵ Z, non-uniform bounds for the normal approximation in the Kolmogorov metric are established. The underlying weak dependence assumption includes many popular linear and nonlinear time series from the literature, such as ARMA or GARCH models. Depending on the number of moments p, typical bounds in this context are of the size O(mp−1 n−p/2+1), where we often find that m = mn = log n. In our setup, we can essentially improve upon this rate by the factor m−p/2, yielding a bound of O(mp/2−1 n−p/2+1). Among other things, this allows us to recover a result from the literature, which is due to Ibragimov.

An empirical almost sure central limit theorem under the weak dependence assumptions and its application to copula processes

80%

Dudziński M.

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

2017

tom 71

nr 1

Let: \(\mathbf{Y=}\left( \mathbf{Y}_{i}\right)\), where \(\mathbf{Y}_{i}=\left( Y_{i,1},...,Y_{i,d}\right)\), \(i=1,2,\dots \), be a \(d\)-dimensional, identically distributed, stationary, centered process with uniform marginals and a joint cdf \(F\), and \(F_{n}\left( \mathbf{x}\right) :=\frac{1}{n}\sum_{i=1}^{n}\mathbb{I}\left(Y_{i,1}\leq x_{1},\dots ,Y_{i,d}\leq x_{d}\right)\) denote the corresponding empirical cdf. In our work, we prove the almost sure central limit theorem for an empirical process \(B_{n}=\sqrt{n}\left( F_{n}-F\right)\) under some weak dependence conditions due to Doukhan and Louhichi. Some application of the established result to copula processes is also presented.

An invariance principle for weakly dependent stationary general models

80%

Doukhan P. , Wintenberger O.

Probability and Mathematical Statistics

2007

tom Vol. 27, Fasc. 1

45--73

The aim of this paper is to refine a weak invariance principle for stationary sequences given by Doukhan and Louhichi [10]. Since our conditions are not causal, our assumptions need to be stronger than the mixing and causal 0-weak dependence assumptions used in Dedecker and Doukhan [5]. Here, if moments of order greater than 2 exist, a weak invariance principle and convergence rates in the CLT are obtained; Doukhan and Louhichi [10] assumed the existence of moments with order greater than 4. Besides the η and к-weak dependence conditions used previously, we introduce a weaker one, λ, which fits the Bernoulli shifts with dependent inputs.

J1 convergence of partial sum processes with a reduced number of jumps

60%

Krizmanić D.

Probability and Mathematical Statistics

2015

tom Vol. 35, Fasc. 1

107--128

Various functional limit theorems for partial sum processes of strictly stationary sequences of regularly varying random variables in the space of càdlàg functions D[0, 1] with one of the Skorokhod topologies have already been obtained. The mostly used Skorokhod J1 topology is inappropriate when clustering of large values of the partial sum processes occurs. When all extremes within each cluster of high-threshold excesses do not have the same sign, Skorokhod M1 topology also becomes inappropriate. In this paper we alter the definition of the partial sum process in order to shrink all extremes within each cluster to a single one, which allows us to obtain the functional J1 convergence. We also show that this result can be applied to some standard time series models, including the GARCH(1, 1) process and its squares, the stochastic volatility models and m-dependent sequences.

Prediction of time series by statistical learning: general losses and fast rates

51%

Alquier P. , Li X. , Wintenberger O.

2013

tom 1

65-93

We establish rates of convergences in statistical learning for time series forecasting. Using the PAC-Bayesian approach, slow rates of convergence √ d/n for the Gibbs estimator under the absolute loss were given in a previous work [7], where n is the sample size and d the dimension of the set of predictors. Under the same weak dependence conditions, we extend this result to any convex Lipschitz loss function. We also identify a condition on the parameter space that ensures similar rates for the classical penalized ERM procedure. We apply this method for quantile forecasting of the French GDP. Under additional conditions on the loss functions (satisfied by the quadratic loss function) and for uniformly mixing processes, we prove that the Gibbs estimator actually achieves fast rates of convergence d/n. We discuss the optimality of these different rates pointing out references to lower bounds when they are available. In particular, these results bring a generalization the results of [29] on sparse regression estimation to some autoregression.