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LAMN property for hidden processes : the case of integrated diffusions

Arnaud Gloter, Emmanuel Gobet (2008)

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

In this paper we prove the Local Asymptotic Mixed Normality (LAMN) property for the statistical model given by the observation of local means of a diffusion process X. Our data are given by ∫01X(s+i)/n dμ(s) for i=0, …, n−1 and the unknown parameter appears in the diffusion coefficient of the process X only. Although the data are neither markovian nor gaussian we can write down, with help of Malliavin calculus, an explicit expression for the log-likelihood of the model, and then study the asymptotic...

Least empirical risk procedures in statistical inference

Wojciech Niemiro (1993)

Applicationes Mathematicae

We consider the empirical risk function Q n ( α ) = 1 n ∑ i = 1 n · f ( α , Z i ) (for iid Z i ’s) under the assumption that f(α,z) is convex with respect to α. Asymptotics of the minimum of Q n ( α ) is investigated. Tests for linear hypotheses are derived. Our results generalize some of those concerning LAD estimators and related tests.

Least squares estimator consistency: a geometric approach

João Tiago Mexia, João Lita da Silva (2006)

Discussiones Mathematicae Probability and Statistics

Consistency of LSE estimator in linear models is studied assuming that the error vector has radial symmetry. Generalized polar coordinates and algebraic assumptions on the design matrix are considered in the results that are established.

Likelihood and parametric heteroscedasticity in normal connected linear models

Joao Tiago Mexia, Pedro Corte Real (2000)

Discussiones Mathematicae Probability and Statistics

A linear model in which the mean vector and covariance matrix depend on the same parameters is connected. Limit results for these models are presented. The characteristic function of the gradient of the score is obtained for normal connected models, thus, enabling the study of maximum likelihood estimators. A special case with diagonal covariance matrix is studied.

Likelihood and quasi - likelihood estimation of transition probabilities

Ewa Bakinowska, Radosław Kala (2004)

Discussiones Mathematicae Probability and Statistics

In the paper two approaches to the problem of estimation of transition probabilities are considered. The approach by McCullagh and Nelder [5], based on the independent model and the quasi-likelihood function, is compared with the approach based on the marginal model and the standard likelihood function. The estimates following from these two approaches are illustrated on a simple example which was used by McCullagh and Nelder.

Local Asymptotic Normality Property for Lacunar Wavelet Series multifractal model

Jean-Michel Loubes, Davy Paindaveine (2011)

ESAIM: Probability and Statistics

We consider a lacunar wavelet series function observed with an additive Brownian motion. Such functions are statistically characterized by two parameters. The first parameter governs the lacunarity of the wavelet coefficients while the second one governs its intensity. In this paper, we establish the local and asymptotic normality (LAN) of the model, with respect to this couple of parameters. This enables to prove the optimality of an estimator for the lacunarity parameter, and to build optimal...

Local Asymptotic Normality Property for Lacunar Wavelet Series multifractal model*

Jean-Michel Loubes, Davy Paindaveine (2012)

ESAIM: Probability and Statistics

We consider a lacunar wavelet series function observed with an additive Brownian motion. Such functions are statistically characterized by two parameters. The first parameter governs the lacunarity of the wavelet coefficients while the second one governs its intensity. In this paper, we establish the local and asymptotic normality (LAN) of the model, with respect to this couple of parameters. This enables to prove the optimality of an estimator for the lacunarity parameter, and to build optimal...

Log-periodogram regression in asymmetric long memory

Josu Arteche (2000)

Kybernetika

The long memory property of a time series has long been studied and several estimates of the memory or persistence parameter at zero frequency, where the spectral density function is symmetric, are now available. Perhaps the most popular is the log periodogram regression introduced by Geweke and Porter–Hudak [gewe]. In this paper we analyse the asymptotic properties of this estimate in the seasonal or cyclical long memory case allowing for asymmetric spectral poles or zeros. Consistency and asymptotic...

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