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Schémas de discrétisation anticipatifs et estimation du paramètre de dérive d'une diffusion

Sandie Souchet Samos (2010)

ESAIM: Probability and Statistics

Let YT = (Yt)t∈[0,T] be a real ergodic diffusion process which drift depends on an unkown parameter θ 0 ∈ ℝ p . Our aim is to estimate θ0 from a discrete observation of the process YT, (Ykδ)k=0,n, for a fixed and small δ, as T = nδ goes to infinity. For that purpose, we adapt the Generalized Method of Moments (see Hansen) to the anticipative and approximate discrete-time trapezoidal scheme, and then to Simpson's. Under some general assumptions, the trapezoidal scheme (respectively Simpson's scheme)...

Sensitivity analysis of M -estimators of non-linear regression models

Asunción Rubio, Francisco Quintana, Jan Ámos Víšek (1994)

Commentationes Mathematicae Universitatis Carolinae

An asymptotic formula for the difference of the M -estimates of the regression coefficients of the non-linear model for all n observations and for n - 1 observations is presented under conditions covering the twice absolutely continuous ϱ -functions. Then the implications for the M -estimation of the regression model are discussed.

Simple large sample estimators of scale and location parameters based on blocks of order statistics.

Peter Kubat (1982)

Trabajos de Estadística e Investigación Operativa

In this paper quite efficient large sample estimation procedures are derived for jointly estimating the parameters of the location-scale family of distributions. These estimators are linear combinations of the means of suitably chosen blocks of order statistics. For specific distributions, such as the extreme-value, normal, and logistic, little is to be gained by using more than three blocks. For these distributions we can obtain joint relative asymptotic efficiencies of 97-98% using the means of...

Strong law of large numbers for additive extremum estimators

João Tiago Mexia, Pedro Corte Real (2001)

Discussiones Mathematicae Probability and Statistics

Extremum estimators are obtained by maximizing or minimizing a function of the sample and of the parameters relatively to the parameters. When the function to maximize or minimize is the sum of subfunctions each depending on one observation, the extremum estimators are additive. Maximum likelihood estimators are extremum additive whenever the observations are independent. Another instance of additive extremum estimators are the least squares estimators for multiple regressions when the usual assumptions...

Strong uniform consistency rates of some characteristics of the conditional distribution estimator in the functional single-index model

Amina Angelika Bouchentouf, Tayeb Djebbouri, Abbes Rabhi, Khadidja Sabri (2014)

Applicationes Mathematicae

The aim of this paper is to establish a nonparametric estimate of some characteristics of the conditional distribution. Kernel type estimators for the conditional cumulative distribution function and for the successive derivatives of the conditional density of a scalar response variable Y given a Hilbertian random variable X are introduced when the observations are linked with a single-index structure. We establish the pointwise almost complete convergence and the uniform almost complete convergence...

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