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Consistencia de un estimador no paramétrico, recursivo, de la regresión bajo condiciones generales.

Juan Manuel Vilar Fernández (1991)

Trabajos de Estadística

Se define un estimador no paramétrico, recursivo, de la función de regresión r(x) = E(Y/X = x), que se calcula a partir de un conjunto de n observaciones {(X1,Yi): i = 1, ..., n} del vector aleatorio (X,Y). Bajo la hipótesis de que los datos son idénticamente distribuidos pero no necesariamente independientes, lo que permite utilizar el estimador definido para estimar la función de autorregresión de una serie de tiempo, se obtienen resultados sobre la consistencia puntual débil (en probabilidad)...

Consistency of linear and quadratic least squares estimators in regression models with covariance stationary errors

František Štulajter (1991)

Applications of Mathematics

The least squres invariant quadratic estimator of an unknown covariance function of a stochastic process is defined and a sufficient condition for consistency of this estimator is derived. The mean value of the observed process is assumed to fulfil a linear regresion model. A sufficient condition for consistency of the least squares estimator of the regression parameters is derived, too.

Consistency of the least weighted squares under heteroscedasticity

Jan Ámos Víšek (2011)

Kybernetika

A robust version of the Ordinary Least Squares accommodating the idea of weighting the order statistics of the squared residuals (rather than directly the squares of residuals) is recalled and its properties are studied. The existence of solution of the corresponding extremal problem and the consistency under heteroscedasticity is proved.

Consistency of the LSE in Linear regression with stationary noise

Guy Cohen, Michael Lin, Arkady Tempelman (2004)

Colloquium Mathematicae

We obtain conditions for L₂ and strong consistency of the least square estimators of the coefficients in a multi-linear regression model with a stationary random noise. For given non-random regressors, we obtain conditions which ensure L₂-consistency for all wide sense stationary noise sequences with spectral measure in a given class. The condition for the class of all noises with continuous (i.e., atomless) spectral measures yields also L p -consistency when the noise is strict sense stationary with...

Consistency of trigonometric and polynomial regression estimators

Waldemar Popiński (1998)

Applicationes Mathematicae

The problem of nonparametric regression function estimation is considered using the complete orthonormal system of trigonometric functions or Legendre polynomials e k , k=0,1,..., for the observation model y i = f ( x i ) + η i , i=1,...,n, where the η i are independent random variables with zero mean value and finite variance, and the observation points x i ∈ [ a , b ] , i=1,...,n, form a random sample from a distribution with density ϱ ∈ L 1 [ a , b ] . Sufficient and necessary conditions are obtained for consistency in the sense of the errors ∥ f - f ^ N ∥ , | f ( x ) - N ( x ) | , x ∈ [ a , b ] ,...

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