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Censored regression models with double exponential error distributions: an iterattive estimation procedure based on medians for correcting bias.

Carmen Anido, Teófilo Valdés (2000)

Revista Matemática Complutense

In this paper, we consider a simple iterative estimation procedure for censored regression models with symmetrical exponential error distributions. Although each step requires to impute the censored data with conditional medians, its tractability is guaranteed as well as its convergence at geometrical rate. Finally, as the final estimate coincides with a Huber M-estimator, its consistency and asymptotic normality are easily proved.

Change-point estimator in continuous quadratic regression

Daniela Jarušková (2001)

Commentationes Mathematicae Universitatis Carolinae

The paper deals with the asymptotic distribution of the least squares estimator of a change point in a regression model where the regression function has two phases --- the first linear and the second quadratic. In the case when the linear coefficient after change is non-zero the limit distribution of the change point estimator is normal whereas it is non-normal if the linear coefficient is zero.

Change-point estimator in gradually changing sequences

Daniela Jarušková (1998)

Commentationes Mathematicae Universitatis Carolinae

Recently Hušková (1998) has studied the least squares estimator of a change-point in gradually changing sequence supposing that the sequence increases (or decreases) linearly after the change-point. The present paper shows that the limit behavior of the change-point estimator for more complicated gradual changes is similar. The limit variance of the estimator can be easily calculated from the covariance function of a limit process.

Compact hypothesis and extremal set estimators

João Tiago Mexia, Pedro Corte Real (2003)

Discussiones Mathematicae Probability and Statistics

In extremal estimation theory the estimators are local or absolute extremes of functions defined on the cartesian product of the parameter by the sample space. Assuming that these functions converge uniformly, in a convenient stochastic way, to a limit function g, set estimators for the set ∇ of absolute maxima (minima) of g are obtained under the compactness assumption that ∇ is contained in a known compact U. A strongly consistent test is presented for this assumption. Moreover, when the true...

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 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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