Displaying similar documents to “Intrinsic linearization of nonlinear regression by principal components method.”

Estimation and prediction in regression models with random explanatory variables

Nguyen Bac-Van

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The regression model X(t),Y(t);t=1,...,n with random explanatory variable X is transformed by prescribing a partition S 1 , . . . , S k of the given domain S of X-values and specifying X ( 1 ) , . . . , X ( n ) S i = X i 1 , . . . , X i α ( i ) , i = 1 , . . . , k . Through the conditioning α ( i ) = a ( i ) , i = 1 , . . . , k , X i 1 , . . . , X i α ( i ) ; i = 1 , . . . , k = x 11 , . . . , x k a ( k ) the initial model with i.i.d. pairs (X(t),Y(t)),t=1,...,n, becomes a conditional fixed-design ( x 11 , . . . , x k a ( k ) ) model Y i j , i = 1 , . . . , k ; j = 1 , . . . , a ( i ) where the response variables Y i j are independent and distributed according to the mixed conditional distribution Q ( · , x i j ) of Y given X at the observed value x i j .Afterwards, we investigate the case ( Q ) E ( Y ' | x ) = i = 1 k b i ( x ) θ i I S i ( x ) , ( Q ) D ( Y | x ) = i = 1 k d i ( x ) Σ i I S i ( x ) which...

Bias correction on censored least squares regression models

Jesus Orbe, Vicente Núñez-Antón (2012)

Kybernetika

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This paper proposes a bias reduction of the coefficients' estimator for linear regression models when observations are randomly censored and the error distribution is unknown. The proposed bias correction is applied to the weighted least squares estimator proposed by Stute [28] [W. Stute: Consistent estimation under random censorship when covariables are present. J. Multivariate Anal. 45 (1993), 89-103.], and it is based on model-based bootstrap resampling techniques that also allow...

Robust median estimator for generalized linear models with binary responses

Tomáš Hobza, Leandro Pardo, Igor Vajda (2012)

Kybernetika

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The paper investigates generalized linear models (GLM's) with binary responses such as the logistic, probit, log-log, complementary log-log, scobit and power logit models. It introduces a median estimator of the underlying structural parameters of these models based on statistically smoothed binary responses. Consistency and asymptotic normality of this estimator are proved. Examples of derivation of the asymptotic covariance matrix under the above mentioned models are presented. Finally...

Bayesian nonparametric estimation of hazard rate in monotone Aalen model

Jana Timková (2014)

Kybernetika

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This text describes a method of estimating the hazard rate of survival data following monotone Aalen regression model. The proposed approach is based on techniques which were introduced by Arjas and Gasbarra [4]. The unknown functional parameters are assumed to be a priori piecewise constant on intervals of varying count and size. The estimates are obtained with the aid of the Gibbs sampler and its variants. The performance of the method is explored by simulations. The results indicate...