Calculating summary measures of unimodal response curves by means of nonlinear regression models.
Change-point estimator in gradually changing sequences
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.
Confidence regions in nonlinear models with constraints
Confidence regions in nonlinear regression models
New curvature measures for nonlinear regression models are developed and methods of their computing are given. Using these measures, more accurate confidence regions for parameters than those based on linear or quadratic approximations are obtained.
Consistency of the least weighted squares under heteroscedasticity
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.
Corrections of estimators in linearized models