‎in this paper‎, ‎we study spectral element approximation for a constrained‎ ‎optimal control problem in one dimension‎. ‎the equivalent a posteriori error estimators are derived for‎ ‎the control‎, ‎the state and the adjoint state approximation‎. ‎such estimators can be used to‎ ‎construct adaptive spectral elements for the control problems.

We propose the COMP-AODE classifier, which adopts the compression-based approach [1] to average the posterior probabilities computed by different non-naive classifiers (SPODEs). COMP-AODE improves classification performance over the wellknown AODE [10] model. COMP-AODE assumes a uniform prior over the SPODEs; we then develop the credal classifier COMPAODE*, substituting the uniform prior by a s...

The problem of covariate measurement error with heteroscedastic measurement error variance is considered. Standard regression calibration assumes that the measurement error has a homoscedastic measurement error variance. An estimator is proposed to correct regression coefficients for covariate measurement error with heteroscedastic variance. Point and interval estimates are derived. Validation ...

The leverage effect has become an extensively studied phenomenon that describes the (usually) negative correlation between stock returns and volatility. All the previous studies have focused on the origin and properties of the leverage effect. Even though most studies of the leverage effect are based on cross-sectional calibration with parametric models, few of them have carefully studied its e...

In [3] we gave an algorithm for deciding the existence of a rational general solution of strongly parametrization first-order AODEs (SP1AODEs). This report shall give, on the one hand a list of strongly parametrizable AODEs and their solutions and on the other hand a statistical investigation on the relative number of such AODEs in well known collections such as Kamke [1] and Polyanin and Sajze...

The measurement of weak gravitational lensing is currently limited to a precision of ∼10% by instabilities in galaxy shape measurement techniques and uncertainties in their calibration. The potential of large, on-going and future cosmic shear surveys will only be realised with the development of more accurate image analysis methods. We present a description of several possible shear measurement...

Partial Least Squares (PLS) is a standard statistical method in chemometrics. It can be considered as an incomplete, or “partial”, version of the Least Squares estimator of regression, applicable when high or perfect multicollinearity is present in the predictor variables. The Least Squares estimator is well-known to be an optimal estimator for regression, but only when the error terms are norm...

Estimation of the regression parameters and variance components in a longitudinal mixed model with measurement error in a time-varying covariate is considered. The positive bias in variance estimators caused by covariate measurement error in a normal linear mixed model has recently been identified and studied (Tosteson, Buonaccorsi and Demidenko (1997)). The methods suggested there for correcti...

Three estimators are proposed for the regression coefficients in Poisson regression model which the covariates are measured with error. The measurement errors are assumed to be normally distributed, while the correlation coefficient between the latent covariate and the observe covariate is assumed to be known. The adjusted estimator is obtained by adjusting the naive estimator without consideri...

We characterize the robustness of subsampling procedures by deriving a formula for the breakdown point of subsampling quantiles. This breakdown point can be very low for moderate subsampling block sizes, which implies the fragility of subsampling procedures, even when they are applied to robust statistics. This instability arises also for data driven block size selection procedures minimizing t...