The quasi-optimality criterion chooses the regularization parameter in inverse problems without taking into account the noise level. This rule works remarkably well in practice, although Bakushinskii has shown that there are always counterexamples with very poor performance. We propose an average case analysis of quasi-optimality for spectral cut-off estimators and we prove that the quasi-optim...

In the present investigation, we propose a penalized chi square distance function for estimating the total/mean of a finite population. The function produces a general class of estimators for the population total that includes, among others, the estimators of Searls (1964), Singh and Srivastava (1980), and the famous unbiased ratio estimator of Hartley and Ross (1954). Several of the estimators...

Accurate calibration of sensory estimators is critical for maintaining accurate estimates of the environment. Classically, it was assumed that sensory calibration occurs by one sense changing to become consistent with vision; this is visual dominance. Recently, it has been proposed that changes in estimators occur according to their relative reliabilities; this is the reliability-based model. W...

Uncertainty in probabilistic classifiers predictions is a key concern when models are used to support human decision making, broader pipelines or sensitive automatic decisions have be taken. Studies shown that most not intrinsically well calibrated, meaning their scores consistent with posterior probabilities. Hence being able calibrate these models, enforce calibration while learning them, has...

In survey sampling, the use of auxiliary information can greatly improve precision estimates population total and/or means. Calibration estimation has developed into an important field research in sampling where plays role. this paper, calibration estimator for cluster with equal clusters have been introduced to variance aid and proposed estimator. Six distances measures, presented approach est...

This paper concerns Laurent series solutions of algebraic ordinary differential equations (AODEs). We first present several approaches to compute formal power series solutions of a given AODE. Then we determine a bound for orders of its Laurent series solutions. Using the order bound, one can transform a given AODE into a new one whose Laurent series solutions are only formal power series. The ...

The investigation of ordinal pattern distributions is a novel approach to quantifying the complexity of time series and detecting changes in the underlying dynamics. Being fast and robust against monotone distortions, this method is particularly well-suited for the analysis of long biophysical time series where the exact calibration of the measurement device is unknown. In this paper we investi...

This paper describes a new robust and fully automatic method for calibration of three-dimensional (3D) freehand ultrasound. 3D Freehand ultrasound consists in mounting a position sensor on a standard probe. The echographic B-scans can be localized in 3D, and can be compounded into a volume. However, especially for quantitative use, this process dramatically requires a calibration procedure that...