Optimal dimension and optimal auxiliary vector to construct calibration estimators of the distribution function

Abstract

The calibration technique ([? ]) to estimate the nite distribution function have been studied in several papers. Calibration seeks for new weights close enough to sampling weights according to some distance function and that, at the same time, match benchmark constraints on available auxiliary information.The non smooth character of the nite population distribution function causes certain complexities that are resolved by dierent authors in dierent ways. One of these is to have consistency at a number of arbitrarily chosen points. This paper deals with the problem of the optimal selection of the number of points and with the optimal selections of these points, when auxiliary information is used by means of calibration.

The optimization problem of quantile and poverty measures estimation based on calibration

“…We show that the problem of optimizing the variance of a quantile estimator is equivalent to the optimization of the variance of the distribution function estimator at one point. We demonstrate that under certain conditions, the estimators obtained through the optimal selection proposed in [29] meet the distribution function properties and can be directly used in the quantile estimation. Due to the complexity of the quantile estimation and the optimal selection for calibration estimators, a practical mathematical expression for the variances of the quantile estimator could not be established.…”

“…Recenlty, under simple random sampling, the problem of optimal selection points in order to obtain the best estimation is treated in [26]- [29]. Unfortunately, the quantile estimation through the estimation of the distribution function needs the estimation for all value t and the optimal selection of auxiliary points depends on the point t in which we want to estimate the distribution function.…”

“…In this work, we will adapt and employ the optimal selection proposals in [29] in the estimation of quantiles. We show that the problem of optimizing the variance of a quantile estimator is equivalent to the optimization of the variance of the distribution function estimator at one point.…”

Comments on: Deville and Särndal’s calibration: revisiting a 25 years old successful optimization problem

“…Under some conditions, the estimator F yc (t) is a genuine distribution function. [15], [16] and [17] addressed the problem of selecting the optimal auxiliary vector included in the constraints. In a similiar way, [18] used a global penalised calibration method to define a new estimator for the fdf.…”

Dimension Synthesis of a 3T2R Labelling Robot with Hybrid Mechanism

“…Dimension synthesis is an important aspect of the design of labelling robot [7,8]. The performance of a labelling robot with hybrid mechanism varies greatly with its dimensions [9,10].…”