Parametric statistics

About: Parametric statistics is a research topic. Over the lifetime, 39200 publications have been published within this topic receiving 765761 citations.

Parametric Interaction of Focused Gaussian Light Beams

Abstract: A theoretical study is presented on the optimization of second harmonic generation (SHG) and parametric generation (PG) by a laser beam in a uniaxial nonlinear crystal. Numerically computed curves show the dependence of the SHG power, and the reciprocal of the PG threshold power, on the parameter l/b, where l is the optical path length in the crystal and b is the confocal parameter (determined by the focal length of the focusing lens and the minimum radius of the laser beam, assumed to be in the TEM00 mode of an optical resonator). The calculations take full account of diffraction and double refraction. In the absence of double refraction, the optimum focusing condition is found to be l/b=2.84. For PG the optimization of the crystal length l is also discussed, and curves are given showing the dependence of the threshold on l for the case in which signal and idler have the same losses. It is shown that the computed functions are also relevant to the mixing of two Gaussian beams and to parametric amplificat...

Empirical Likelihood and General Estimating Equations

Abstract: For some time, so-called empirical likelihoods have been used heuristically for purposes of nonparametric estimation. Owen showed that empirical likelihood ratio statistics for various parameters $\theta(F)$ of an unknown distribution $F$ have limiting chi-square distributions and may be used to obtain tests or confidence intervals in a way that is completely analogous to that used with parametric likelihoods. Our objective in this paper is twofold: first, to link estimating functions or equations and empirical likelihood; second, to develop methods of combining information about parameters. We do this by assuming that information about $F$ and $\theta$ is available in the form of unbiased estimating functions. Empirical likelihoods for parameters are developed and shown to have properties similar to those for parametric likelihood. Efficiency results for estimates of both $\theta$ and $F$ are obtained. The methods are illustrated on several problems, and areas for future investigation are noted.

Output feedback H∞ control of systems with parameter uncertainty

Abstract: This paper deals with H ∞ control problem for systems with parametric uncertainty in all matrices of the system and output equations. The parametric uncertainty under consideration is of a linear fractional form. Both the continuous and the discrete-time cases are considered. Necessary and sufficient conditions for quadratic stability with H ∞ disturbance attenuation are obtained.

A study on the use of non-parametric tests for analyzing the evolutionary algorithms' behaviour: a case study on the CEC'2005 Special Session on Real Parameter Optimization

Abstract: In recent years, there has been a growing interest for the experimental analysis in the field of evolutionary algorithms. It is noticeable due to the existence of numerous papers which analyze and propose different types of problems, such as the basis for experimental comparisons of algorithms, proposals of different methodologies in comparison or proposals of use of different statistical techniques in algorithms' comparison. In this paper, we focus our study on the use of statistical techniques in the analysis of evolutionary algorithms' behaviour over optimization problems. A study about the required conditions for statistical analysis of the results is presented by using some models of evolutionary algorithms for real-coding optimization. This study is conducted in two ways: single-problem analysis and multiple-problem analysis. The results obtained state that a parametric statistical analysis could not be appropriate specially when we deal with multiple-problem results. In multiple-problem analysis, we propose the use of non-parametric statistical tests given that they are less restrictive than parametric ones and they can be used over small size samples of results. As a case study, we analyze the published results for the algorithms presented in the CEC'2005 Special Session on Real Parameter Optimization by using non-parametric test procedures.

Analysis of semiparametric regression models for repeated outcomes in the presence of missing data

Abstract: We propose a class of inverse probability of censoring weighted estimators for the parameters of models for the dependence of the mean of a vector of correlated response variables on a vector of explanatory variables in the presence of missing response data. The proposed estimators do not require full specification of the likelihood. They can be viewed as an extension of generalized estimating equations estimators that allow for the data to be missing at random but not missing completely at random. These estimators can be used to correct for dependent censoring and nonrandom noncompliance in randomized clinical trials studying the effect of a treatment on the evolution over time of the mean of a response variable. The likelihood-based parametric G-computation algorithm estimator may also be used to attempt to correct for dependent censoring and nonrandom noncompliance. But because of possible model misspecification, the parametric G-computation algorithm estimator, in contrast with the proposed w...