Parametric statistics

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

Relative Density-Ratio Estimation for Robust Distribution Comparison

Abstract: Divergence estimators based on direct approximation of density-ratios without going through separate approximation of numerator and denominator densities have been successfully applied to machine learning tasks that involve distribution comparison such as outlier detection, transfer learning, and two-sample homogeneity test. However, since density-ratio functions often possess high fluctuation, divergence estimation is still a challenging task in practice. In this paper, we propose to use relative divergences for distribution comparison, which involves approximation of relative density-ratios. Since relative density-ratios are always smoother than corresponding ordinary density-ratios, our proposed method is favorable in terms of the non-parametric convergence speed. Furthermore, we show that the proposed divergence estimator has asymptotic variance independent of the model complexity under a parametric setup, implying that the proposed estimator hardly overfits even with complex models. Through experiments, we demonstrate the usefulness of the proposed approach.

Active disturbance rejection adaptive control of uncertain nonlinear systems: theory and application

Abstract: This paper proposes an active disturbance rejection adaptive controller for tracking control of a class of uncertain nonlinear systems with consideration of both parametric uncertainties and uncertain nonlinearities by effectively integrating adaptive control with extended state observer via backstepping method. Parametric uncertainties are handled by the synthesized adaptive law and the remaining uncertainties are estimated by extended state observer and then compensated in a feedforward way. Moreover, both matched uncertainties and unmatched uncertainties can be estimated by constructing an extended state observer for each channel of the considered nonlinear plant. Since parametric uncertainties can be reduced by parameter adaptation, the learning burden of extended state observer is much reduced. Consequently, high-gain feedback is avoided and improved tracking performance can be expected. The proposed controller theoretically guarantees a prescribed transient tracking performance and final tracking accuracy in general while achieving asymptotic tracking when the uncertain nonlinearities are not time-variant. The motion control of a motor-driven robot manipulator is investigated as an application example with some suitable modifications and improvements, and comparative simulation results are obtained to verify the high tracking performance nature of the proposed control strategy.

Dilution assay statistics.

Abstract: A parametric method of statistical analysis for dilution assays is developed in detail from first principles of probability and statistics. The method is based on a simple product binomial model for the experiment and produces an estimate for the concentration of target entities, a confidence interval for this concentration, and an indicator of the quality of the assay called the p value for goodness of fit. The procedure is illustrated with data from a virologic quantitative micrococulture assay used to quantify free human immunodeficiency virus in clinical trials. The merits of the procedure versus those of nonparametric methods of estimating the dilution inducing a 50% response rate are discussed. Advantages of the proposed approach include plausibility of the underlying assumptions, ability to assess plausibility of specific experimental outcomes through their likelihood, and plausibility of confidence intervals.