Parametric statistics

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

Locally Optimized Product Quantization for Approximate Nearest Neighbor Search

Abstract: We present a simple vector quantizer that combines low distortion with fast search and apply it to approximate nearest neighbor (ANN) search in high dimensional spaces. Leveraging the very same data structure that is used to provide non-exhaustive search, i.e., inverted lists or a multi-index, the idea is to locally optimize an individual product quantizer (PQ) per cell and use it to encode residuals. Local optimization is over rotation and space decomposition, interestingly, we apply a parametric solution that assumes a normal distribution and is extremely fast to train. With a reasonable space and time overhead that is constant in the data size, we set a new state-of-the-art on several public datasets, including a billion-scale one.

Robust adaptive neural control for a class of perturbed strict feedback nonlinear systems

Abstract: This paper presents a robust adaptive neural control design for a class of perturbed strict feedback nonlinear system with both completely unknown virtual control coefficients and unknown nonlinearities. The unknown nonlinearities comprise two types of nonlinear functions: one naturally satisfies the "triangularity condition" and can be approximated by linearly parameterized neural networks, while the other is assumed to be partially known and consists of parametric uncertainties and known "bounding functions." With the utilization of iterative Lyapunov design and neural networks, the proposed design procedure expands the class of nonlinear systems for which robust adaptive control approaches have been studied. The design method does not require a priori knowledge of the signs of the unknown virtual control coefficients. Leakage terms are incorporated into the adaptive laws to prevent parameter drifts due to the inherent neural-network approximation errors. It is proved that the proposed robust adaptive scheme can guarantee the uniform ultimate boundedness of the closed-loop system signals.. The control performance can be guaranteed by an appropriate choice of the design parameters. Simulation studies are included to illustrate the effectiveness of the proposed approach.

Chapter 45 Estimation and inference for dependent processes

Abstract: This chapter provides an overview of asymptotic results available for parametric estimators in dynamic models. Three cases are treated: stationary (or essentially stationary) weakly dependent data, weakly dependent data containing deterministic trends, and nonergodic data (or data with stochastic trends). Estimation of asymptotic covariance matrices and computation of the major test statistics are covered. Examples include multivariate least squares estimation of a dynamic conditional mean, quasi-maximum likelihood estimation of a jointly parameterized conditional mean and conditional variance, and generalized method of moments estimation of orthogonality conditions. Some results for linear models with integrated variables are provided, as are some abstract limiting distribution results for nonlinear models with trending data.