On Asymptotically Efficient Recursive Estimation of a Location Parameter

1981 ◽  
Vol 25 (3) ◽  
pp. 569-579
Author(s):  
M. B. Nevel’son
Keyword(s):  
Location Parameter ◽  
Recursive Estimation ◽  
Asymptotically Efficient

scholarly journals Fast, Asymptotically Efficient, Recursive Estimation in a Riemannian Manifold

Entropy ◽  
2019 ◽  
Vol 21 (10) ◽  
pp. 1021 ◽  
Author(s):  
Jialun Zhou ◽  
Salem Said
Keyword(s):  
Riemannian Manifold ◽  
Rate Of Convergence ◽  
Statistical Parameter ◽  
Recursive Estimation ◽  
Numerical Application ◽  
Stochastic Optimisation ◽  
Asymptotic Rate ◽  
Fisher Information Metric ◽  
Convexity Assumptions ◽  
Asymptotically Efficient

Stochastic optimisation in Riemannian manifolds, especially the Riemannian stochastic gradient method, has attracted much recent attention. The present work applies stochastic optimisation to the task of recursive estimation of a statistical parameter which belongs to a Riemannian manifold. Roughly, this task amounts to stochastic minimisation of a statistical divergence function. The following problem is considered: how to obtain fast, asymptotically efficient, recursive estimates, using a Riemannian stochastic optimisation algorithm with decreasing step sizes. In solving this problem, several original results are introduced. First, without any convexity assumptions on the divergence function, we proved that, with an adequate choice of step sizes, the algorithm computes recursive estimates which achieve a fast non-asymptotic rate of convergence. Second, the asymptotic normality of these recursive estimates is proved by employing a novel linearisation technique. Third, it is proved that, when the Fisher information metric is used to guide the algorithm, these recursive estimates achieve an optimal asymptotic rate of convergence, in the sense that they become asymptotically efficient. These results, while relatively familiar in the Euclidean context, are here formulated and proved for the first time in the Riemannian context. In addition, they are illustrated with a numerical application to the recursive estimation of elliptically contoured distributions.

Fixed Length Interval Estimation of the Location Parameter of a Pareto Distribution

1986 ◽  
Vol 35 (1-2) ◽  
pp. 67-76 ◽  
Author(s):  
Malay Ghosh ◽  
Dennis Wackerly
Keyword(s):  
Confidence Interval ◽  
Shape Parameter ◽  
Pareto Distribution ◽  
Interval Estimation ◽  
Location Parameter ◽  
Fixed Length ◽  
Asymptotically Efficient ◽  
Width Confidence Interval

A sequential fixed-width confidence interval for the location parameter of a Pareto distribution with unknown shape parameter is developed. The procedure Is shown to be asymptotically consistent and asymptotically efficient in the sense of Chow and Robbins (1965).

scholarly journals Recent Developments in Recursive Estimation for Time Series Models

2016 ◽  
Vol 5 (2) ◽  
pp. 59
Author(s):  
You Liang ◽  
A. Thavaneswaran ◽  
B. Abraham
Keyword(s):  
Location Parameter ◽  
Recursive Estimation ◽  
Joint Estimation ◽  
Infinite Variance ◽  
Finite Variance ◽  
Estimating Functions ◽  
Unified Approach ◽  
Scale Parameters ◽  
Combined Estimation ◽  
Recent Developments

Recently there has been a growing interest in joint estimation of the location and scale parameters using combined estimation functions. Combined estimating functions had been studied in Liang et al. (2011) for models with finite variance errors  and in Thavaneswaran et al. (2013) for models with infinite variance<br />stable errors. In this paper, first a theorem on recursive estimation based on estimating functions is extended to multi-parameter setup and it is shown that the unified approach can be used to estimate the location parameter recursively for models with finite variance/infinite variance  errors. The method is applied for the joint estimation of the location and scale parameters for regression models with ARCH errors and RCA models with GARCH errors.

Sign in / Sign up

Export Citation Format

Share Document