Statistical Manifolds Admitting Torsion, Pre-contrast Functions and Estimating Functions

2017 ◽  
pp. 153-161 ◽  
Author(s):  
Masayuki Henmi
Keyword(s):  
Estimating Functions ◽  
Statistical Manifolds

PG-less Vector Control with Estimating Functions of Motor Parameter.

1991 ◽  
Vol 111 (5) ◽  
pp. 373-378 ◽  
Author(s):  
Naoki Yamamura ◽  
Masahiko Iwasaki ◽  
Hirotaka Sakurai ◽  
Yuzuru Tunehiro
Keyword(s):  
Vector Control ◽  
Estimating Functions ◽  
Motor Parameter

scholarly journals Hooke’s law in statistical manifolds and divergences

2000 ◽  
Vol 159 ◽  
pp. 1-24 ◽  
Author(s):  
Masayuki Henmi ◽  
Ryoichi Kobayashi
Keyword(s):  
Classical Mechanics ◽  
Riemannian Metric ◽  
Legendre Transform ◽  
Point Function ◽  
Hooke’S Law ◽  
Affine Connections ◽  
Statistical Manifolds ◽  
Dual Affine ◽  
Hooke's Law

The concept of the canonical divergence is defined for dually flat statistical manifolds in terms of the Legendre transform between dual affine coordinates. In this article, we introduce a new two point function defined for any triple (g,∇, ∇*) of a Riemannian metric g and two affine connections ∇ and ∇*. We show that this interprets the canonical divergence without refering to the existence of special coordinates (dual affine coordinates) but in terms of only classical mechanics concerning ∇- and ∇*-geodesics. We also discuss the properties of the two point function and show that this shares some important properties with the canonical divergence defined on dually flat statistical manifolds.

scholarly journals Manifolds of differentiable densities

2018 ◽  
Vol 22 ◽  
pp. 19-34 ◽  
Author(s):  
Nigel J. Newton
Keyword(s):  
Continuous Function ◽  
Likelihood Function ◽  
Probability Measures ◽  
Fréchet Spaces ◽  
Finite Sample ◽  
Infinite Dimensional ◽  
Statistical Manifolds ◽  
Covariant Derivatives ◽  
Finite Measures ◽  
Non Parametric

We develop a family of infinite-dimensional (non-parametric) manifolds of probability measures. The latter are defined on underlying Banach spaces, and have densities of class Cbk with respect to appropriate reference measures. The case k = ∞, in which the manifolds are modelled on Fréchet spaces, is included. The manifolds admit the Fisher-Rao metric and, unusually for the non-parametric setting, Amari’s α-covariant derivatives for all α ∈ ℝ. By construction, they are C∞-embedded submanifolds of particular manifolds of finite measures. The statistical manifolds are dually (α = ±1) flat, and admit mixture and exponential representations as charts. Their curvatures with respect to the α-covariant derivatives are derived. The likelihood function associated with a finite sample is a continuous function on each of the manifolds, and the α-divergences are of class C∞.

Combining estimating functions for volatility

2009 ◽  
Vol 139 (4) ◽  
pp. 1449-1461 ◽  
Author(s):  
M. Ghahramani ◽  
A. Thavaneswaran
Keyword(s):  
Estimating Functions

scholarly journals Sasakian statistical manifolds

2017 ◽  
Vol 117 ◽  
pp. 179-186 ◽  
Author(s):  
Hitoshi Furuhata ◽  
Izumi Hasegawa ◽  
Yukihiko Okuyama ◽  
Kimitake Sato ◽  
Mohammad Hasan Shahid
Keyword(s):  
Statistical Manifolds

Restricted quasi-score estimating functions for sample survey data

2004 ◽  
Vol 41 (A) ◽  
pp. 119-130
Author(s):  
Y.-X. Lin ◽  
D. Steel ◽  
R. L Chambers
Keyword(s):  
Maximum Likelihood ◽  
Survey Data ◽  
Sample Survey ◽  
Likelihood Method ◽  
Sample Surveys ◽  
Estimating Functions ◽  
Limit Theory ◽  
Normal Probability ◽  
Probability Structure ◽  
Sample Survey Data

This paper applies the theory of the quasi-likelihood method to model-based inference for sample surveys. Currently, much of the theory related to sample surveys is based on the theory of maximum likelihood. The maximum likelihood approach is available only when the full probability structure of the survey data is known. However, this knowledge is rarely available in practice. Based on central limit theory, statisticians are often willing to accept the assumption that data have, say, a normal probability structure. However, such an assumption may not be reasonable in many situations in which sample surveys are used. We establish a framework for sample surveys which is less dependent on the exact underlying probability structure using the quasi-likelihood method.

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