Consistency of the least squares estimator of an infinite-dimensional parameter

1992 ◽  
Vol 33 (4) ◽  
pp. 603-607
Author(s):  
A. Ya. Dorogovtsev
Keyword(s):  
Least Squares ◽  
Least Squares Estimator ◽  
Dimensional Parameter ◽  
Infinite Dimensional

Bias correction for the least squares estimator of Weibull shape parameter with complete and censored data

2006 ◽  
Vol 91 (8) ◽  
pp. 930-939 ◽  
Author(s):  
L.F. Zhang ◽  
M. Xie ◽  
L.C. Tang
Keyword(s):  
Least Squares ◽  
Censored Data ◽  
Bias Correction ◽  
Shape Parameter ◽  
Least Squares Estimator

A note on the distribution of the least squares estimator of a random walk with drift

1989 ◽  
Vol 29 (3) ◽  
pp. 225-230 ◽  
Author(s):  
Svend Hylleberg ◽  
Grayham E. Mizon
Keyword(s):  
Random Walk ◽  
Least Squares ◽  
Least Squares Estimator ◽  
Random Walk With Drift

hIPPYlib

2021 ◽  
Vol 47 (2) ◽  
pp. 1-34
Author(s):  
Umberto Villa ◽  
Noemi Petra ◽  
Omar Ghattas
Keyword(s):  
Inverse Problems ◽  
Large Scale ◽  
Low Rank ◽  
Scalable Algorithms ◽  
Low Rank Approximation ◽  
Dimensional Parameter ◽  
Infinite Dimensional ◽  
Bayesian Inverse Problems ◽  
Rank Approximation ◽  
Extensible Software

We present an extensible software framework, hIPPYlib, for solution of large-scale deterministic and Bayesian inverse problems governed by partial differential equations (PDEs) with (possibly) infinite-dimensional parameter fields (which are high-dimensional after discretization). hIPPYlib overcomes the prohibitively expensive nature of Bayesian inversion for this class of problems by implementing state-of-the-art scalable algorithms for PDE-based inverse problems that exploit the structure of the underlying operators, notably the Hessian of the log-posterior. The key property of the algorithms implemented in hIPPYlib is that the solution of the inverse problem is computed at a cost, measured in linearized forward PDE solves, that is independent of the parameter dimension. The mean of the posterior is approximated by the MAP point, which is found by minimizing the negative log-posterior with an inexact matrix-free Newton-CG method. The posterior covariance is approximated by the inverse of the Hessian of the negative log posterior evaluated at the MAP point. The construction of the posterior covariance is made tractable by invoking a low-rank approximation of the Hessian of the log-likelihood. Scalable tools for sample generation are also discussed. hIPPYlib makes all of these advanced algorithms easily accessible to domain scientists and provides an environment that expedites the development of new algorithms.

scholarly journals Consistency for the least squares estimator in nonparametric regression

1996 ◽  
Vol 24 (6) ◽  
pp. 2513-2523 ◽  
Author(s):  
Sara van de Geer ◽  
Marten Wegkamp
Keyword(s):  
Least Squares ◽  
Nonparametric Regression ◽  
Least Squares Estimator
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