Estimation for diffusion processes under misspecified models

1984 ◽  
Vol 21 (3) ◽  
pp. 511-520 ◽  
Author(s):  
Ian W. McKeague
Keyword(s):  
Asymptotic Behavior ◽  
Maximum Likelihood ◽  
Diffusion Processes ◽  
Parametric Model ◽  
Likelihood Estimator ◽  
Ergodic Diffusion Process ◽  
Misspecified Models ◽  
Drift Term ◽  
Noise Function ◽  
Ergodic Diffusion

The asymptotic behavior of the maximum likelihood estimator of a parameter in the drift term of a stationary ergodic diffusion process is studied under conditions in which the true drift function and true noise function do not coincide with those specified by the parametric model.

Estimation for diffusion processes under misspecified models

1984 ◽  
Vol 21 (03) ◽  
pp. 511-520 ◽  
Author(s):  
Ian W. McKeague
Keyword(s):  
Asymptotic Behavior ◽  
Maximum Likelihood ◽  
Diffusion Processes ◽  
Parametric Model ◽  
Likelihood Estimator ◽  
Ergodic Diffusion Process ◽  
Misspecified Models ◽  
Drift Term ◽  
Noise Function ◽  
Ergodic Diffusion

The asymptotic behavior of the maximum likelihood estimator of a parameter in the drift term of a stationary ergodic diffusion process is studied under conditions in which the true drift function and true noise function do not coincide with those specified by the parametric model.

Sequential Maximum Likelihood Estimation for the Parameter of the Linear Drift Term of the Rayleigh Diffusion Process

2015 ◽  
Vol 16 (1) ◽  
pp. 35-41
Author(s):  
Nenghui Kuang ◽  
Chunli Li ◽  
Huantian Xie
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Diffusion Process ◽  
Simulation Study ◽  
Likelihood Estimation ◽  
Likelihood Estimator ◽  
Linear Drift ◽  
Drift Term ◽  
Strongly Consistent ◽  
Drift Parameter

AbstractIn this paper, we investigate the properties of a sequential maximum likelihood estimator of the unknown linear drift parameter for the Rayleigh diffusion process. The estimator is shown to be closed, unbiased, normally distributed and strongly consistent. Finally a simulation study is presented to illustrate the efficiency of the estimator.

OPTIMAL INVARIANT INFERENCE WHEN THE NUMBER OF INSTRUMENTS IS LARGE

2009 ◽  
Vol 25 (3) ◽  
pp. 793-805 ◽  
Author(s):  
Laura Chioda ◽  
Michael Jansson
Keyword(s):  
Asymptotic Behavior ◽  
Maximum Likelihood ◽  
Sample Size ◽  
Maximum Likelihood Estimator ◽  
Instrumental Variables ◽  
Asymptotic Efficiency ◽  
Rotation Invariance ◽  
Limited Information ◽  
Likelihood Estimator ◽  
Rotation Invariant

This paper studies the asymptotic behavior of a Gaussian linear instrumental variables model in which the number of instruments diverges with the sample size. Asymptotic efficiency bounds are obtained for rotation invariant inference procedures and are shown to be attainable by procedures based on the limited information maximum likelihood estimator. The bounds are obtained by characterizing the limiting experiment associated with the model induced by the rotation invariance restriction.

scholarly journals ASYMPTOTIC INFERENCE FOR NEARLY UNSTABLE AR(p) PROCESSES

1999 ◽  
Vol 15 (2) ◽  
pp. 184-217 ◽  
Author(s):  
Tjacco van der Meer ◽  
Gyula Pap ◽  
Martien C.A. van Zuijlen
Keyword(s):  
Asymptotic Behavior ◽  
Maximum Likelihood ◽  
Limit Distribution ◽  
Continuous Time ◽  
Convergence Result ◽  
Likelihood Estimator ◽  
Characteristic Roots ◽  
Least Squares Estimators ◽  
General Complex ◽  
Complex Valued

In this paper nearly unstable AR(p) processes (in other words, models with characteristic roots near the unit circle) are studied. Our main aim is to describe the asymptotic behavior of the least-squares estimators of the coefficients. A convergence result is presented for the general complex-valued case. The limit distribution is given by the help of some continuous time AR processes. We apply the results for real-valued nearly unstable AR(p) models. In this case the limit distribution can be identified with the maximum likelihood estimator of the coefficients of the corresponding continuous time AR processes.

scholarly journals Comparison of Risk Ratios of Shrinkage Estimators in High Dimensions

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 52
Author(s):  
Abdenour Hamdaoui ◽  
Waleed Almutiry ◽  
Mekki Terbeche ◽  
Abdelkader Benkhaled
Keyword(s):  
Asymptotic Behavior ◽  
Performance Evaluation ◽  
Maximum Likelihood ◽  
Parameter Space ◽  
Shrinkage Estimators ◽  
High Dimensions ◽  
Likelihood Estimator ◽  
Positive Part ◽  
Stein Estimator ◽  
Risk Ratios

In this paper, we analyze the risk ratios of several shrinkage estimators using a balanced loss function. The James–Stein estimator is one of a group of shrinkage estimators that has been proposed in the existing literature. For these estimators, sufficient criteria for minimaxity have been established, and the James–Stein estimator’s minimaxity has been derived. We demonstrate that the James–Stein estimator’s minimaxity is still valid even when the parameter space has infinite dimension. It is shown that the positive-part version of the James–Stein estimator is substantially superior to the James–Stein estimator, and we address the asymptotic behavior of their risk ratios to the maximum likelihood estimator (MLE) when the dimensions of the parameter space are infinite. Finally, a simulation study is carried out to verify the performance evaluation of the considered estimators.

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