LARGE SYSTEM OF SEEMINGLY UNRELATED REGRESSIONS: A PENALIZED QUASI-MAXIMUM LIKELIHOOD ESTIMATION PERSPECTIVE

2019 ◽  
Vol 36 (3) ◽  
pp. 526-558
Author(s):  
Qingliang Fan ◽  
Xiao Han ◽  
Guangming Pan ◽  
Bibo Jiang
Keyword(s):  
Maximum Likelihood ◽  
Sample Size ◽  
Covariance Matrix ◽  
Large System ◽  
Seemingly Unrelated Regression ◽  
Frobenius Norm ◽  
Error Covariance Matrix ◽  
Error Covariance ◽  
Model Selection Consistency ◽  
Quasi Maximum Likelihood

In this article, using a shrinkage estimator, we propose a penalized quasi-maximum likelihood estimator (PQMLE) to estimate a large system of equations in seemingly unrelated regression models, where the number of equations is large relative to the sample size. We develop the asymptotic properties of the PQMLE for both the error covariance matrix and model coefficients. In particular, we derive the asymptotic distribution of the coefficient estimator and the convergence rate of the estimated covariance matrix in terms of the Frobenius norm. The model selection consistency of the covariance matrix estimator is also established. Simulation results show that when the number of equations is large relative to the sample size and the error covariance matrix is sparse, the PQMLE outperforms other contemporary estimators.

scholarly journals An Extension of the Ensemble Kalman Filter for Estimating the Observation Error Covariance Matrix Based on the Variational Bayes’s Method

2016 ◽  
Vol 145 (1) ◽  
pp. 199-213 ◽  
Author(s):  
Akio Nakabayashi ◽  
Genta Ueno
Keyword(s):  
Kalman Filter ◽  
Maximum Likelihood ◽  
Covariance Matrix ◽  
Ensemble Kalman Filter ◽  
Numerical Experiments ◽  
Observation Error ◽  
Error Covariance Matrix ◽  
Error Covariance ◽  
Long Run ◽  
The Stability

Abstract This paper presents an extension of the ensemble Kalman filter (EnKF) that can simultaneously estimate the state vector and the observation error covariance matrix by using the variational Bayes’s (VB) method. In numerical experiments, this capability is examined for a time-variant observation error covariance matrix, and it is noteworthy that this method works well even when the true observation error covariance matrix is nondiagonal. In addition, two complementary studies are presented. First, the stability of a long-run assimilation is demonstrated when there are unmodeled disturbances. Second, a maximum-likelihood (ML) method is derived and demonstrated for optimizing the hyperparameters used in this method.

Enhancing the impact of IASI observations through an updated observation-error covariance matrix

2016 ◽  
Vol 142 (697) ◽  
pp. 1767-1780 ◽  
Author(s):  
Niels Bormann ◽  
Massimo Bonavita ◽  
Rossana Dragani ◽  
Reima Eresmaa ◽  
Marco Matricardi ◽  
...  
Keyword(s):  
Covariance Matrix ◽  
Observation Error ◽  
Error Covariance Matrix ◽  
Error Covariance ◽  
The Impact

Impact of AMSU-A Radiances in a Column Ensemble Kalman Filter

2018 ◽  
Vol 146 (12) ◽  
pp. 3949-3976 ◽  
Author(s):  
Herschel L. Mitchell ◽  
P. L. Houtekamer ◽  
Sylvain Heilliette
Keyword(s):  
Covariance Matrix ◽  
Background Error ◽  
Error Covariance Matrix ◽  
Background Error Covariance ◽  
Error Covariance ◽  
Microwave Sounding Unit ◽  
The Matrix ◽  
Microwave Sounding ◽  
Background Temperature ◽  
The Difference

Abstract A column EnKF, based on the Canadian global EnKF and using the RTTOV radiative transfer (RT) model, is employed to investigate issues relating to the EnKF assimilation of Advanced Microwave Sounding Unit-A (AMSU-A) radiance measurements. Experiments are performed with large and small ensembles, with and without localization. Three different descriptions of background temperature error are considered: 1) using analytical vertical modes and hypothetical spectra, 2) using the vertical modes and spectrum of a covariance matrix obtained from the global EnKF after 2 weeks of cycling, and 3) using the vertical modes and spectrum of the static background error covariance matrix employed to initiate a global data assimilation cycle. It is found that the EnKF performs well in some of the experiments with background error description 1, and yields modest error reductions with background error description 3. However, the EnKF is virtually unable to reduce the background error (even when using a large ensemble) with background error description 2. To analyze these results, the different background error descriptions are viewed through the prism of the RT model by comparing the trace of the matrix , where is the RT model and is the background error covariance matrix. Indeed, this comparison is found to explain the difference in the results obtained, which relates to the degree to which deep modes are, or are not, present in the different background error covariances. The results suggest that, after 2 weeks of cycling, the global EnKF has virtually eliminated all background error structures that can be “seen” by the AMSU-A radiances.

RECURSIVE UPDATING OF ERROR COVARIANCE MATRIX IN SUBSPACE METHODS

2006 ◽  
Vol 39 (1) ◽  
pp. 285-290 ◽  
Author(s):  
Yoshinori Takei ◽  
Hidehito Nanto ◽  
Shunshoku Kanae ◽  
Zi-Jiang Yang ◽  
Kiyoshi Wada
Keyword(s):  
Covariance Matrix ◽  
Subspace Methods ◽  
Error Covariance Matrix ◽  
Error Covariance ◽  
Recursive Updating

Intelligent Error Covariance Matrix Resetting for Maneuver Target Tracking

2008 ◽  
Vol 8 (12) ◽  
pp. 2279-2285 ◽  
Author(s):  
M.H. Bahari ◽  
A. Karsaz ◽  
M.B. Naghibi-S
Keyword(s):  
Target Tracking ◽  
Covariance Matrix ◽  
Error Covariance Matrix ◽  
Error Covariance

scholarly journals Best linear unbiased estimation for varying probability with and without replacement sampling

2019 ◽  
Vol 7 (1) ◽  
pp. 78-91
Author(s):  
Stephen Haslett
Keyword(s):  
Parameter Estimation ◽  
Covariance Matrix ◽  
Linear Models ◽  
Unbiased Estimation ◽  
Error Covariance Matrix ◽  
Best Linear Unbiased Estimation ◽  
Error Covariance ◽  
Inclusion Probabilities ◽  
Best Linear Unbiased ◽  
Linear Unbiased Estimation

Abstract When sample survey data with complex design (stratification, clustering, unequal selection or inclusion probabilities, and weighting) are used for linear models, estimation of model parameters and their covariance matrices becomes complicated. Standard fitting techniques for sample surveys either model conditional on survey design variables, or use only design weights based on inclusion probabilities essentially assuming zero error covariance between all pairs of population elements. Design properties that link two units are not used. However, if population error structure is correlated, an unbiased estimate of the linear model error covariance matrix for the sample is needed for efficient parameter estimation. By making simultaneous use of sampling structure and design-unbiased estimates of the population error covariance matrix, the paper develops best linear unbiased estimation (BLUE) type extensions to standard design-based and joint design and model based estimation methods for linear models. The analysis covers both with and without replacement sample designs. It recognises that estimation for with replacement designs requires generalized inverses when any unit is selected more than once. This and the use of Hadamard products to link sampling and population error covariance matrix properties are central topics of the paper. Model-based linear model parameter estimation is also discussed.

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