跳至主要内容

Some Properties of a Recursive Procedure for High Dimensional Parameter Estimation in Linear Model with Regularization

Read full paper at:
http://www.scirp.org/journal/PaperInformation.aspx?PaperID=52853#.VKs7s8nQrzE

Author(s)  
Theoretical results related to properties of a regularized recursive algorithm for estimation of a high dimensional vector of parameters are presented and proved. The recursive character of the procedure is proposed to overcome the difficulties with high dimension of the observation vector in computation of a statistical regularized estimator. As to deal with high dimension of the vector of unknown parameters, the regularization is introduced by specifying a priori non-negative covariance structure for the vector of estimated parameters. Numerical example with Monte-Carlo simulation for a low-dimensional system as well as the state/parameter estimation in a very high dimensional oceanic model is presented to demonstrate the efficiency of the proposed approach.
Cite this paper
Hoang, H. and Baraille, R. (2014) Some Properties of a Recursive Procedure for High Dimensional Parameter Estimation in Linear Model with Regularization. Open Journal of Statistics, 4, 921-932. doi: 10.4236/ojs.2014.411087. 
 

[1] Hoang, H.S. and Baraille, R. (2013) A Regularized Estimator for Linear Regression Model with Possibly Singular Covariance. IEEE Transactions on Automatic Control, 58, 236-241.
http://dx.doi.org/10.1109/TAC.2012.2203552
[2] Daley, R. (1991) Atmospheric Data Analysis. Cambridge University Press, New York.
[3] Albert, A. (1972) Regression and the Moore-Penrose Pseudo-Inverse. Academy Press, New York.
[4] Hoang, H.S. and Baraille, R. (2014) A Low Cost Filter Design for State and Parameter Estimation in Very High Dimensional Systems. Proceedings of the 19th IFAC Congress, Cape Town, 24-29 August 2014, 3156-3161.
[5] Hoang, H.S. and Baraille, R. (2011) Approximate Approach to Linear Filtering Problem with Correlated Noise. Engineering and Technology, 5, 11-23.
[6] Golub, G.H. and van Loan, C.F. (1996) Matrix Computations. 3rd Edition, Johns Hopkins University Press, Baltimore.
[7] Hoang, H.S., Baraille, R. and Talagrand, O. (2001) On the Design of a Stable Adaptive Filter for High Dimensional Systems. Automatica, 37, 341-359.
http://dx.doi.org/10.1016/S0005-1098(00)00175-8
[8] Hoang, H.S. and Baraille, R. (2011) Prediction Error Sampling Procedure Based on Dominant Schur Decomposition. Application to State Estimation in High Dimensional Oceanic Model. Applied Mathematics and Computation, 218, 3689-3709.
http://dx.doi.org/10.1016/j.amc.2011.09.012
[9] Kalman, R.E. (1960) A New Approach to Linear Filtering and Prediction Problems. Journal of Basic Engineering, 82, 35-45.
http://dx.doi.org/10.1115/1.3662552
[10] Cooper, M. and Haines, K. (1996) Altimetric Assimilation with Water Property Conservation. Journal of Geophysical Research, 101, 1059-1077.
http://dx.doi.org/10.1029/95JC02902
[11] Greenslade, D.J.M. and Young, I.R. (2005) The Impact of Altimeter Sampling Patterns on Estimates of Background Errors in a Global Wave Model. Journal of Atmospheric and Oceanic Technology, 1895-1917.
[12] Spall. J.C. (2000) Adaptive Stochastic Approximation by the Simultaneous Perturbation Method. IEEE Transactions on Automatic Control, 45, 1839-1853.
http://dx.doi.org/10.1109/TAC.2000.880982                 eww150105lx
标签：

评论

发表评论

此博客中的热门博文

A Comparison of Methods Used to Determine the Oleic/Linoleic Acid Ratio in Cultivated Peanut (Arachis hypogaea L.)

Cultivated peanut ( Arachis hypogaea L.) is an important oil and food crop. It is also a cheap source of protein, a good source of essential vitamins and minerals, and a component of many food products. The fatty acid composition of peanuts has become increasingly important with the realization that oleic acid content significantly affects the development of rancidity. And oil content of peanuts significantly affects flavor and shelf-life. Early generation screening of breeding lines for high oleic acid content greatly increases the efficiency of developing new peanut varieties. The objective of this study was to compare the accuracy of methods used to classify individual peanut seed as high oleic or not high oleic. Three hundred and seventy-four (374) seeds, spanning twenty-three (23) genotypes varying in oil composition (i.e. high oleic (H) or normal/not high oleic (NH) inclusive of all four peanut market-types (runner, Spanish, Valencia and Virginia), were individually tested ...
发表评论
阅读全文

Location Optimization of a Coal Power Plant to Balance Costs against Plant’s Emission Exposure

Fuel and its delivery cost comprise the biggest expense in coal power plant operations. Delivery of electricity from generation to consumers requires investment in power lines and transmission grids. Placing a coal power plant or multiple power plants near dense population centers can lower transmission costs. If a coalmine is nearby, transportation costs can also be reduced. However, emissions from coal plants play a key role in worsening health crises in many countries. And coal upon combustion produces CO 2 , SO 2 , NO x , CO, Metallic and Particle Matter (PM10 & PM2.5). The presence of these chemical compounds in the atmosphere in close vicinity to humans, livestock, and agriculture carries detrimental health consequences. The goal of the research was to develop a methodology to minimize the public’s exposure to harmful emissions from coal power plants while maintaining minimal operational costs related to electric distribution losses and coal logistics. The objective was...
发表评论
阅读全文

Evaluation of the Safety and Efficacy of Continuous Use of a Home-Use High-Frequency Facial Treatment Appliance

At present, many home-use beauty devices are available in the market. In particular, many products developed for facial treatment use light, e.g., a flash lamp or a light-emitting diode (LED). In this study, the safety of 4 weeks’ continuous use of NEWA TM , a high-frequency facial treatment appliance, every alternate day at home was verified, and its efficacy was evaluated in Japanese individuals with healthy skin aged 30 years or older who complained of sagging of the facial skin.  Transepidermal water loss (TEWL), melanin levels, erythema levels, sebum secretion levels, skin color changes and wrinkle improvement in the facial skin were measured before the appliance began to be used (study baseline), at 2 and 4 weeks after it had begun to be used, and at 2 weeks after completion of the 4-week treatment period (6 weeks from the study baseline). In addition, data obtained by subjective evaluation by the subjects themselves on a visual analog scale (VAS) were also analyzed. Fur...
发表评论
阅读全文