ROBUST ESTIMATION OF VARIANCE COMPONENTS MODEL

１ＩＮＴＲＯＤＵＣＴＩＯＮＴｈｅｌｅａｓｔｓｑｕａｒｅｓｍｅｔｈｏｄｉｓａｖｅｒｙｐｏｐｕｌａｒｅｓｔｉｍａｔｉｏｎｔｅｃｈｎｉｑｕｅｉｎｔｈｅｌｉｎｅａｒｒｅｇｒｅｓｉｏｎ（ａｄｊｕｓｔｍｅｎｔ）ｍｏｄｅｌ．Ｂｕｔｉｎｓｐｉｔｅｏｆｉｔｓｍａｔｈ...

MAXIMUM ORTHOGONAL COMPLEMENT LIKELIHOOD ESTIMATION FOR VARIANCE COMPONENTS

ＭＡＸＩＭＵＭＯＲＴＨＯＧＯＮＡＬＣＯＭＰＬＥＭＥＮＴＬＩＫＥＬＩＨＯＯＤＥＳＴＩＭＡＴＩＯＮＦＯＲＶＡＲＩＡＮＣＥＣＯＭＰＯＮＥＮＴＳＱｉｎＨｕｉ（ＤｅｐａｒｔｍｅｎｔｏｆＡｒｃｈｉｔｅｃｔｕｒａｌＥｎｇｉｎｅｅｒｉｎｇ，ＷｕｙｉＵｎｉｖｅｒｓｉｔ...

Robust Variance Components Estimation in the PERG Mixed Distributions of Empirical Variances—PEROBVC Method

A mixed distribution of empirical variances, composed of two distributions the basic and contaminating ones, and referred to as PERG mixed distribution of empirical variances, is considered. In the paper a robust inverse problem solution is given, namely a (new) robust method for estimation of variances of both distributions—PEROBVC Method, as well as the estimates for the numbers of observations for both distributions and, in this way also the estimate of contamination degree.

Single channel signal component separation using Bayesian estimation

A Bayesian estimation method to separate multicomponent signals with single channel observation is presented in this paper. By using the basis function projection, the component separation becomes a problem of limited parameter estimation. Then, a Bayesian model for estimating parameters is set up. The reversible jump MCMC （Monte Carlo Markov Chain） algorithmis adopted to perform the Bayesian computation. The method can jointly estimate the parameters of each component and the component number. Simulation results demonstrate that the method has low SNR threshold and better performance.

Nonlinear total least-squares variance component estimation for GM(1,1)model

The solution of the grey model(GM(1,1)model)generally involves equal-precision observations,and the(co)variance matrix is established from the prior information.However,the data are generally available with unequal-precision measurements in reality.To deal with the errors of all observations for GM(1,1)model with errors-in-variables(EIV)structure,we exploit the total least-squares(TLS)algorithm to estimate the parameters of GM(1,1)model in this paper.Ignoring that the effect of the improper prior stochastic model and the homologous observations may degrade the accuracy of parameter estimation,we further present a nonlinear total least-squares variance component estimation approach for GM(1,1)model,which resorts to the minimum norm quadratic unbiased estimation(MINQUE).The practical and simulative experiments indicate that the presented approach has significant merits in improving the predictive accuracy in comparison with control methods.

Multivariate Statistical Process Monitoring of an Industrial Polypropylene Catalyzer Reactor with Component Analysis and Kernel Density Estimation

Data-driven tools,such as principal component analysis(PCA)and independent component analysis (ICA)have been applied to different benchmarks as process monitoring methods.The difference between the two methods is that the components of PCA are still dependent while ICA has no orthogonality constraint and its latent variables are independent.Process monitoring with PCA often supposes that process data or principal components is Gaussian distribution.However,this kind of constraint cannot be satisfied by several practical processes.To ex- tend the use of PCA,a nonparametric method is added to PCA to overcome the difficulty,and kernel density esti- mation(KDE)is rather a good choice.Though ICA is based on non-Gaussian distribution information,KDE can help in the close monitoring of the data.Methods,such as PCA,ICA,PCA with KDE(KPCA),and ICA with KDE (KICA),are demonstrated and compared by applying them to a practical industrial Spheripol craft polypropylene catalyzer reactor instead of a laboratory emulator.

UNIVERSAL FORMULAE OF ROBUST ESTIMATES OF PARAMETER VECTOR AND VARIANCE COMPONENTS

ＵＮＩＶＥＲＳＡＬＦＯＲＭＵＬＡＥＯＦＲＯＢＵＳＴＥＳＴＩＭＡＴＥＳＯＦＰＡＲＡＭＥＴＥＲＶＥＣＴＯＲＡＮＤＶＡＲＩＡＮＣＥＣＯＭＰＯＮＥＮＴＳ①ＷａｎｇＺｈｉｚｈｏｎｇＩｎｓｔｉｔｕｔｅｏｆＳｕｒｖｅｙｉｎｇＥｎｇｉｎｅｒｉｎｇａｎｄＬａｎｄＩｎｆ...

Estimation on principal component of multi-collinearity Gauss-Markov model based on minimum description length

Gauss-Markov model is frequently used in data analysis; the analysis and estimation of its parameters is always a hot issue. Based on the information theory and from the viewpoint of optimal information on description—minimum description length, this paper discusses a case: where there is multi-collinearity in the coefficient matrix, principal component estimation is used to estimate and select the original parameters, so as to reduce its multi-collinearity and improve its credibility. From the viewpoint of minimum description length, this paper discusses the approach of selecting principal components and uses this approach to solve a practical problem.

Comparison of REML and MINQUE for Estimated Variance Components and Predicted Random Effects

Linear mixed model (LMM) approaches have been widely applied in many areas of research data analysis because they offer great flexibility for different data structures and linear model systems. In this study, emphasis is placed on comparing the properties of two LMM approaches: restricted maximum likelihood (REML) and minimum norm quadratic unbiased estimation (MINQUE) with and without resampling techniques being included. Bias, testing power, Type I error, and computing time were compared between REML and MINQUE approaches with and without Jackknife technique based on 500 simulated data sets. Results showed that MINQUE and REML methods performed equally regarding bias, Type I error, and power. Jackknife-based MINQUE and REML greatly improved power compared to non-Jackknife based linear mixed model approaches. Results also showed that MINQUE is more time-saving compared to REML, especially with the use of resampling techniques and large data set analysis. Results from the actual cotton data analysis were in agreement with our simulated results. Therefore, Jackknife-based MINQUE approaches could be recommended to achieve desirable power with reduced time for a large data analysis and model simulations.

The Pre－test Principal Components Estimator in the Two Seemingly Unrelated Regression System

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Instantaneous frequency estimation of multi-component Chirp signals in noisy environments

A classical time-varying signal,the multi-component Chirp signal has been widely used and the ability to estimate its instantaneous frequency(IF) is very useful. But in noisy environments,it is hard to estimate the IF of a multi-component Chirp signal accurately. Wigner distribution maxima(WDM) are usually utilized for this estimation. But in practice,estimation bias increases when some points deviate from the true IF in high noise environments. This paper presents a new method of multi-component Chirp signal IF estimation named Wigner Viterbi fit(WVF) ,based on Wigner-Ville distribution(WVD) and the Viterbi algorithm. First,we transform the WVD of the Chirp signal into digital image,and apply the Viterbi algorithm to separate the components and estimate their IF. At last,we establish a linear model to fit the estimation results. Theoretical analysis and simulation results prove that this new method has high precision and better performance than WDM in high noise environments,and better suppression of interference and the edge effect. Compared with WDM,WVF can reduce the mean square error(MSE) by 50% when the signal to noise ration(SNR) is in the range of -15dB to -11dB. WVF is an effective and promising IF estimation method.

Application of K-means and PCA approaches to estimation of gold grade in Khooni district(central Iran)

Grade estimation is an important phase of mining projects, and one that is considered a challenge due in part to the structural complexities in mineral ore deposits.To overcome this challenge, various techniques have been used in the past. This paper introduces an approach for estimating Au ore grades within a mining deposit using k-means and principal component analysis(PCA). The Khooni district was selected as the case study. This region is interesting geologically, in part because it is considered an important gold source. The study area is situated approximately 60km northeast of the Anarak city and 270km from Esfahan. Through PCA, we sought to understand the relationship between the elements of gold,arsenic, and antimony. Then, by clustering, the behavior of these elements was investigated. One of the most famous and efficient clustering methods is k-means, based on minimizing the total Euclidean distance from each class center. Using the combined results and characteristics of the cluster centers, the gold grade was determined with a correlation coefficient of 91%. An estimation equation for gold grade was derived based on four parameters: arsenic and antimony content, and length and width of the sampling points. The results demonstrate that this approach is faster and more accurate than existing methodologies for ore grade estimation.

Vibration Source Number Estimation of A Shell Structure

It has been challenging to correctly separate the mixed signals into source components when the source number is not known a priori.To reveal the complexity of the measured vibration signals,and provide the priori information for the blind source separation,in this paper,we propose a novel source number estimation based on independent component analysis(ICA)and clustering evaluation analysis,and then carry out experiment studies with typical mechanical vibration signals from a shell structure.The results demonstrate that the proposed ICA based source number estimation performs stably and robustly for the shell structure.

A novel chemical composition estimation model for cement raw material blending process

Raw material blending process is an essential part of the cement production process. The main purpose of the process is to guarantee a certain oxide composition for the raw meal at the outlet of the mill by regulating the four raw materials. But the chemical compositions of raw materials vary from time to time, resulting in difficulties to control the oxide compositions to a predefined value. Therefore, a novel algorithm to estimate the chemical compositions of the raw materials is developed. The paper mainly consists of two parts. In model construction part, a novel constrained least square model is proposed to overcome the deviation introduced by long-term drift of the material components, and the model parameters are estimated with an online strategy. And in validation part, the approach is implemented to two examples including datasets from simulation model and the actual industrial process. The final results show the effectiveness of the proposed method.

Head pose estimation method based on pose manifold and tensor decomposition

Pose manifold and tensor decomposition are used to represent the nonlinear changes of multi-view faces for pose estimation,which cannot be well handled by principal component analysis or multilinear analysis methods.A pose manifold generation method is introduced to describe the nonlinearity in pose subspace.And a nonlinear kernel based method is used to build a smooth mapping from the low dimensional pose subspace to the high dimensional face image space.Then the tensor decomposition is applied to the nonlinear mapping coefficients to build an accurate multi-pose face model for pose estimation.More importantly,this paper gives a proper distance measurement on the pose manifold space for the nonlinear mapping and pose estimation.Experiments on the identity unseen face images show that the proposed method increases pose estimation rates by 13.8% and 10.9% against principal component analysis and multilinear analysis based methods respectively.Thus,the proposed method can be used to estimate a wide range of head poses.

A General Theory of Estimation of Variance-Covariance Components

Starting from the more general functional model and being based on their work of K. R. Koch (1986) and Ou Ziqiang (1989), marginal likelihood function of variance components is derived and is identical to the orthogonal complement likelihood function in this paper. Minimum norm quadratic unibiased estimator (MINQUE) is developed, which expands the formula by C. R. Rao (1973). It is proved that Helmert type estimation, MINQUE, BQUE and maximum likelihood estimation are identical to one another. Besides, a universal formula for accuracy evalution is presented. Through these work, the paper establishes a universal theory of variance covariance components.

A novel image fusion algorithm based on 2D scale-mixing complex wavelet transform and Bayesian MAP estimation for multimodal medical images

In this paper,we propose a new image fusion algorithm based on two-dimensional Scale-Mixing Complex Wavelet Transform(2D-SMCWT).The fusion of the detail 2D-SMCWT cofficients is performed via a Bayesian Maximum a Posteriori(MAP)approach by considering a trivariate statistical model for the local neighboring of 2D-SMCWT coefficients.For the approx imation coefficients,a new fusion rule based on the Principal Component Analysis(PCA)is applied.We conduct several experiments using three different groups of multimodal medical images to evaluate the performance of the proposed method.The obt ained results prove the superiority of the proposed method over the state of the art fusion methods in terms of visual quality and several commonly used metrics.Robustness of the proposed method is further tested against different types of noise.The plots of fusion met rics establish the accuracy of the proposed fusion method.

An algorithm for frequency estimation of signals composed of multiple single-tones

The high-accuracy, wide-range frequency estimation algorithm for multi-component signals presented in this paper, is based on a numerical differentiation and central Lagrange interpolation. With the sample sequences, which need at most 7 points and are sampled at a sample frequency of 25600 Hz, and computation sequences, using employed a formulation proposed in this paper, the frequencies of each component of the signal are all estimated at an accuracy of 0.001% over 1 Hz to 800 kHz with the amplitudes of each component of the signal varying from 1 V to 200 V and the phase angle of each component of the signal varying from 0° to 360°. The proposed algorithm needs at most a half cycle for the frequencies of each component of the signal under noisy or non-noisy conditions. A testing example is given to illustrate the proposed algorithm in Matlab environment.

ESTIMATION OF ROCK-AGGREGATE VOLUME BASED ON PCA AND LM-OPTIMIZED NEURAL NETWORK

In granule processing industries,acquisition of particle size and shape parameters is a common procedure,and volumetric measurement is of great importance in dealing with particle sizing and gradation. To eradicate the major drawbacks with manual gauge,this paper proposes an optical approach using Back Propagation (BP) neural network to estimate the particle volume based on the two-Dimensional (2D) image information. To achieve the better network efficiency and structure simplicity,Principal Component Analysis (PCA) is adopted to reduce the dimensions of network inputs. To overcome the shortcomings of generic BP network for being slow to converge and vulnerable to being trapped in local minimum,Levenberg-Marquardt (LM) algorithm is applied to achieve a higher speed and a lower error rate. The real particle data is utilized in training and testing the presented network. The experimental result suggests that the proposed neural network is capable of estimating aggregate volume with satisfactory precision and superior to the generic BP network in terms of performance capacity.