• Title/Summary/Keyword: covariance matrix

Search Result 418, Processing Time 0.079 seconds

A Covariance Matrix Estimation Method for Position Uncertainty of the Wheeled Mobile Robot

  • Doh, Nakju Lett;Chung, Wan-Kyun;Youm, Young-Il
    • 제어로봇시스템학회:학술대회논문집
    • /
    • 2003.10a
    • /
    • pp.1933-1938
    • /
    • 2003
  • A covariance matrix is a tool that expresses odometry uncertainty of the wheeled mobile robot. The covariance matrix is a key factor in various localization algorithms such as Kalman filter, topological matching and so on. However it is not easy to acquire an accurate covariance matrix because we do not know the real states of the robot. Up to the authors knowledge, there seems to be no established result on the covariance matrix estimation for the odometry. In this paper, we propose a new method which can estimate the covariance matrix from empirical data. It is based on the PC-method and shows a good estimation ability. The experimental results validate the performance of the proposed method.

  • PDF

Poisson linear mixed models with ARMA random effects covariance matrix

  • Choi, Jiin;Lee, Keunbaik
    • Journal of the Korean Data and Information Science Society
    • /
    • v.28 no.4
    • /
    • pp.927-936
    • /
    • 2017
  • To analyze longitudinal count data, Poisson linear mixed models are commonly used. In the models the random effects covariance matrix explains both within-subject variation and serial correlation of repeated count outcomes. When the random effects covariance matrix is assumed to be misspecified, the estimates of covariates effects can be biased. Therefore, we propose reasonable and flexible structures of the covariance matrix using autoregressive and moving average Cholesky decomposition (ARMACD). The ARMACD factors the covariance matrix into generalized autoregressive parameters (GARPs), generalized moving average parameters (GMAPs) and innovation variances (IVs). Positive IVs guarantee the positive-definiteness of the covariance matrix. In this paper, we use the ARMACD to model the random effects covariance matrix in Poisson loglinear mixed models. We analyze epileptic seizure data using our proposed model.

Bayesian Modeling of Random Effects Covariance Matrix for Generalized Linear Mixed Models

  • Lee, Keunbaik
    • Communications for Statistical Applications and Methods
    • /
    • v.20 no.3
    • /
    • pp.235-240
    • /
    • 2013
  • Generalized linear mixed models(GLMMs) are frequently used for the analysis of longitudinal categorical data when the subject-specific effects is of interest. In GLMMs, the structure of the random effects covariance matrix is important for the estimation of fixed effects and to explain subject and time variations. The estimation of the matrix is not simple because of the high dimension and the positive definiteness; subsequently, we practically use the simple structure of the covariance matrix such as AR(1). However, this strong assumption can result in biased estimates of the fixed effects. In this paper, we introduce Bayesian modeling approaches for the random effects covariance matrix using a modified Cholesky decomposition. The modified Cholesky decomposition approach has been used to explain a heterogenous random effects covariance matrix and the subsequent estimated covariance matrix will be positive definite. We analyze metabolic syndrome data from a Korean Genomic Epidemiology Study using these methods.

Negative binomial loglinear mixed models with general random effects covariance matrix

  • Sung, Youkyung;Lee, Keunbaik
    • Communications for Statistical Applications and Methods
    • /
    • v.25 no.1
    • /
    • pp.61-70
    • /
    • 2018
  • Modeling of the random effects covariance matrix in generalized linear mixed models (GLMMs) is an issue in analysis of longitudinal categorical data because the covariance matrix can be high-dimensional and its estimate must satisfy positive-definiteness. To satisfy these constraints, we consider the autoregressive and moving average Cholesky decomposition (ARMACD) to model the covariance matrix. The ARMACD creates a more flexible decomposition of the covariance matrix that provides generalized autoregressive parameters, generalized moving average parameters, and innovation variances. In this paper, we analyze longitudinal count data with overdispersion using GLMMs. We propose negative binomial loglinear mixed models to analyze longitudinal count data and we also present modeling of the random effects covariance matrix using the ARMACD. Epilepsy data are analyzed using our proposed model.

Bayesian modeling of random effects precision/covariance matrix in cumulative logit random effects models

  • Kim, Jiyeong;Sohn, Insuk;Lee, Keunbaik
    • Communications for Statistical Applications and Methods
    • /
    • v.24 no.1
    • /
    • pp.81-96
    • /
    • 2017
  • Cumulative logit random effects models are typically used to analyze longitudinal ordinal data. The random effects covariance matrix is used in the models to demonstrate both subject-specific and time variations. The covariance matrix may also be homogeneous; however, the structure of the covariance matrix is assumed to be homoscedastic and restricted because the matrix is high-dimensional and should be positive definite. To satisfy these restrictions two Cholesky decomposition methods were proposed in linear (mixed) models for the random effects precision matrix and the random effects covariance matrix, respectively: modified Cholesky and moving average Cholesky decompositions. In this paper, we use these two methods to model the random effects precision matrix and the random effects covariance matrix in cumulative logit random effects models for longitudinal ordinal data. The methods are illustrated by a lung cancer data set.

A Comparative Study of Covariance Matrix Estimators in High-Dimensional Data (고차원 데이터에서 공분산행렬의 추정에 대한 비교연구)

  • Lee, DongHyuk;Lee, Jae Won
    • The Korean Journal of Applied Statistics
    • /
    • v.26 no.5
    • /
    • pp.747-758
    • /
    • 2013
  • The covariance matrix is important in multivariate statistical analysis and a sample covariance matrix is used as an estimator of the covariance matrix. High dimensional data has a larger dimension than the sample size; therefore, the sample covariance matrix may not be suitable since it is known to perform poorly and event not invertible. A number of covariance matrix estimators have been recently proposed with three different approaches of shrinkage, thresholding, and modified Cholesky decomposition. We compare the performance of these newly proposed estimators in various situations.

INFLUENCE ANALYSIS OF CHOLESKY DECOMPOSITION

  • Kim, Myung-Geun
    • Journal of applied mathematics & informatics
    • /
    • v.28 no.3_4
    • /
    • pp.913-921
    • /
    • 2010
  • The derivative influence measure is adapted to the Cholesky decomposition of a covariance matrix. Formulas for the derivative influence of observations on the Cholesky root and the inverse Cholesky root of a sample covariance matrix are derived. It is easy to implement this influence diagnostic method for practical use. A numerical example is given for illustration.

Multivariate EWMA control charts for monitoring the variance-covariance matrix

  • Jeong, Jeong-Im;Cho, Gyo-Young
    • Journal of the Korean Data and Information Science Society
    • /
    • v.23 no.4
    • /
    • pp.807-814
    • /
    • 2012
  • We know that the exponentially weighted moving average (EWMA) control charts are sensitive to detecting relatively small shifts. Multivariate EWMA control charts are considered for monitoring of variance-covariance matrix when the distribution of process variables is multivariate normal. The performances of the proposed EWMA control charts are evaluated in term of average run length (ARL). The performance is investigated in three types of shifts in the variance-covariance matrix, that is, the variances, covariances, and variances and covariances are changed respectively. Numerical results show that all multivariate EWMA control charts considered in this paper are effective in detecting several kinds of shifts in the variance-covariance matrix.

Multivariate control charts based on regression-adjusted variables for covariance matrix

  • Kwon, Bumjun;Cho, Gyo-Young
    • Journal of the Korean Data and Information Science Society
    • /
    • v.28 no.4
    • /
    • pp.937-945
    • /
    • 2017
  • The purpose of using a control chart is to detect any change that occurs in the process. When control charts are used to monitor processes, we want to identify this changes as quickly as possible. Many problems in quality control involve a vector of observations of several characteristics rather than a single characteristic. Multivariate CUSUM or EWMA charts have been developed to address the problem of monitoring covariance matrix or the joint monitoring of mean vector and covariance matrix. However, control charts tend to work poorly when we use the highly correlatted variables. In order to overcome it, Hawkins (1991) proposed the use of regression adjustment variables. In this paper, to monitor covariance matrix, we investigate the performance of MEWMA-type control charts with and without the use of regression adjusted variables.

Covariance Matrix Synthesis Using Maximum Ratio Combining in Coherent MIMO Radar with Frequency Diversity

  • Jeon, Hyeonmu;Chung, Yongseek;Chung, Wonzoo;Kim, Jongmann;Yang, Hoongee
    • Journal of Electrical Engineering and Technology
    • /
    • v.13 no.1
    • /
    • pp.445-450
    • /
    • 2018
  • Reliable detection and parameter estimation of a radar cross section(RCS) fluctuating target have been known as a difficult task. To reduce the effect of RCS fluctuation, various diversity techniques have been considered. This paper presents a new method for synthesizing a covariance matrix applicable to a coherent multi-input multi-output(MIMO) radar with frequency diversity. It is achieved by efficiently combining covariance matrices corresponding to different carrier frequencies such that the signal-to-noise ratio(SNR) in the combined covariance matrix is maximized. The value of a synthesized covariance matrix is assessed by examining the phase curves of its entries and the improvement on direction of arrival(DOA) estimation.