• Communications for Statistical Applications and Methods
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• v.19 no.5
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• pp.721-729
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• 2012

Various methods control the influence of a covariate on a response variable. These methods are analysis of covariance(ANCOVA), RANK ANCOVA, ANOVA of (covariate-adjusted) residuals, and Kruskal-Wallis tests on residuals. Covariate-adjusted residuals are obtained from the overall regression line fit to the entire data set that ignore the treatment levels or factors. It is demonstrated that the methods on covariate-adjusted residuals are only appropriate when the regression lines are parallel and covariate means are equal for all treatments. In this paper, we proposed the new nonparametric method on the ANCOVA model, as applying joint placement in a one-way layout on residuals as described in Chung and Kim (2007). A Monte Carlo simulation study is adapted to compare the power of the proposed procedure with those of the previous procedure.

• The Korean Journal of Applied Statistics
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• v.33 no.3
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• pp.281-296
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• 2020

Repeated outcomes from the same subjects are referred to as longitudinal data. Analysis of the data requires different methods unlike cross-sectional data analysis. It is important to model the covariance matrix because the correlation between the repeated outcomes must be considered when estimating the effects of covariates on the mean response. However, the modeling of the covariance matrix is tricky because there are many parameters to be estimated, and the estimated covariance matrix should be positive definite. In this paper, we consider analysis of multivariate longitudinal data via two modeling methodologies for the covariance matrix for multivariate longitudinal data. Both methods describe serial correlations of multivariate longitudinal outcomes using a modified Cholesky decomposition. However, the two methods consider different decompositions to explain the correlation between simultaneous responses. The first method uses enhanced linear covariance models so that the covariance matrix satisfies a positive definiteness condition; in addition, and principal component analysis and maximization-minimization algorithm (MM algorithm) were used to estimate model parameters. The second method considers variance-correlation decomposition and hypersphere decomposition to model covariance matrix. Simulations are used to compare the performance of the two methodologies.

• Journal of Korean Society for Quality Management
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• v.29 no.1
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• pp.1-10
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• 2001

We consider the problem of detecting special variations in multivariate $T^2$-control chart when two or more multivariate outliers are present. Since a multivariate outlier may reflect slippage in mean, variance, or correlation, it can distort the sample mean vector and sample covariance matrix. Damaged sample mean vector and sample covariance matrix have difficulty in examining special variations clearly, An alternative to detection outliers or special variations is to use robust estimators of mean vector and covariance matrix that are less sensitive to extreme observations than are the standard estimators $\bar{x}$ and $\textbf{S}$. We applied popular minimum volume ellipsoid(MVE) and minimum covariance determinant(MCD) method to estimate mean vector and covariance matrix and compared its results with standard $T^2$-control chart using simulated multivariate data with outliers. We found that the modified $T^2$-control chart based on the above robust methods were more effective in detecting special variations clearly than the standard $T^2$-control chart.

• Communications for Statistical Applications and Methods
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• v.6 no.3
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• pp.929-938
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• 1999

We propose a criterion for testing homogeneity of diagonal covariance matrices of K multivariate normal populations. It is based on a factorization of usual likelihood ratio intended to propose and develop a criterion that makes use of properties of structures of the diagonal convariance matrices. The criterion then leads to a simple test as well as to an accurate asymptotic distribution of the test statistic via general result by Box (1949).

• Journal of Environmental Science International
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• v.22 no.1
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• pp.119-129
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• 2013

We compared equilibrium evaporation($E_{equili}$) eddy-covariance($E_{eddy}$) with soil moisture data($E_{SMseries}$) which were measured with a 2 hours sampling interval at three points for a humid forest hillslope from May 5th to May 31th in 2009. Accumulations of $E_{eddy}$, $E_{equili}$ for the study period were estimated as 2.52, 3.28 mm and those of $E_{SMseries}$ were ranged from 1.91 to 2.88 mm. It suggested that the eddy-covariance method considering the spatial heterogeneity of soil evaporation is useful to evaluate the soil evaporation. Method A, B and C were proposed using mean meterological data and daily moisture variation and the computations were compared to eddy-covariance method and equilibrium evaporation. The methods using soil moisture data can describe the variations of soil evaporation from eddy-covariance through simple moving average analysis. Method B showed a good matched with eddy-covariance method. This indicated that Dry Surface Layer (DSL) at 14:00 which was used for method B is important variable for the evaluation of soil evaporation. The total equilibrium evaporation was not significantly different to those of the others. However, equilibrium evaporation showed a problem in estimating soil evaporation because the temporal tendency of $E_{equili}$ was not related with the those of the other methods. The improved understanding of the soil evaporation presented in this study will contribute to the understandings of water cycles in a forest hillslope.

• Communications for Statistical Applications and Methods
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• v.14 no.2
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• pp.301-307
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• 2007

A effective teaching method on correlation coefficient for elementary level statistics course is discussed in this article. The well known inequalities, such as Theorem 368 of Hardy et al. (1952), are used for the interpretation of concept of covariance. An Excel example is provided for the illustration of concept of correlation coefficient.

• Communications for Statistical Applications and Methods
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• v.7 no.3
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• pp.959-966
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• 2000

A dimensionality assessment procedure DETECT uses the property of being near zero of conditional covariances as an indication of unidimensionality .This study provides the convergent properties to zero of conditional covariances when the dta is unidimensional, with which DETECT extends its theoretical grounds.

• Communications for Statistical Applications and Methods
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• v.7 no.1
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• pp.285-290
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• 2000

We noted a property of a stationary distribution on the matrix C, which is the covariance matrix of order statistics of standard normal distribution That is the sup norm of th powers of C is ee' divided by its dimension. The matrix C can be taken as a transition probability matrix in an acyclic Markov chain.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.7 no.3
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• pp.437-447
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• 2003

We propose the methods to design the finite impulse response (FIR) and the infinite impulse response (IIR) lattice filters using Schur algorithm through the spectral factorization of the covariance matrix by circulant matrix factorization (CMF). Circulant matrix factorization is also very powerful tool used fur spectral factorization of the covariance polynomial in matrix domain to obtain the minimum phase polynomial without the polynomial root finding problem. Schur algorithm is the method for a fast Cholesky factorization of Toeplitz matrix, which easily determines the lattice filter parameters. Examples for the case of the FIR Inter and for the case of the IIR filter are included, and performance of our method check by comparing of our method and another methods (polynomial root finding and cepstral deconvolution).

• Korean Journal of Clinical Laboratory Science
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• v.45 no.2
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• pp.60-65
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• 2013

Data from repeated measurements are accomplished through repeatedly processing the same subject under different conditions and different points of view. The power of testing enhances the choice of pertinent analysis methods that agrees with the characteristics of data concerned and the situation involved. Along with the clinical example, this paper compares the analysis of the variance on ex-post tests, gain score analysis, analysis by mixed design and analysis of covariance employable for repeating measure. Comparing the analysis of variance on ex post test, and gain score analysis on correlations, leads to the fact that the latter enhances the power of the test and diminishes the variance of error terms. The concluded probability, identified that the gain score analysis and the mixed design on interaction between "between subjects factor" and "within subjects factor", are identical. The analysis of covariance, demonstrated better power of the test and smaller error terms than the gain score analysis. Research on four analysis method found that the analysis of covariance is the most appropriate in clinical data than two repeated test with high correlation and ex ante affects ex post.