• Journal of Preventive Medicine and Public Health
• /
• v.31 no.4 s.63
• /
• pp.875-884
• /
• 1998

Missing observations are common in medical research and health survey research. Several statistical methods to handle the missing data problem have been proposed. The EM algorithm (Expectation-Maximization algorithm) is one of the ways of efficiently handling the missing data problem based on sufficient statistics. In this paper, we developed statistical models and methods for survey data with multivariate missing observations. Especially, we adopted the EM algorithm to handle the multivariate missing observations. We assume that the multivariate observations follow a multivariate normal distribution, where the mean vector and the covariance matrix are primarily of interest. We applied the proposed statistical method to analyze data from a health survey. The data set we used came from a physician survey on Resource-Based Relative Value Scale(RBRVS). In addition to the EM algorithm, we applied the complete case analysis, which uses only completely observed cases, and the available case analysis, which utilizes all available information. The residual and normal probability plots were evaluated to access the assumption of normality. We found that the residual sum of squares from the EM algorithm was smaller than those of the complete-case and the available-case analyses.

• Journal of the Korean Statistical Society
• /
• v.28 no.4
• /
• pp.479-488
• /
• 1999

Moore and Stubblebine(1981) suggested a chi-square test for multivariate normality based on cell counts calculated from the sample Mahalanobis distances. They derived the limiting distribution of the test statistic only when equiprobable cells are employed. Using conditional limit theorems, we derive the limiting distribution of the statistic as well as the asymptotic normality of the cell counts. These distributions are valid even when equiprobable cells are not employed. We finally apply this method to a real data set.

• Communications for Statistical Applications and Methods
• /
• v.18 no.3
• /
• pp.357-365
• /
• 2011

This paper investigates a penalized likelihood method for estimating the parameter of normal mixtures in multivariate settings with full covariance matrices. The proposed model estimates the number of components through the addition of a penalty term to the usual likelihood function and the construction of a penalized likelihood function. We prove the consistency of the estimator and present the simulation results on the multi-dimensional nor-mal mixtures up to the 8-dimension.

• 제어로봇시스템학회:학술대회논문집
• /
• 2001.10a
• /
• pp.116.3-116
• /
• 2001

A diagnosis methodology for thickness quality in hot finishing mill is proposed based on multivariate statistical analysis. The thickness of hot strip is a key quality factor that is measured by x-ray thickness gauge. Currently, the thickness quality is guaranteed by upper and lower limit of thickness deviation from target thickness. But if any over-limit is occurred, there is no in-line method to identify the causes. In this paper, many parameters are extracted from the thickness deviation signal such as mean deviation(top, middle, tail), rms deviation(top, middle, tail) and peak deviation(top, middle, tail) as time domain parameters ...

• Communications for Statistical Applications and Methods
• /
• v.12 no.2
• /
• pp.473-481
• /
• 2005

The testing problem for sphericity structure of the covariance matrix in a multivariate normal distribution is introduced when there is a sample with 2-step monotone missing data pattern. The maximum likelihood method is described to estimate the parameters on the basis of the sample. Using these estimates, the likelihood ratio criterion for testing sphericity is derived.

• Communications for Statistical Applications and Methods
• /
• v.3 no.2
• /
• pp.205-216
• /
• 1996

Consider the problem of estimating a multivariate normal mean with an unknown covarience matrix under a weighted sum of squared error losses. We first provide hierarchical Bayes estimators which shrink the usual (maximum liklihood, uniformly minimum variance unbiased) estimator towards a regression surface and then prove the admissibility of these estimators using Blyth's (1951) method.

• Communications for Statistical Applications and Methods
• /
• v.6 no.3
• /
• pp.755-760
• /
• 1999

In multivariate stratified sampling surveys it is general to use a few stratification variables which are highly correlated with the important variables at design stage. But there might be some secondary study variables which are not so highly correlated with those stratification variables. In that case it is not efficient to use the same type of estimator due to the secondary variables as the one base on the important variables. A post-stratified estimation is proposed to increase the efficiency of the estimator with existence of secondary variables. The proposed method is illustrated with a set of fishery household population survey data.

• Journal of the Korean Data and Information Science Society
• /
• v.17 no.3
• /
• pp.953-961
• /
• 2006

Let's say that we are given a k number of random variables following Poisson distribution that are individually dependent and which forms multivariate Poisson distribution. We particularly dealt with a method of creating random numbers that satisfies the covariance matrix, where the elements of covariance matrix are parameters forming a multivariate Poisson distribution. To create such random numbers, we propose a new algorithm based on the method reducing the number of parameter set and deal with its relationship to the Park et al.(1996) algorithm used in creating multivariate Bernoulli random numbers.

• Smart Structures and Systems
• /
• v.14 no.3
• /
• pp.377-395
• /
• 2014

Vibration-based fault detection and condition monitoring of rotating machinery, using statistical process control (SPC) combined with statistical pattern recognition methodology, has been widely investigated by many researchers. In particular, the discrete wavelet transform (DWT) is considered as a powerful tool for feature extraction in detecting fault on rotating machinery. Although DWT significantly reduces the dimensionality of the data, the number of retained wavelet features can still be significantly large. Then, the use of standard multivariate SPC techniques is not advised, because the sample covariance matrix is likely to be singular, so that the common multivariate statistics cannot be calculated. Even though many feature-based SPC methods have been introduced to tackle this deficiency, most methods require a parametric distributional assumption that restricts their feasibility to specific problems of process control, and thus limit their application. This study proposes a nonparametric multivariate control chart method, based on multiscale wavelet scalogram (MWS) features, that overcomes the limitation posed by the parametric assumption in existing SPC methods. The presented approach takes advantage of multi-resolution analysis using DWT, and obtains MWS features with significantly low dimensionality. We calculate Hotelling's $T^2$-type monitoring statistic using MWS, which has enough damage-discrimination ability. A bootstrap approach is used to determine the upper control limit of the monitoring statistic, without any distributional assumption. Numerical simulations demonstrate the performance of the proposed control charting method, under various damage-level scenarios for a bearing system.

• Communications for Statistical Applications and Methods
• /
• v.19 no.1
• /
• pp.107-115
• /
• 2012

Yoo and Cook (2007) developed an optimal sufficient dimension reduction methodology for the conditional mean in multivariate regression and it is known that their method is asymptotically optimal and its test statistic has a chi-squared distribution asymptotically under the null hypothesis. To check the effect of dimension used in estimation on regression coefficients and the explanatory power of the conditional mean model in multivariate regression, we applied their method to several simulated data sets with various dimensions. A small simulation study showed that it is quite helpful to search for an appropriate dimension for a given data set if we use the asymptotic test for the dimension as well as results from the estimation with several dimensions simultaneously.