• Communications for Statistical Applications and Methods
• /
• v.12 no.1
• /
• pp.71-86
• /
• 2005

Testing for normality has always been an important part of statistical methodology. In this paper a test statistic for multivariate normality is proposed. The underlying idea is to investigate all the possible linear combinations that reduce to the standard normal distribution under the null hypothesis and compare the order statistics of them with the theoretical normal quantiles. The suggested statistic is invariant with respect to nonsingular matrix multiplication and vector addition. We show that the limit distribution of an approximation to the suggested statistic is representable as the supremum over an index set of the integral of a suitable Gaussian process.

• Proceedings of the Korean Statistical Society Conference
• /
• 2000.11a
• /
• pp.187-191
• /
• 2000

In the analysis of repeated measurements, multivariate regression models that account for the correlations among the observations from the same subject are widely used. Like the usual univariate regression models, these multivariate regression models also need some model diagnostic procedures. In this paper, we propose a simple graphical method to detect outliers and to investigate the goodness of model fit in repeated measures data. The graphical method is based on the quantile-quantile(Q-Q) plots of the $X^2$ distribution and the standard normal distribution. We also propose diagnostic measures to detect influential observations. The proposed method is illustrated using two examples.

• Communications for Statistical Applications and Methods
• /
• v.28 no.5
• /
• pp.463-475
• /
• 2021

Desgagné and de Micheaux (2018) proposed an alternative univariate normality test to the Jarque-Bera test. The proposed statistic is based on the sample second power skewness and kurtosis while the Jarque-Bera statistic uses sample Pearson's skewness and kurtosis that are the third and fourth standardized sample moments, respectively. In this paper, we generalize their statistic to a multivariate version based on orthogonalization or an empirical standardization of data. The proposed multivariate statistic follows chi-squared distribution approximately. A simulation study shows that the proposed statistic has good control of type I error even for a very small sample size when critical values from the approximate distribution are used. It has comparable power to the multivariate version of the Jarque-Bera test with exactly the same idea of the orthogonalization. It also shows much better power for some mixed normal alternatives.

• Communications for Statistical Applications and Methods
• /
• v.7 no.1
• /
• pp.55-64
• /
• 2000

We propose a criterion for testing homogeneity of matrix intraclass covariance matrices of K multivariate normal populations, It is based on a variable transformation intended to propose and develop a likelihood ratio criterion that makes use of properties of eigen structures of the matrix intraclass covariance matrices. The criterion then leads to a simple test that uses an asymptotic distribution obtained from Box's (1949) theorem for the general asymptotic expansion of random variables.

• 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.6 no.3
• /
• pp.929-938
• /
• 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).

• Honam Mathematical Journal
• /
• v.11 no.1
• /
• pp.85-105
• /
• 1989

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.18 no.8
• /
• pp.2082-2102
• /
• 2024

Accurate segmentation of magnetic resonance (MR) images is crucial for providing doctors with effective quantitative information for diagnosis. However, the presence of weak boundaries, intensity inhomogeneity, and noise in the images poses challenges for segmentation models to achieve optimal results. While deep learning models can offer relatively accurate results, the scarcity of labeled medical imaging data increases the risk of overfitting. To tackle this issue, this paper proposes a novel fuzzy c-means (FCM) model that integrates a deep learning approach. To address the limited accuracy of traditional FCM models, which employ Euclidean distance as a distance measure, we introduce a measurement function based on the skewed normal distribution. This function enables us to capture more precise information about the distribution of the image. Additionally, we construct a regularization term based on the Kullback-Leibler (KL) divergence of high-confidence deep learning results. This regularization term helps enhance the final segmentation accuracy of the model. Moreover, we incorporate orthogonal basis functions to estimate the bias field and integrate it into the improved FCM method. This integration allows our method to simultaneously segment the image and estimate the bias field. The experimental results on both simulated and real brain MR images demonstrate the robustness of our method, highlighting its superiority over other advanced segmentation algorithms.

• Communications for Statistical Applications and Methods
• /
• v.30 no.3
• /
• pp.227-244
• /
• 2023

In this paper, a depth-based nonparametric test for a multivariate two-sample scale problem is proposed. The proposed test statistic is based on the depth-induced ranks and is thus distribution-free. In this article, the depth values of data points of one sample are calculated with respect to the other sample or distribution and vice versa. A comprehensive simulation study is used to examine the performance of the proposed test for symmetric as well as skewed distributions. Comparison of the proposed test with the existing depth-based nonparametric tests is accomplished through empirical powers over different depth functions. The simulation study admits that the proposed test outperforms existing nonparametric depth-based tests for symmetric and skewed distributions. Finally, an actual life data set is used to demonstrate the applicability of the proposed test.

• Communications for Statistical Applications and Methods
• /
• v.9 no.1
• /
• pp.101-113
• /
• 2002

In this paper we introduce a new score generating (unction for the rank regression in the linear regression model. The score function compares the $\gamma$'th and s\`th power of the tail probabilities of the underlying probability distribution. We show that the rank estimate asymptotically converges to a multivariate normal. further we derive the asymptotic Pitman relative efficiencies and the most efficient values of $\gamma$ and s under the symmetric distribution such as uniform, normal, cauchy and double exponential distributions and the asymmetric distribution such as exponential and lognormal distributions respectively.