• Communications for Statistical Applications and Methods
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• v.25 no.2
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• pp.109-130
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• 2018

Several measures of multivariate skewness for scale mixtures of skew-normal distributions are derived. As a special case, those of multivariate skew-t distribution are considered in detail. Furthermore, the similarities, differences, and behavior of these measures are explored for cases of some specific members of the multivariate skew-normal and skew-t distributions using a simulation study. Since some measures are vectors, it is better to take all measures in the same scale when comparing them. In order to attain such a set of comparable indices, the sample version is considered for each of the skewness measures that are taken as test statistics for the hypothesis of t distribution against skew-t distribution. An application is reported for the data set consisting of 71 total glycerol and magnesium contents in Grignolino wine.

• Journal of the Korean Statistical Society
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• v.34 no.2
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• pp.109-123
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• 2005

Variogram estimation is an important step of spatial statistics since it determines the kriging weights. Matheron's variogram estimator can be written as a quadratic form of the observed data. In this paper, we extend a skew t distribution to a generalized skew t distribution and moments of the variogram estimator for a generalized skew t distribution are derived in closed forms. After calculating the correlation structure of the variogram estimator, variogram fitting by generalized least squares is discussed.

• Journal of the Korean Mathematical Society
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• v.47 no.3
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• pp.455-466
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• 2010

For an endomorphism $\alpha$ of a ring R, we introduce the weak $\alpha$-skew Armendariz rings which are a generalization of the $\alpha$-skew Armendariz rings and the weak Armendariz rings, and investigate their properties. Moreover, we prove that a ring R is weak $\alpha$-skew Armendariz if and only if for any n, the $n\;{\times}\;n$ upper triangular matrix ring $T_n(R)$ is weak $\bar{\alpha}$-skew Armendariz, where $\bar{\alpha}\;:\;T_n(R)\;{\rightarrow}\;T_n(R)$ is an extension of $\alpha$ If R is reversible and $\alpha$ satisfies the condition that ab = 0 implies $a{\alpha}(b)=0$ for any a, b $\in$ R, then the ring R[x]/($x^n$) is weak $\bar{\alpha}$-skew Armendariz, where ($x^n$) is an ideal generated by $x^n$, n is a positive integer and $\bar{\alpha}\;:\;R[x]/(x^n)\;{\rightarrow}\;R[x]/(x^n)$ is an extension of $\alpha$. If $\alpha$ also satisfies the condition that ${\alpha}^t\;=\;1$ for some positive integer t, the ring R[x] (resp, R[x; $\alpha$) is weak $\bar{\alpha}$-skew (resp, weak) Armendariz, where $\bar{\alpha}\;:\;R[x]\;{\rightarrow}\;R[x]$ is an extension of $\alpha$.

• Journal of the Korean Mathematical Society
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• v.52 no.6
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• pp.1271-1286
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• 2015

An operator T on a complex Hilbert space H is called skew symmetric if T can be represented as a skew symmetric matrix relative to some orthonormal basis for H. In this paper, we study skew symmetric operators with eigenvalues. First, we provide an upper-triangular operator matrix representation for skew symmetric operators with nonzero eigenvalues. On the other hand, we give a description of certain skew symmetric triangular operators, which is based on the geometric relationship between eigenvectors.

• Communications for Statistical Applications and Methods
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• v.29 no.3
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• pp.333-351
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• 2022

The skew-t distribution is an attractive family of asymmetrical heavy-tailed densities that includes the normal, skew-normal and Student's-t distributions as special cases. In this work, we propose an EM-type algorithm for computing the maximum likelihood estimates for skew-t linear regression models with censored response. In contrast with previous proposals, this algorithm uses analytical expressions at the E-step, as opposed to Monte Carlo simulations. These expressions rely on formulas for the mean and variance of a truncated skew-t distribution, and can be computed using the R library MomTrunc. The standard errors, the prediction of unobserved values of the response and the log-likelihood function are obtained as a by-product. The proposed methodology is illustrated through the analyses of simulated and a real data application on Letter-Name Fluency test in Peruvian students.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1269-1283
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• 2015

An operator $T{{\in}}{\mathcal{L}}({\mathcal{H}})$ is said to be skew complex symmetric if there exists a conjugation C on ${\mathcal{H}}$ such that $T=-CT^*C$. In this paper, we study properties of skew complex symmetric operators including spectral connections, Fredholmness, and subspace-hypercyclicity between skew complex symmetric operators and their adjoints. Moreover, we consider Weyl type theorems and Browder type theorems for skew complex symmetric operators.

• Journal of the Korean Mathematical Society
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• v.52 no.2
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• pp.403-416
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• 2015

An operator T on a complex Hilbert space $\mathcal{H}$ is called skew symmetric if T can be represented as a skew symmetric matrix relative to some orthonormal basis for $\mathcal{H}$. In this note, we explore the structure of skew symmetric operators with disconnected spectra. Using the classical Riesz decomposition theorem, we give a decomposition of certain skew symmetric operators with disconnected spectra. Several corollaries and illustrating examples are provided.

• Proceedings of the Korean Statistical Society Conference
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• 2004.11a
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• pp.91-95
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• 2004

Moments of skew t random vectors and their quadratic forms are derived. It is shown that the moments of the sample autocovariance function and of the sample variogram estimator do not depend on a skewness parameter.

• Communications for Statistical Applications and Methods
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• v.30 no.6
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• pp.605-629
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• 2023

This paper proposes some diagnostics procedures for the skew-t linear regression model with censored response. The skew-t distribution is an attractive family of asymmetrical heavy-tailed densities that includes the normal, skew-normal and student's-t distributions as special cases. Inspired by the power and wide applicability of the EM-type algorithm, local and global influence analysis, based on the conditional expectation of the complete-data log-likelihood function are developed, following Zhu and Lee's approach. For the local influence analysis, four specific perturbation schemes are discussed. Two real data sets, from education and economics, which are right and left censoring, respectively, are analyzed in order to illustrate the usefulness of the proposed methodology.

• Communications for Statistical Applications and Methods
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• v.8 no.3
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• pp.867-873
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• 2001

In this paper we propose a family of skew- f distributions. The family is derived by a scale mixtures of skew-normal distributions introduced by Azzalini (1985) and Henze (1986). The salient features of the family are mathematical tractability and strict inclusion of the normal law. Further it includes a shape parameter, to some extent, controls the index of skewness. Necessary theory involved in deriving the family of distributions is provided and main properties of the family are also studied.