• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.209-222
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• 2006

Estimation of the spectral measure, covariance and spectral density functions of a strictly stationary r-vector valued time series is considered, under the assumption that some of the observations are missed. The modified periodograms are calculated using data window. The asymptotic normality is studied.

• 응용통계연구
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• 제24권5호
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• pp.883-891
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• 2011

수명시간에 대한 모형으로 로그정규분포가 자주 사용되며, 이는 자료의 변환에 의하여 정규성 검정과 동일한 문제로 생각할 수 있다. 따라서 자료의 로그정규성 검정을 위하여, 정규성 검정에 자주 이용되는 Shapiro-Wilk 형태의 검정통계량을 Kaplan-Meier의 product limit 경험분포함수를 이용하여 임의중도절단자료로 일반화한다. Cram er von Mises 통계량을 임의중도절단자료로 일반화한 Koziol과 Green (1976)의 통계량과 비교하였으며 이를 위하여 단순귀무가설을 가정하였다. 중도절단분포에 대한 모형으로는 Koziol과 Green (1976)에서 제시한 모형과 이와 유사한 다른 모형 두 가지를 고려하였다. 검정력 비교 결과 제시한 통계량이 로그정규성 또는 정규성 검정에 더 좋은 검정력을 보여주었으며 검정력은 중도절단분포 모형보다는 자료의 중도절단비율에 영향을 받는다는 것을 볼 수 있었다.

• Communications for Statistical Applications and Methods
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• 제31권1호
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• pp.1-35
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• 2024

The assumption of homoscedasticity is one of the most crucial assumptions for many parametric tests used in the biological sciences. The aim of this paper is to compare the empirical probability of type I error and the power of ten parametric and two non-parametric tests for homoscedasticity with simulations under different types of distributions, number of groups, number of samples per group, variance ratio and significance levels, as well as through empirical data from an agricultural experiment. According to the findings of the simulation study, when there is no violation of the assumption of normality and the groups have equal variances and equal number of samples, the Bhandary-Dai, Cochran's C, Hartley's Fmax, Levene (trimmed mean) and Bartlett tests are considered robust. The Levene (absolute and square deviations) tests show a high probability of type I error in a small number of samples, which increases as the number of groups rises. When data groups display a nonnormal distribution, researchers should utilize the Levene (trimmed mean), O'Brien and Brown-Forsythe tests. On the other hand, if the assumption of normality is not violated but diagnostic plots indicate unequal variances between groups, researchers are advised to use the Bartlett, Z-variance, Bhandary-Dai and Levene (trimmed mean) tests. Assessing the tests being considered, the test that stands out as the most well-rounded choice is the Levene's test (trimmed mean), which provides satisfactory type I error control and relatively high power. According to the findings of the study and for the scenarios considered, the two non-parametric tests are not recommended. In conclusion, it is suggested to initially check for normality and consider the number of samples per group before choosing the most appropriate test for homoscedasticity.

• 응용통계연구
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• 제17권3호
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• pp.507-518
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• 2004

Malkovich & Afifi (1973)는 합교원리 (union-intersection principle)를 이용하여 왜도와 첨도를 다변량으로 일반화하였으나 이는 자료의 차원이 클 경우에는 사용이 용이하지 않다. 본 논문에서는 이러한 단점을 보완하는 이들의 근사통계량을 제안한다. 그리고 제안된 근사통계량, Malkovich & Afifi (1973)의 통 계 량, Mardia(1970)의 왜도와 첨도의 검 정력을 모의실험을 통하여 비교한다.

• Communications for Statistical Applications and Methods
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• 제28권5호
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• pp.463-475
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• 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.

• Journal of the Korean Statistical Society
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• 제30권3호
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• pp.419-433
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• 2001

In this paper we introduce a method of improving efficiency of the moment estimator of Dekkers, Einmahl and de Haan(1989) for the extreme value index $\beta$. a new estimator of $\beta$ is proposed by adding the third moment ot the original moment estimator which is composed of the first two moments of the log-transformed sample data. We establish asymptotic normality of the new estimator and examine and adaptive procedure for the new estimator. The resulting adaptive estimator proves to be asymptotically better than the moment estimator particularly for $\beta$<0.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2002년도 추계 학술발표회 논문집
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• pp.3-9
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• 2002

In financial time series, the autoregressive conditional heteroscedastic (ARCH) models have been widely used for modeling conditional variances. In many cases, non-normality or heavy-tailed distributions of the data have influenced the estimation methods under normality assumption. To solve this problem, a robust function for the conditional variances of the errors is proposed and compared the relative efficiencies of the estimators with other conventional models.

• 대한수학회보
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• 제47권5호
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• pp.889-905
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• 2010

In this paper, a distribution free approach to the parameter estimation of a simple bilinear model with periodic coefficients is presented. The proposed method relies on minimum distance estimator based on the autocovariances of the squared process. Consistency and asymptotic normality of the estimator, as well as hypotheses testing, are derived. Numerical experiments on simulated data sets are presented to highlight the theoretical results.

• 통합자연과학논문집
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• 제13권2호
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• pp.76-82
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• 2020

If normality of an observed data is not a viable assumption, we can carry out normal-theory analyses by suitable transforming data. Power transformation by Box and Cox, one of the transformation methods, is derived the power which maximized the likelihood function. But it doesn't induces the closed form in mathematical analysis. In this paper, we compose some R the syntax of which is easier than other statistical packages for deriving the power with using numerical methods. Also, by using R, we show the transformed data approximately distributed the normal through Q-Q plot in univariate and bivariate cases with some examples. Finally, we present the value of a goodness-of-fit statistic(AD) and its p-value for normal distribution. In the similar procedure, this method can be extended to more than bivariate case.

• Communications for Statistical Applications and Methods
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• 제29권3호
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• pp.373-391
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• 2022

The distribution of observations in most econometric studies with spatial heterogeneity is skewed. Usually, a single transformation of the data is used to approximate normality and to model the transformed data with a normal assumption. This assumption is however not always appropriate due to the fact that panel data often exhibit non-normal characteristics. In this work, the normality assumption is relaxed in spatial mixed models, allowing for spatial heterogeneity. An inference procedure based on Bayesian mixed modeling is carried out with a multivariate skew-elliptical distribution, which includes the skew-t, skew-normal, student-t, and normal distributions as special cases. The methodology is illustrated through a simulation study and according to the empirical literature, we fit our models to non-life insurance consumption observed between 1998 and 2002 across a spatial panel of 103 Italian provinces in order to determine its determinants. Analyzing the posterior distribution of some parameters and comparing various model comparison criteria indicate the proposed model to be superior to conventional ones.