• Ocean and Polar Research
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• v.38 no.2
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• pp.149-159
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• 2016

The statistical measures of the coastal environmental data are used in a variety of statistical inferences, hypothesis tests, and data-driven modeling. If the measures are biased, then the statistical estimations and models may also be biased and this potential for bias is great when data contain some outliers defined as extraordinary large or small data values. This study aims to suggest more robust statistical measures as alternatives to more commonly used measures and to assess the performance these robust measures through a quantitative evaluation of more typical measures, such as in terms of locations, spreads, and shapes, with regard to environmental monitoring data in the Busan coastal sea. The detection of outliers within the data was carried out on the basis of Rosner's test. About 5-10% of the nutrient data were found to contain outliers based on Rosner's test. After removal (zero-weighting) of the outliers in the data sets, the relative change ratios of the mean and standard deviation between before and after outlier-removal conditions revealed the figures 13 and 33%, respectively. The variation magnitudes of skewness and kurtosis are 1.36 and 8.11 in a decreasing trend, respectively. On the other hand, the change ratios for more robust measures regarding the mean and standard deviation are 3.7-10.5%, and the variation magnitudes of robust skewness and kurtosis are about only 2-4% of the magnitude of the non-robust measures. The robust measures can be regarded as outlier-resistant statistical measures based on the relatively small changes in the scenarios before and after outlier removal conditions.

• Journal of the Korean Statistical Society
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• v.22 no.2
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• pp.347-351
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• 1993

The dichotomy of absolute continuity and singularity for a pair of stationary and ergodic measures (one of which need not be ergodic) is obtained using the ergodic decomposition theorem. The known fact that two different stationary and ergodic measures are mutually singular is obtained as a corollary of our result. An example of a pair of stationary-ergodic measures enjoying the dichotomy is presented.

• Journal of the Korean Statistical Society
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• v.25 no.3
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• pp.445-456
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• 1996

In this paper, we derive unbiased estimators for the sensitivities of expected performance measures in a Markov renewal process. We restrict our derivation to the performance measures during a busy cycle and apply smoothed perturbation analysis method to find those esti-mators. The results show all the terms in the derived estimators can be obtained from a single sample path.

• Communications for Statistical Applications and Methods
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• v.12 no.3
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• pp.635-642
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• 2005

In statistical diagnostics a large number of influence measures have been proposed for identifying outliers and influential observations. However it seems to be few accounts of the influence diagnostics on test statistics. We study influence analysis on the likelihood ratio test statistic whether the two sets of variables are uncorrelated with one another or not. The influence of observations is measured using the case-deletion approach, the influence function. We compared the proposed influence measures through two illustrative examples.

• The Mathematical Education
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• v.50 no.4
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• pp.489-505
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• 2011

This study is an analysis on the focus of textbooks regarding the statistical chapters of "measures of representative(central tendency) and of the spread". Applying the summary-concept criteria of Juhyeon Nam(2007), 4 kinds of aspect of the chapter; (1) definition and its teleological validity of the measures of representative, (2) definition and practical value of the measures of spread (3) distributional form on the measures of representative and of spread (4) location and scale preservation or invariance of the measures of representative and of spread were observed. On the measures of representative, some definitions were insufficient to check the teleological validity of the measure. Most definitions of the measure of spread were based on the practical view points but no preparation for the future statistical inferences were found even by implication. Some books mention about the measures of representative and of spread for distributions, but we could not find any comments on the correspondence between the sample mean and the expectation of a distribution or population mean. However it is stimulant that some books check the validity of corresponding measures with the location and scale preservation or invariant property, that were not found in the previous curriculum.

• Journal of the Korean Statistical Society
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• v.35 no.2
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• pp.213-224
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• 2006

We investigate the influence of subjects or observations on regression coefficients of generalized estimating equations using the influence function and the derivative influence measures. The influence function for regression coefficients is derived and its sample versions are used for influence analysis. The derivative influence measures under certain perturbation schemes are derived. It can be seen that the influence function method and the derivative influence measures yield the same influence information. An illustrative example in longitudinal data analysis is given and we compare the results provided by the influence function method and the derivative influence measures.

• Communications for Statistical Applications and Methods
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• v.2 no.2
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• pp.303-309
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• 1995

Many measures to detect multicollinearity in linear regression have been proposed in statistics and numerical analysis literature. Among them, condition number and variance inflation factor(VIF) are most popular. In this study, we give new interpretations of condition number and VIF in linear regression, using geometry on the explanatory space. In the same line, we derive natural measures of condition number and VIF for logistic regression. These computer intensive measures can be easily extended to evaluate multicollinearity in generalized linear models.

• Journal of the Korean Statistical Society
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• v.23 no.2
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• pp.271-292
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• 1994

The comparison of statistical experiments with a common parameter and parameter space is discussed using the concept of the Blackwell's sufficiency and the Shannon's entropy. Binomial and censored experiments are considered as applications. The loss of information is studied under teh aggregated experiments and truncated experiments, and summerized in some tables which make it possible to indicate the choice of an appropriate experiment.

• Proceedings of the IEEK Conference
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• 2003.11b
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• pp.23-26
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• 2003

Westfeld[1] analyzed a sequential LSB embedding steganography effectively through the $\chi$$^2$-statistical test which measures the frequencies of PoVs(pairs of values). Fridrich also proposed another statistical analysis, so-called RS steganalysis by which the embedding message rate can be estimated. In this paper, we propose a new steganographic scheme which preserves the above two statistics. The proposed scheme embeds the secret message in the innocent image by randomly adding one to real pixel value or subtracting one from it, then adjusts the statistical measures to equal those of the original image.

• Journal of the Korean Statistical Society
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• v.20 no.2
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• pp.177-190
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• 1991

In this paper, we discuss and review various measures which have been presented for studying outliers. high-leverage points, and influential observations when principal component regression is adopted. We suggest several diagnostics measures when principal component regression is used. A numerical example is illustrated. Some individual data points may be flagged as outliers, high-leverage point, or influential points.