• Journal of the Korean Statistical Society
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• v.34 no.3
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• pp.173-183
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• 2005

The Box-Cox power transformation is generally used for variance stabilization. Recently, Shin and Kang (2001) showed, under the Box-Cox transformation, invariant properties to the original model under the large mean and relatively small variance assumptions in time series analysis. In this paper we obtain some invariant properties in spatial statistics. Spatial statistics, Invariant Property, Variogram, Box-Cox power Transformation.

• Journal of the Korean Statistical Society
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• v.36 no.1
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• pp.149-156
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• 2007

This study suggests a new method for testing seasonal unit roots in a momentum threshold autoregressive (MTAR) process. This sign test is robust against heteroscedastic or heavy tailed errors and is invariant to monotone data transformation. The proposed test is a seasonal extension of the sign test of Park and Shin (2006). In the case of partial seasonal unit root in an MTAR model, a Monte-Carlo study shows that the proposed test has better power than the seasonal sign test developed for AR model.

• Communications for Statistical Applications and Methods
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• v.7 no.1
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• pp.97-106
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• 2000

In time series analysis we generally use Box-Cox power transformation for variance stabilization. In this paper we show that order estimator and one step ahead forecast of transformed AR(1) model are approximately invariant to those of the original model under some assumptions. A small Monte-Carlo simulation is performed to support the results.

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.235-243
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• 2002

In this paper, we show that NQD ordering is preserved under mixture, limits in distribution, invariant under transformation of increasing functions. Finally, we explore the characterization and limit in distribution of RTD(LTI) ordering and some properties.

• Journal of applied mathematics & informatics
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• v.35 no.3_4
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• pp.261-265
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• 2017

Let X and Y be independent identically distributed nondegenerate random variables with common absolutely continuous probability distribution function F(x) and the corresponding probability density function f(x) and $E(X^2)$<${\infty}$. Put Z = max(X, Y) and W = min(X, Y). In this paper, it is proved that Z - W and Z + W or$(X-Y)^2$ and X + Y are independent if and only if X and Y have normal distribution.