• Journal of the Korean Statistical Society
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• v.7 no.2
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• pp.109-119
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• 1978

When a response surface by a seconde order polynomial regression model, the stationary point is obtained by solving simultaneous linear equations. But the point is a function of random variables. We can find a confidence region for this point as Box and Hunter provided. However, the confidence region is often too large to be useful for the experiments, and it is necessary to augment additional design points in order to obtain a satisfactory confidence region for the stationary point. In this note, the author suggests a method how to augment design points "eficiently", and shows the change of the confidence region of the estimated stationary point in a response surface.e surface.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.201-213
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• 2003

In this paper we present a second order PVT (parallel variable transformation) algorithm converging to second order stationary points for minimizing smooth functions, based on the first order PVT algorithm due to Fukushima (1998). The corresponding stopping criterion, descent condition and descent step for the second order PVT algorithm are given.

• Communications for Statistical Applications and Methods
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• v.30 no.4
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• pp.369-388
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• 2023

In this paper, we develop the two-step procedure that detects and estimates the position of structural changes for multivariate nonstationary time series, either on mean parameters or second-order structures. We first investigate the presence of mean structural change by monitoring data through the aggregated cumulative sum (CUSUM) type statistic, a sequential procedure identifying the likely position of the change point on its trend. If no mean change point is detected, the proposed method proceeds to scan the second-order structural change by modeling the multivariate nonstationary time series with a multivariate locally stationary Wavelet process, allowing the time-localized auto-correlation and cross-dependence. Under this framework, the estimated dynamic spectral matrices derived from the local wavelet periodogram capture the time-evolving scale-specific auto- and cross-dependence features of data. We then monitor the change point from the lower-dimensional approximated space of the spectral matrices over time by applying the dynamic principal component analysis. Different from existing methods requiring prior information on the type of changes between mean and covariance structures as an input for the implementation, the proposed algorithm provides the output indicating the type of change and the estimated location of its occurrence. The performance of the proposed method is demonstrated in simulations and the analysis of two real finance datasets.

• Nonlinear Functional Analysis and Applications
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• v.28 no.3
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• pp.831-850
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• 2023

Our long-standing Metatheorem in Ordered Fixed Point Theory is applied to some well-known order theoretic fixed point theorems. In the first half of this article, we introduce extended versions of the Zermelo fixed point theorem, Zorn's lemma, and the Caristi fixed point theorem based on the Brøndsted-Jachymski principle and our 2023 Metatheorem. We show some of their applications to other fixed point theorems or theorems on the existence of maximal elements in partially ordered sets. In the second half, we collect and improve order theoretic fixed point theorems in the collection of Howard-Rubin in 1991 and others. In fact, we improve or extend several ordering principles or fixed point theorems due to Brézis-Browder, Brøndsted, Knaster-Tarski, Tarski-Kantorovitch, Turinici, Granas-Horvath, Jachymski, and others.

• Korea journal of population studies
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• v.32 no.1
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• pp.139-164
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• 2009

The first demographic transition refers to the historical decline in mortality and fertility, as shown from the 18th Century in several European populations, and continuing present in most developing countries. The end point of the first demographic transition(FDT) was supposed to be a stationary and stable population corresponding with replacement fertility and zero population growth. In addition, households in all parts of the world would converge toward the nuclear and conjugal types, composed of married couples and their offspring. The second demographic transition(SDT), on the other hand, sees no such equilibrium as the end-point. Rather, new developments bring sub-replacement fertility, a multitude of living arrangements other than marriage, and the disconnection between marriage and procreation. Populations would face declining sizes if not complemented by new migrants. Over the last decades birth rates have been on the decline in all countries of the world, and it is estimated that already more than half of he world's population has below replacement level fertility. Measured in terms of the Total Fertility Rate (TFR), currently 34 countries have fertility levels of 1.5 or less. Similarly, Korea has been below lowest-low fertility for eight consecutive years since 2001 and below the replacement level for more than twenty years. In explaining the low fertility in Korea, some researchers explain the low fertility as revenge against a male-dominated society and institution, while others focus the impact of the employment instability. These studies share the basic ideas (spread of individualism, delayed marriage and childbearing, high divorce rate etc.) of a second demographic transition in order to explain the low fertility in Korea.