• 대한수학회논문집
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• 제37권1호
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• pp.163-176
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• 2022

In this paper, we introduce some new classes of generalized mappings and prove some common fixed point theorems for a pair of asymptotically regular mappings. Our results extend and improve various well-known results due to Kannan, Reich, Wong, Hardy and Rogers, Ćirić, Jungck, Górnicki and many others. In addition to it, a sequential fixed point for a mapping which is the point-wise limit of a sequence of functions satisfying Ćirić-Proinov-Górnicki type mapping has been proved. Supporting examples have been given in strengthening hypotheses of our established theorems.

• 한국정밀공학회지
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• 제14권4호
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• pp.88-96
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• 1997

This paper suggests a new non-linear friction compensation for digital control systems. This control adopts a hysteresis nonlinear element which can introduce the phase lead of the control system to compensate the phase delay comes from the inherent time delay of a digital control. A proper Lyapunov function is selected and the Lyapunov direct method is used to prove the asymptotic stability of the suggested control.

• Journal of the Korean Statistical Society
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• 제21권2호
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• pp.167-177
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• 1992

In this paper, we investigate the limiting distribution of $M_n = max (X_1, X-2, \cdots, X_n)$ in the infinite moving average process ${X_t = \sum c_i Z_{t-i}}$ generated from i.i.d. negative binomial variables $Z_i$'s. While no limit result is possible, nonetheless asymptotic bounds are derived. We also present the tail behavior of $X_t$, i.e., weighted sum of i.i.d. random variables. This continues a study made by Rootzen (1986) for discrete innovation sequences.

• Journal of the Korean Statistical Society
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• 제28권4호
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• pp.479-488
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• 1999

Moore and Stubblebine(1981) suggested a chi-square test for multivariate normality based on cell counts calculated from the sample Mahalanobis distances. They derived the limiting distribution of the test statistic only when equiprobable cells are employed. Using conditional limit theorems, we derive the limiting distribution of the statistic as well as the asymptotic normality of the cell counts. These distributions are valid even when equiprobable cells are not employed. We finally apply this method to a real data set.

• Journal of the Korean Statistical Society
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• 제28권4호
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• pp.435-441
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• 1999

A 'convergence in probability' rate of the empirical distributions and quantiles of linear processes is obtained. As an application of the limit theorems, a trimmed mean for the location of the linear process is considered. It is shown that the trimmed mean is asymptotically normal. A consistent estimator for the asymptotic variance of the trimmed mean is provided.

• Communications for Statistical Applications and Methods
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• 제6권2호
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• pp.645-658
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• 1999

One of the most popular graphical techniques for goodness of fit problems is the quantile-quantile plot(Q-Q plot) Easton and McCulloch(1990) suggested a way of generalizing Q-Q plots to multivariate cases bases on finding a matching between the points of the data set whose shape is being examined and a reference sample. in this paper we investigated the asymptotic behavior of the generalized Q-Q plot for bivariate cases. As a result we concluded that the standard univariate Q-Q plot and the generalized Q-Q plot have the same limit if two variables are independent.

• Communications for Statistical Applications and Methods
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• 제6권1호
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• pp.267-274
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• 1999

We consider a doubly stochastically perturbed dynamical system {$X_n$} generated by $X_n\Gamma_n(X_{n-1})+W_n where \Gamma_n$ is a Markov chain of random functions and $W_n$ is i.i.d. random elements. Sufficient conditions for stationarity and geometric ergodicity of $X_n$ are obtained by considering asymptotic behaviours of the associated Markov chain. Ergodic theorem and functional central limit theorem are proved.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제12권3호
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• pp.169-178
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• 2005

In this paper we study the existence and local asymptotic limit of the topological Chern-Simons vortices of the CP(1) model in $\mathbb{R}^2$. After reducing to semilinear elliptic partial differential equations, we show the existence of topological solutions using iteration and variational arguments & prove that there is a sequence of topological solutions which converges locally uniformly to a constant as the Chern­Simons coupling constant goes to zero and the convergence is exponentially fast.

• Journal of the Korean Statistical Society
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• 제32권2호
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• pp.163-174
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• 2003

We propose a test for independence of bivariate censored data under univariate censorship. To do this, we first introduce a process defined by the difference between bivariate survival function estimator proposed by Lin and Ying (1993) and the product of the product-limit estimators (Kaplan and Meier, 1958) for the marginal survival functions, and derive its asymptotic properties under the null hypothesis of independence. We propose a Cramer-von Mises-type test procedure based on the process . We conduct simulation studies to investigate the finite-sample performance of the proposed test and illustrate the proposed test with a real example.

• Journal of the Korean Statistical Society
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• 제28권4호
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• pp.469-478
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• 1999

We propose a Kolmogorov-Smirnov-type test for independence of paired failure times in the presence of independent censoring times. This independent censoring mechanism is often assumed in case-control studies. To do this end, we first introduce a process defined as the difference between the bivariate survival function estimator proposed by Wang and Wells (1997) and the product of the product-limit estimators (Kaplan and Meier (1958)) for the marginal survival functions. Then, we derive its asymptotic properties under the null hypothesis of independence. Finally, we assess the performance of the proposed test by simulations, and illustrate the proposed methodology with a dataset for remission times of 21 pairs of leukemia patients taken from Oakes(1982).