• Journal of the Korean Mathematical Society
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• v.45 no.3
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• pp.683-693
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• 2008

In this paper, we study the asymptotic behavior of the residual empirical process from diffusion processes. For this task, adopting the discrete sampling scheme as in Florens-Zmirou [9], we calculate the residuals and construct the residual empirical process. It is shown that the residual empirical process converges weakly to a Brownian bridge.

• Journal of the Korean Mathematical Society
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• v.47 no.6
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• pp.1137-1146
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• 2010

In this paper, we study the divergence based goodness of fit test for partially observed sample from diffusion processes. In order to derive the limiting distribution of the test, we study the asymptotic behavior of the residual empirical process based on the observed sample. It is shown that the residual empirical process converges weakly to a Brownian bridge and the associated phi-divergence test has a chi-square limiting null distribution.

• Journal of the Korean Mathematical Society
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• v.43 no.2
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• pp.225-239
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• 2006

In [5], Csorgo and Zitikis exposed the strong $uniform-over-[0,\;{\infty}]$ consistency, and weak $uniform-over-[0,\;{\infty}]$ approximation of the empirical mean residual life process by employing weight functions. We carry on the uniform asymptotic behaviors of the empirical mean residual life process over the whole positive half line by representing the process as an integral form. We compare our results with those of Yang [15], Hall and Wellner [8], and Csorgo and Zitikis [5].

• Journal of the Korean Mathematical Society
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• v.58 no.1
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• pp.237-264
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• 2021

In this work the stationary bootstrap of Politis and Romano [27] is applied to the empirical distribution function of stationary and associated random variables. A weak convergence theorem for the stationary bootstrap empirical processes of associated sequences is established with its limiting to a Gaussian process almost surely, conditionally on the stationary observations. The weak convergence result is proved by means of a random central limit theorem on geometrically distributed random block size of the stationary bootstrap procedure. As its statistical applications, stationary bootstrap quantiles and stationary bootstrap mean residual life process are discussed. Our results extend the existing ones of Peligrad [25] who dealt with the weak convergence of non-random blockwise empirical processes of associated sequences as well as of Shao and Yu [35] who obtained the weak convergence of the mean residual life process in reliability theory as an application of the association.

• Communications for Statistical Applications and Methods
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• v.8 no.1
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• pp.291-297
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• 2001

For a stochastic regression model in which the errors are assumed to form a stationary linear process, we show that the difference between the empirical distribution functions of the errors and the estimates of those errors converges uniformly in probability to zero at the rate of $o_{p}$ ( $n^{-}$$\frac{1}{2}$) as the sample size n increases.

• Journal of the Korean Statistical Society
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• v.32 no.1
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• pp.25-32
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• 2003

In this paper, we define the mean life process for the right censored data and show the asymptotic equivalence between two kinds of the mean life processes. We use the Kaplan-Meier and Susarla-Van Ryzin estimates as the estimates of survival function for the construction of the mean life processes. Also we show the asymptotic equivalence between two mean residual life processes as an application and finally discuss some difficulties caused by the censoring mechanism.

• Journal of the Korean Statistical Society
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• v.33 no.2
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• pp.191-202
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• 2004

The paper considers nonparametric empirical Bayes estimation of residual survival function at age t using a Dirichlet process prior V(a). Empirical Bayes estimators are proposed for the case where both the function ${\alpha}$(0, $\chi$] and the size a(R$\^$+/) are unknown. It is shown that the proposed empirical Bayes estimators are asymptotically optimal at a rate n$\^$-1/, where n is the number of past data available for the present estimation problem. Therefore, the result of Lahiri and Park (1988) in which a(R$\^$+/) is assumed to be known and a rate n$\^$-1/ is achieved, is extended to a(R$\^$+/) unknown case.

• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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• pp.191-197
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• 2003

This paper considers the independence test for two stationary infinite order autoregressive processes. For a test, we follow the empirical process method devised by Hoeffding (1948) and Blum, Kiefer and Rosenblatt (1961), and construct the Cram${\acute{e}}$r-von Mises type test statistics based on the least squares residuals. It is shown that the proposed test statistics behave asymptotically the same as those based on true errors.

• Journal of the Semiconductor & Display Technology
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• v.12 no.2
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• pp.79-84
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• 2013

Nanoimprint lithography (NIL) is the next generation photolithography process in which the photoresist is dispensed onto the substrate in its liquid form and then imprinted and cured into a desired pattern instead of using traditional optical system. There have been considerable attentions on NIL due to its potential abilities that enable cost-effective and high-throughput nanofabrication to the display device and semiconductor industry. Although one of the current major research trends of NIL is large-area patterning, the technical difficulties to keep the uniformity of the residual layer become severer as the imprinting area increases more and more. In this paper, with the rolling type imprinting process, a mold, placed upon the $2^{nd}$ generation TFT-LCD glass sized substrate($370{\times}470mm^2$), is rolled by a rubber roller to achieve a uniform residual layer. The prediction of residual layer thickness of the photoresist by rolling of the rubber roller is crucial to design the rolling type imprinting process, determine the rubber roller operation conditions-mpressing force & feeding speed, operate smoothly the following etching process, and so forth. First, using the elasticity theory of contact problem and the empirical equation of rubber hardness, the contact length between rubber roller and mold is calculated with consideration of the shape and hardness of rubber roller and the pressing force to rubber roller. Next, using the squeeze flow theory to photoresist flow, the residual layer thickness of the photoresist is calculated with information of the viscosity and initial layer thickness of photoresist, the shape of mold pattern, feeding speed of rubber roller, and the contact length between rubber roller and mold previously calculated. Last, the effects of rubber roller operation conditions, impressing force & feeding speed, on the residual layer thickness are analyzed with consideration of the shape and hardness of rubber roller.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2003.06a
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• pp.1799-1802
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• 2003

The commercial success of a new product is influenced by the time to market. Shorter product leadtimes are of importance in a competitive market. This can be achieved only if the product development process can be realized in a relatively small time period. New cutting inserts are developed by a time consuming trial and error process guided by empirical knowledge of the mechanical cutting process. The effect of previous cutting on chip formation and the surface residual stresses has been studied. The chip formation is not affected much. There is only a minor influence from the residual stress on the surface from tile first cutting on the second pass chip formation. Thus, it is deemed to be sufficient to simulate only the first pass. The influence of the cutting speed and feed on the residual stresses has been computed and verified by the experiments. It is shown that the state of residual stresses in the workpiece increases with the cutting speed. This paper presents experimental results which can be used for evaluating computational models to assure robust solutions. The general finite element code ABAQUS/Standard has been used in the simulations. A quasi-static simulation with adiabatic heating was performed. The path for separating the chip from the workpiece is predetermined. The agreement between measurements and calculation is good considering the simplifications introduced.