• Journal of the Korean Data and Information Science Society
• /
• v.27 no.5
• /
• pp.1241-1251
• /
• 2016

We consider a correlated discrete-time random walk in which the current jump size depends on the previous jump size and a noncorrelated discrete-time random walk where the jump size is determined independently. By using the strong law of large numbers of Markov chains we derive the formula for the asymptotic means of the random mixture and the periodic pattern of these two random walks and then we show that there exists Parrondo's paradox where each random walk has mean 0 but their random mixture and periodic pattern have negative or positive means. We describe the parameter sets at which Parrondo's paradox holds in each case.

• Proceedings of the Korean Statistical Society Conference
• /
• 2002.11a
• /
• pp.103-108
• /
• 2002

We consider an estimation of discontinuous variance function in nonparametric heteroscedastic random design regression model. We first propose estimators of a change point and jump size in variance function and then construct an estimator of entire variance function. We examine the rates of convergence of these estimators and give results on their asymptotics. Numerical work reveals that the effectiveness of change point analysis in variance function estimation is quite significant.

• Journal of the Korean Statistical Society
• /
• v.33 no.1
• /
• pp.59-78
• /
• 2004

A regression function in generalized linear model may have a discontinuity/change point at unknown location. In order to estimate the location of the discontinuity point and its jump size, the strategy is to use a nonparametric approach based on one-sided kernel weighted local-likelihood functions. Weak convergences of the proposed estimators are established. The finite-sample performances of the proposed estimators with practical aspects are illustrated by simulated examples.

• The Korean Journal of Applied Statistics
• /
• v.30 no.2
• /
• pp.259-269
• /
• 2017

Due to the nonnegativity of variance, most of nonparametric estimations of discontinuous variance function have used the Nadaraya-Watson estimation with residuals. By the modification of Chen et al. (2009) and Yu and Jones (2004), Huh (2014, 2016a) proposed the estimators of the log-variance function instead of the variance function using the local linear estimator which has no boundary effect. Huh (2016b) estimated the variance function using the adjusted squared residuals by the estimated jump size in the discontinuous variance function. In this paper, we propose an estimator of the discontinuous log-variance function using the local linear estimator with the adjusted log-squared residuals by the estimated jump size of log-variance function like Huh (2016b). The numerical work demonstrates the performance of the proposed method with simulated and real examples.

• Bulletin of the Korean Mathematical Society
• /
• v.47 no.6
• /
• pp.1105-1119
• /
• 2010

We consider jump processes which has only downward jumps with size a fixed fraction of the current process. The jumps of the pro cesses are interpreted as crashes and we assume that the jump intensity is a nondecreasing function of the current process say $\lambda$(X) (X = X(t) process). For the case of $\lambda$(X) = $X^{\alpha}$, $\alpha$ > 0, we show that the process X shold explode in finite time, say $t_e$, conditional on no crash For the case of $\lambda$(X) = (lnX)$^{\alpha}$, we show that $\alpha$ = 1 is the borderline of two different classes of processes. We generalize the model by adding a Brownian noise and examine the blow up properties of the sample paths.

• Journal of the Korean Data and Information Science Society
• /
• v.20 no.1
• /
• pp.1-9
• /
• 2009

Let us consider that the variance function in regression model has a discontinuity/change point at unknown location. Yu and Jones (2004) proposed the local polynomial fit to estimate the log-variance function which break the positivity of the variance. Using the local polynomial fit, Huh (2008) estimate the discontinuity point of the log-variance function. We propose a test for the existence of a discontinuity point in the log-variance function with the estimated jump size in Huh (2008). The proposed method is based on the asymptotic distribution of the estimated jump size. Numerical works demonstrate the performance of the method.

• Proceedings of the Korean Operations and Management Science Society Conference
• /
• 1989.10a
• /
• pp.90-90
• /
• 1989

• Journal of the Korean Data and Information Science Society
• /
• v.13 no.2
• /
• pp.251-260
• /
• 2002

The aim of this paper is to consider of detecting the location, the jump size and the number of change-points in regression functions by using the local linear fit which is one of nonparametric regression techniques. It is obtained the asymptotic properties of the change points and the jump sizes. and the correspondin grates of convergence for change-point estimators.

• Communications for Statistical Applications and Methods
• /
• v.10 no.1
• /
• pp.31-38
• /
• 2003

A simple method is proposed to detect the number of change points and test the location and size of multiple change points with jump discontinuities in an otherwise smooth regression model. The proposed estimators are based on a local linear regression fit by the comparison of left and right one-side kernel smoother. Our proposed methodology is explained and applied to real data and simulated data.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.27 no.1
• /
• pp.48-57
• /
• 2003

This study presents nonlinear vibration of a cantilever beam subjected to electromagnetic forces. The dynamic responses of the beam show various nonlinear phenomena with the variation of the system parameters, such as the jump phenomenon, multiple solutions, and the movement of the natural frequency. In this study the nonlinear stiffness due to electromagnetic forces which depends on air gap size is measured experimentally, and the system is modeled by a single degree of freedom nonlinear dynamic system and solutions are solved numerically. The numerical results show good agreements with the experimental results, which demonstrate the nonlinearity of electromagnetic force. Finally the occurrences of the jump phenomenon and the first, second and fourth harmonic components are confirmed in using the method of multiple scales.