Jae-Sik Bae

In this paper we consider the uniform central limit theorem for a martingale-difference array of a function-indexed stochastic process under the uniformly integrable entropy condition. We prove a maximal inequality for martingale-difference arrays of process indexed by a class of measurable functions by a method as Ziegler [19] did for triangular arrays of row wise independent process. The main tools are the Freedman inequality for the martingale-difference and a sub-Gaussian inequality based on

In this paper we propose a new method for solving multiclass problem with leastsquares support vector machine(LS-SVM) regression. This method implements one-against-all scheme which is as accurate as any other approach. We also propose crossvalidation(CV) method to select eectively the optimal values of hyper-parameterswhich aect the performance of the proposed multiclass method. Experimentalresults are then presented which indicate the performance of the proposed multiclassmethod method.

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].

In Bae et al. [2], we have considered the uniform CLT for the martingale difference arrays under the uniformly integrable entropy. In this paper, we prove the same problem under the bracketing entropy condition. The proofs are based on Freedman inequality combined with a chaining argument that utilizes majorizing measures. The results of present paper generalize those for a sequence of stationary martingale differences. The results also generalize independent problems.

This paper deals with the estimations of the least squares support vector regression when the responses are subject to randomly right censoring. The estimation is performed via two steps - the ordinary least squares support vector regression and the least squares support vector regression with censored data. We use the empirical fact that the estimated regression functions subject to randomly right censoring are close to the true regression functions than the observed failure times subject to ra

Smoothly clipped absolute deviation (SCAD) penalty is known to satisfy the desirable properties for penalty functions like as unbiasedness, sparsity and continuity. In this paper, we deal with the regression function estimation and variable selection based on SCAD penalized censored regression model. We use the local linear approximation and the iteratively reweighted least squares algorithm to solve SCAD penalized log likelihood function. The proposed method provides an efficient method for var

We investigate a uniform local asymptotic normality for likelihoodratio processes based on an independent and identicallydistributed local asymptotic problem. Our tool is an empiricalprocess theory.

The standard logistic map is an iterative function, which forms a discrete-time dynamic system. The chaotic logistic map is a kind of ergodic map defined over the unit interval. In this paper we study the limiting behaviors on the several processes induced by the chaotic logistic map. We derive the law of large numbers for the process induced by the chaotic logistic map. We also derive the uniform law of large numbers for this process. When deriving the uniform law of large numbers, we study the

This paper considers the asymptotic behaviors of the processesgenerated by the classical ergodic tent map that is defined on the unit interval. We develop a sequential empirical process and get the uniform version of law of iterated logarithm for the tent map by using the bracketing entropy method.

The baker transformation is an ergodic transformation defined on the half open unit square. This paper considers the limiting behavior of the partial sum process of a martingale sequence constructed from the baker transformation. We get the uniform law of large numbers for the baker transformation.

In this paper we propose a robust version of varying coefficient models, which is based on the regularized regression with L1 regularization. We use the iteratively reweighted least squares procedure to solve L1 regularized objective function of varying coefficient model in locally weighted regression form. It provides the efficient computation of coefficient function estimates and the variable selection for given value of smoothing variable. We present the generalized cross validation function

LetZn (s;f) = n1 P [ns ]i=1 (f(Xi) Pf) be the sequen-tial empirical process based on the independent and identically dis-tributed random variables. We prove that convergence problemsof sup(s;f) jZn (s;f)j to zero boil down to those of supf jZn (1;f)j.We employ Ottaviani's inequality and the complete convergence toestablish, under bracketing entropy with the second moment, thealmost sure convergence of sup(s;f) jZn (s;f)j to zero.

We obtain a kernel quantile process based on the kernel quantileestimator and prove the uniform consistency of the kernelquantile process by developing that of the usual sample quantileprocess. We apply our result to the classical kernel typeprocesses.

Multinomial logistic regression is a well known multiclass classicationmethod in the eld of statistical learning. More recently, the developmentof sparse multinomial logistic regression model has found application in mi-croarray classication, where explicit identication of the most informativeobservations is of value. In this paper, we propose a sparse multinomial ker-nel logistic regression model, in which the sparsity arises from the use of aLaplacian prior and a fast exact algorithm is derive

This paper consists of two main parts. Firstly, we introduce an evolving binomial process from a binomial stock model and consider various types of limiting behavior of the logarithm of the evolving binomial process. Among others we find that the logarithm of the binomial process converges weakly to a Gaussian process. Secondly, we provide new approaches for proving the limit theorems for an integral process motivated by the evolving binomial process. We provide a new proof for the uniform stron