• Journal of the Korean Data and Information Science Society
• /
• 제26권2호
• /
• pp.505-516
• /
• 2015

We consider sparse high-dimensional linear regression models. Penalized regressions have been used as effective methods for variable selection and estimation in high-dimensional models. In penalized regressions, it is common practice to standardize variables before fitting a penalized model and then fit a penalized model with standardized variables. Finally, the estimated coefficients from a penalized model are recovered to the scale on original variables. However, these procedures produce a slightly different solution compared to the corresponding original penalized problem. In this paper, we investigate issues on the standardization of variables in penalized regressions and formulate the definition of the standardized penalized estimator. In addition, we compare the original penalized estimator with the standardized penalized estimator through simulation studies and real data analysis.

• Communications for Statistical Applications and Methods
• /
• 제13권1호
• /
• pp.141-150
• /
• 2006

Penalized likelihood regression for exponential families have been considered by Kim (2005) through smoothing parameter selection and asymptotically efficient low dimensional approximations. We derive approximate Bayesian confidence intervals based on Bayes model associated with lower dimensional approximations to provide interval estimates in penalized likelihood regression and conduct empirical studies to access their properties.

• Journal of the Korean Statistical Society
• /
• 제26권1호
• /
• pp.23-30
• /
• 1997

We show that the Maximum Penalized Likelihood Estimate uniquely exits in a Sobolve spece which consists of bivariate density functions. The Maximum Penalized Likehood Estimate is represented as the square of the sum of the solutions of the Modified Helmholtz's equation on the compact subset of R$^{2}$.

• Korean Journal of Mathematics
• /
• 제4권2호
• /
• pp.179-193
• /
• 1996

This paper is concerned with the penalized stationary incompressible Navier-Stokes system with the inhomogeneous Dirichlet boundary condition on the part of the boundary. By taking a generalized velocity space on which the homogeneous essential boundary condition is imposed and corresponding trace space on the boundary, we pose the system to the weak form which the stress force is involved. We show the existence and convergence of the penalized system in the regular branch by extending the div-stability condition.

• Communications for Statistical Applications and Methods
• /
• 제14권1호
• /
• pp.23-32
• /
• 2007

We consider penalized likelihood regression with data from the negative binomial distribution with unknown shape parameter. Smoothing parameter selection and asymptotically efficient low dimensional approximations are employed for negative binomial data along with shape parameter estimation through several different algorithms.

• Communications for Statistical Applications and Methods
• /
• 제20권4호
• /
• pp.259-270
• /
• 2013

This paper considers a penalized composite quantile regression (CQR) that performs a variable selection in the linear model with grouped variables. An adaptive sup-norm penalized CQR (ASCQR) is proposed to select variables in a grouped manner; in addition, the consistency and oracle property of the resulting estimator are also derived under some regularity conditions. To improve the efficiency of estimation and variable selection, this paper suggests the two-stage penalized CQR (TSCQR), which uses the ASCQR to select relevant groups in the first stage and the adaptive lasso penalized CQR to select important variables in the second stage. Simulation studies are conducted to illustrate the finite sample performance of the proposed methods.

• Journal of the Korean Data and Information Science Society
• /
• 제28권6호
• /
• pp.1271-1278
• /
• 2017

Although the $L_0$-penalty is the most natural choice to identify the sparsity structure of the model, it has not been widely used due to the computational bottleneck. Recently, the adaptive ridge procedure is developed to efficiently approximate a $L_q$-penalized problem to an iterative $L_2$-penalized one. In this article, we proposed to apply the adaptive ridge procedure to solve the $L_0$-penalized weighted support vector machine (WSVM) to facilitate the corresponding optimization. Our numerical investigation shows the advantageous performance of the $L_0$-penalized WSVM compared to the conventional WSVM with $L_2$ penalty for both simulated and real data sets.

• Communications for Statistical Applications and Methods
• /
• 제27권3호
• /
• pp.349-363
• /
• 2020

Penalized spline is a suitable nonparametric approach in estimating mean model in small area. However, application of the approach in informative sampling in a published article is uncommon. We propose a semiparametric mixed-model using penalized spline under informative sampling to estimate mean of small area. The response variable is explained in terms of mean model, informative sample effect, area random effect and unit error. We approach the mean model by penalized spline and utilize a penalized spline function of the inclusion probability to account for the informative sample effect. We determine the best and unbiased estimators for coefficient model and derive the restricted maximum likelihood estimators for the variance components. A simulation study shows a decrease in the average absolute bias produced by the proposed model. A decrease in the root mean square error also occurred except in some quadratic cases. The use of linear and quadratic penalized spline to approach the function of the inclusion probability provides no significant difference distribution of root mean square error, except for few smaller samples.

• 응용통계연구
• /
• 제34권2호
• /
• pp.279-293
• /
• 2021

본 논문은 선형 회귀모형에서 벌점 추정량의 신의 성질에 대한 충분조건을 구성하는 방법을 소개하였다. 신의 추정량, 벌점 추정량, 신의 벌점 추정량, 신의 성질을 명확히 정의하였으며 이를 바탕으로 신의 성질에 대한 최적조건과 최적조건에 대한 충분조건을 구성하는 방법을 대부분의 벌점함수에 적용 가능하도록 하나의 통합된 원리로 소개하였다. 추가로 신의 성질에 대한 이해를 돕기 위해 간단한 예제와 함께 가상실험 결과를 첨부하였다.

• 응용통계연구
• /
• 제26권4호
• /
• pp.687-696
• /
• 2013

이상치가 존재하는 경우 모형 적합의 결과가 왜곡될 수 있기 때문에 이상치 탐색은 데이터분석에 있어서 매우 중요하다. 이상치 탐지 방법은 많은 학자들에 의해 연구되어 왔다. 본 논문에서는 Hadi와 Simonoff (1993)가 제안한 직접적 이상치 탐지 방법을 벌점 스플라인 회귀모형에 적용하여 이상치를 탐지하는 과정을 제안하며 모의실험과 실제 데이터에 적용을 통하여 스플라인 회귀모형, 강건 벌점 스플라인 회귀모형과 효율성을 비교한다.