• Journal of the Korean Geophysical Society
• /
• v.4 no.3
• /
• pp.175-182
• /
• 2001

We consider the problem of determining smoothing parameters of Gibbs priors for Bayesian methods used in the medical imaging application of emission tomographic reconstruction. We address a simple smoothing prior (membrane) whose global hyperparameter (the smoothing parameter) controls the bias/variance tradeoff of the solution. We base our maximum-likelihood (ML) estimates of hyperparameters on observed training data, and argue the motivation for this approach. Good results are obtained with a simple ML estimate of the smoothing parameter for the membrane prior.

• The Journal of Engineering Research
• /
• v.4 no.1
• /
• pp.47-54
• /
• 2002

We consider the problem of determining smoothing parameters of Gibbs priors for Bayesian methods used in the medical imaging application of emission tomographic reconstruction. We address a simple smoothing prior (membrane) whose global hyperparameter (the smoothing parameter) controls the bias/variance tradeoff of the solution. We base our maximum-likelihood(ML) estimates of hyperparameters on observed training data, and argue the motivation for this approach. Good results are obtained with a simple ML estimate of the smoothing parameter for the membrane prior.

• Journal of applied mathematics & informatics
• /
• v.17 no.1_2_3
• /
• pp.401-418
• /
• 2005

In this paper, a dual algorithm, based on a smoothing function of Bertsekas (1982), is established for solving unconstrained minimax problems. It is proven that a sequence of points, generated by solving a sequence of unconstrained minimizers of the smoothing function with changing parameter t, converges with Q-superlinear rate to a Kuhn-Thcker point locally under some mild conditions. The relationship between the condition number of the Hessian matrix of the smoothing function and the parameter is studied, which also validates the convergence theory. Finally the numerical results are reported to show the effectiveness of this algorithm.

• Journal of the Korean Statistical Society
• /
• v.30 no.4
• /
• pp.645-660
• /
• 2001

In this paper we propose a goodness-of-fit test statistic for testing the (null) parametric model versus the (alternative) nonparametric model. Most of existing nonparametric test statistics are based on the residuals which are obtained by regressing the data to a parametric model. Our test is based on the bootstrap estimator of the probability that the smoothing parameter estimator is infinite when fitting residuals to cubic smoothing spline. Power performance of this test is investigated and is compared with many other tests. Illustrative examples based on real data sets are given.

• Journal of the Korean Institute of Telematics and Electronics B
• /
• v.29B no.1
• /
• pp.85-93
• /
• 1992

In this paper, we propose a parameter-free smoothing method for speckle images, i.e., an adaptive least squares image smoothing technique implemented in a multistep environment. The pertinent smoothing window size at a given pixel is determined by the discontinuity measure which is defined by the ratio of the local variance and mean squares of intensity values of pixels over the smoothing window centered there. The mode of the discontinuity measure at each step is estimated to replace the noise variance parameter that is required in the adaptive smoothing. Computer simulation shows that the proposed multistep technique can smooth homogeneous regions satisfactorily while preserving fine details near boundaries.

• Journal of the Korean Data and Information Science Society
• /
• v.6 no.1
• /
• pp.63-71
• /
• 1995

We have consider the study of local influence for smoothing parameter estimates in spline regression model with heteroscedasticity. Practically, generalized cross-validation does not work well in the presence of heteroscedasticity. Thus we have proposed the local influence measure for generalized cross-validation estimates when errors are heteroscedastic. And we have examined effects of diagnostic by above measures through Hyperinflation data.

• Communications for Statistical Applications and Methods
• /
• v.2 no.2
• /
• pp.266-276
• /
• 1995

We have considered the study of local influence for smoothing parameter estimates in nonparametric regression model. Practically, generalized cross validation(GCV) does not work well in the presence of data perturbation. Thus we have proposed local influence measures for GCV estimates and examined effects of diagnostic by above measures.

• Communications for Statistical Applications and Methods
• /
• v.13 no.1
• /
• 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 Vacuum Society
• /
• v.5 no.2
• /
• pp.99-106
• /
• 1996

Two types of regularization method (singular system and HMP approaches) for generating depth-concentration profiles from angle-resolved XPS data were evaluated. Both approaches showed qualitatively similar results although they employed different numerical algorithms. The application of the regularization method to simulated data demonhstrates its excellent utility for the complex depth profile system . It includes the stable restoration of depth-concentration profiles from the data with considerable random error and the self choice of smoothing parameter that is imperative for the successful application of the regularization method. The self choice of smoothing parameter is based on generalized cross-validation method which lets the data themselves choose the optimal value of the parameter.

• Communications for Statistical Applications and Methods
• /
• v.12 no.2
• /
• pp.413-423
• /
• 2005

Consider the problem of estimating the underlying regression function from a set of noisy data which is contaminated by a long tailed error distribution. There exist several robust smoothing techniques and these are turned out to be very useful to reduce the influence of outlying observations. However, no matter what kind of robust smoother we use, we should choose the smoothing parameter and relatively less attention has been made for the robust bandwidth selection method. In this paper, we adopt the idea of robust location parameter estimation technique and propose the robust cross validation score functions.