conclusions the use of smoothing methods helps us to eliminate non-linear effects but it is more appropriate to use cox proportional hazards model in medical data because of its’ ease of interpretation and capability of modeling both continuous and discrete covariates. also, cox proportional hazards model and smoothing methods analysis identified that age at diagnosis and tumor size were indepe...

In this paper we present a unified discussion of different approaches to the identification of smoothing spline analysis of variance (ANOVA) models: (i) the “classical” approach (in the line of Wahba in Spline Models for Observational Data, 1990; Gu in Smoothing Spline ANOVA Models, 2002; Storlie et al. in Stat. Sin., 2011) and (ii) the State-Dependent Regression (SDR) approach of Young in Nonl...

Accurate estimation of an underlying function and its derivatives is one of the central problems in statistics. Parametric forms are often proposed based on the expert opinion or prior knowledge of the underlying function. However, these strict parametric assumptions may result in biased estimates when they are not completely accurate. Meanwhile, nonparametric smoothing methods, which do not im...

This paper study about using of nonparametric models for Gross National Product data in Turkey and Stanford heart transplant data. It is discussed two nonparametric techniques called smoothing spline and kernel regression. The main goal is to compare the techniques used for prediction of the nonparametric regression models. According to the results of numerical studies, it is concluded that smo...

For a smoothing spline or general penalized spline model, the smoothing parameter can be estimated using residual maximum likelihood (REML) methods by expressing the spline in the form of a mixed model. The possibility of bimodality in the profile log-likelihood function for the smoothing parameter of these penalized spline mixed models is demonstrated. A canonical transformation into independe...

Smoothing noisy data with spline functions is well known in approximation theory. Smoothing splines have been used to deal with the problem of numerical differentiation. In this paper, we extend this method to estimate the fractional derivatives of a smooth signal from its discrete noisy data. We begin with finding a smoothing spline by solving the Tikhonov regularization problem. Then, we prop...

We proposed the I-spline Smoothing approach for calibrating predictive models by solving a nonlinear monotone regression problem. We took advantage of I-spline properties to obtain globally optimal solutions while keeping the computational cost low. Numerical studies based on three data sets showed the empirical evidences of I-spline Smoothing in improving calibration (i.e.,1.6x, 1.4x, and 1.4x...

in many area of medical research, a relation analysis between one response variable and some explanatory variables is desirable. regression is the most common tool in this situation. if we have some assumptions for such normality for response variable, we could use it. in this paper we propose a nonparametric regression that does not have normality assumption for response variable and we focus ...

The paper discusses asymptotic properties of penalized spline smoothing if the spline basis increases with the sample size. The proof is provided in a generalized smoothing model allowing for non-normal responses. The results are extended in two ways. First, assuming the spline coefficients to be a priori normally distributed links the smoothing framework to generalized linear mixed models (GLM...