We propose an approach to multivariate nonparametric regression that generalizes reduced rank regression for linear models. An additive model is estimated for each dimension of a q-dimensional response, with a shared p-dimensional predictor variable. To control the complexity of the model, we employ a functional form of the Ky-Fan or nuclear norm, resulting in a set of function estimates that h...

In this paper we describe two approaches to nonparametric regression. First, we consider the nearest neighbour approach, as a procedure which serves mainly for obtaining an ad hoc smoothing and interpolating. Next, we describe the roughness penalty approach. This gives a certain compromise between the demand for goodness-of-fit of regression curve to the given data and the condition that the re...

As in many areas of biostatistics, oncological problems often have multivariate predictors. While assuming a linear additive model is convenient and straightforward, it is often not satisfactory when the relation between the outcome measure and the predictors is either nonlinear or nonadditive. In addition, when the number of predictors becomes (much) larger than the number of independent obser...

We present algorithms for nonparametric regression in settings where the data are obtained sequentially. While traditional estimators select bandwidths that depend upon the sample size, for sequential data the effective sample size is dynamically changing. We propose a linear time algorithm that adjusts the bandwidth for each new data point, and show that the estimator achieves the optimal mini...

We deal with nonparametric estimation in a nonlinear cointegration model whose regressor and dependent variable can be contemporaneously correlated. The asymptotic properties of the Nadaraya-Watson estimator are already examined in the literature. In this paper, we consider nonparametric least absolute deviation (LAD) regression and derive the asymptotic distributions of the local constant and ...

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...

This paper deals with ridge estimation of fuzzy nonparametric regression models using triangular fuzzy numbers. This estimation method is obtained by implementing ridge regression learning algorithm in the La- grangian dual space. The distance measure for fuzzy numbers that suggested by Diamond is used and the local linear smoothing technique with the cross- validation procedure for selecting t...

The nonparametric estimation(NE) of kernel polynomial regression (KPR) model is a powerful tool to visually depict the effect of covariates on response variable, when there exist unstructured and heterogeneous data. In this paper we introduce KPR model that is the mixture of nonparametric regression models with bootstrap algorithm, which is considered in a heterogeneous and unstructured framewo...

This paper considers a class of nonparametric autoregression models with nonstationarity in the mean and then a class of nonparametric time series regression models with nonstationarity in both the conditional mean and conditional variance. For the nonparametric autoregression case, we propose a nonparametric unit–root test for the conditional mean. For the nonparametric time series regression ...

This paper gives a detailed overview of the problem of missing data in parametric and nonparametric regression. Theoretical basics, properties as well as simulation results may help the reader to get familiar with the common problem of incomplete data sets. Of course, not all occurences can be discussed so this paper could be seen as an introduction to missing data within regression analysis an...