Almost all of the current nonparametric regression methods such as smoothing splines, generalized additive models and varying coefficients models assume a linear relationship when nonparametric functions are regarded as parameters. In this article, we propose a general class of nonlinear nonparametric models that allow nonparametric functions to act nonlinearly. They arise in many fields as eit...

In this paper, we propose a covariate-adjusted nonlinear regression model. In this model, both the response and predictors can only be observed after being distorted by some multiplicative factors. Because of nonlinearity, existing methods for the linear setting cannot be directly employed. To attack this problem, we propose estimating the distorting functions by nonparametrically regressing th...

This paper is a survey of SAS System features for nonlinear models, with emphasis on new features for nonlinear regression. Topics include automatic calculation of analytic derivatives, estimation with nonlinear parameter restrictions, tests of nonlinear hypotheses, maximum likelihood and generalized method of moments (GMM) estimation, estimation of simultaneous systems of nonlinear regression ...

capital asset pricing model (capm) has been among the common models to estimate expected returns rate. since the linearity assumption is considered in the standard version of the capital asset pricing model, estimating beta in nonlinear setting will be inconsistent and bias-oriented. therefore, this study tries to evaluate predictive power of nonlinear capital asset pricing model as well as sta...

This paper proposes Maximal Associated Regression (MAR), a novel algorithm that performs forward stage-wise regression by applying nonlinear transformations to fit predictor covariates. For each predictor, MAR selects between linear or additive as determined the dataset. The proposed is an adaptation of Least Angle (LARS) and retains its efficiency in building sparse models. Constrained penaliz...

Piecewise regression represents a powerful tool to derive accurate yet modular models describing complex phenomena or physical systems. This paper presents an approach for learning PieceWise NonLinear (PWNL) functions in both supervised and semi-supervised setting. We further equip the proposed technique with method automatic generation of additional unsupervised data, which are leveraged impro...