Fuzzy linear regression analysis with symmetric triangular fuzzy number coefficient has been introduced by Tanaka et al. In this work we propose to approximate the fuzzy nonlinear regression using Artificial Neural Networks. The working of the proposed method is illustrated by the case study with the data for temperature and evaporation for the IARI New Delhi division. MSC: 62J86

This paper derives the asymptotic normality of the nonlinear quantile regression estimator with dependent errors. The required assumptions are weak, and it is neither assumed that the error process is stationary nor that it is mixing. In fact, the notion of weak dependence introduced in this paper, can be considered as a quantile specific local variant of known concepts. The connection of the d...

We consider the problem of modeling the mean function in regression. Often there is enough knowledge to model some components of the mean function parametrically. But for other vague and/or nuisance components, it is often desirable to leave them unspecified and to be modeled nonparametrically. In this article, we propose a general class of smoothing spline semi-parametric nonlinear regression ...

We introduce continuously additive models, which can be motivated as extensions of additive regression models with vector predictors to the case of infinite-dimensional predictors. This approach provides a class of flexible functional nonlinear regression models, where random predictor curves are coupled with scalar responses. In continuously additive modeling, integrals taken over a smooth sur...

The optimization problems occurring in nonlinear regression normally cannot be proven unimodal. In the present paper applicability of global optimization algorithms to this problem is investigated with the focus on interval arithmetic based algorithms.

An asymptotic theory is developed for a weakly identified cointegrating regression model in which the regressor is a nonlinear transformation of an integrated process. Weak identification arises from the presence of a loading coefficient for the nonlinear function that may be close to zero. In that case, standard nonlinear cointegrating limit theory does not provide good approximations to the f...

When doing regression with inputs and outputs that are high-dimensional, it often makes sense to reduce the dimensionality of the inputs before mapping to the outputs. Much work in statistics and machine learning, such as reduced-rank regression, sliced inverse regression and their variants, has focused on linear dimensionality reduction, or on estimating the dimensionality reduction first and ...

This lecture presents some methods which we can apply in searching for confidence regions and intervals for true values of regression parameters. The nonlinear regression models with independent and identically distributed errors and Lp norm estimators are discussed.

We consider kernel quantile estimates for drift and scale functions in nonlinear stochastic regression models. Under a general dependence setting, we establish asymptotic point-wise and uniform Bahadur representations for the kernel quantile estimates. Based on those asymptotic representations, central limit theorems are obtained. Applications to nonlinear autoregressive models and linear proce...

We present a new method for obtaining local error bars for nonlinear regression, i.e., estimates of the confidence in predicted values that depend on the input. We approach this problem by applying a maximumlikelihood framework to an assumed distribution of errors. We demonstrate our method first on computer-generated data with locally varying, normally distributed target noise. We then apply i...