In the context of nonlinear regression, we consider the problem of explaining a variable y from a vector x of explanatory variables and from a vector t of conditionning variables, that influences the link function between y and x. A neural based solution is proposed in the form of a field of nonlinear regression models, by which it is meant that the relation between those variables is modeled b...

Orthogonal nonlinear least squares (ONLS) regression is a not so frequently applied and largely overlooked regression technique that comes into question when one encounters an ”error in variables” problem. While classical nonlinear least squares (NLS) aims to minimize the sum of squared vertical residuals, ONLS minimizes the sum of squared orthogonal residuals. The method is based on finding po...

The various methods of confidence intervals construction for nonlinear regression are considered. The new method named Ž . by a method of associated simulation the AS-method is proposed. Using computerized simulation, it is shown on the example that only two methods, the bootstrap and the AS-method, give a satisfactory accuracy. The advantage of the AS-method is the speed. In comparison with th...

An algorithm of the inductive model generation and model selection is proposed to solve the problem of automatic construction of regression models. A regression model is an admissible superposition of smooth functions given by experts. Coherent Bayesian inference is used to estimate model parameters. It introduces hyperparameters, which describe the distribution function of the model parameters...

Let (X; Y) be a pair of random variables with supp(X) 0; 1] and EY 2 < 1. Let m be the corresponding regression function. Estimation of m from i.i.d. data is considered. The L 2 error with integration with respect to the design measure (i.e., the distribution of X) is used as an error criterion. Estimates are constructed by estimating the coeecients of an orthonormal expansion of the regression...