Abstract: We consider M estimation of a regression model with a nuisance parameter and a vector of other parameters. The unknown distribution of the residuals is not assumed to be normal or symmetric. Simple and easily estimated formulas are given for the dominant terms of the bias and skewness of the parameter estimates. For the linear model these are proportional to the skewness of the ‘indep...

Piecewise affine systems serve as an important approximation of nonlinear systems. The identification of piecewise affine systems is here tackled by overparametrizing and assigning a regressor-parameter to each of the observations. Regressor parameters are then forced to be the same if that not causes a major increase in the fit term. The formulation takes the shape of a least-squares problem w...

Simple point-optimal sign-based tests are developed for inference on linear and nonlinear regression models with non-Gaussian heteroskedastic errors. The tests are exact, distribution-free, robust to heteroskedasticity of unknown form, and may be inverted to build confidence regions for the parameters of the regression function. Since point-optimal sign tests depend on the alternative hypothesi...

It is shown that the the popular least squares method of option pricing converges even under very general assumptions. This substantially increases the freedom of creating different implementations of the method, with varying levels of computational complexity and flexible approach to regression. It is also argued that in many practical applications even modest non-linear extensions of standard...

The consistency and asymptotic normality of the least squares estimator are derived for a particular non-linear regression model, which does not satisfy the standard sufficient conditions of Jennrich (1969) or Wu (19811, under the assumption of normal errors.

PURPOSE Linear least squares estimators are widely used in diffusion MRI for the estimation of diffusion parameters. Although adding proper weights is necessary to increase the precision of these linear estimators, there is no consensus on how to practically define them. In this study, the impact of the commonly used weighting strategies on the accuracy and precision of linear diffusion paramet...

An expression for the second-order approximation to the kurtosis associated with the least squares estimate of an individual parameter in a nonlinear regression model is derived, and connections between this and various other measures of curvature are made. Furthermore a means of predicting the reliability of the commonly-used Wald confidence intervals for individual model parameters, based on ...

We consider nonlinear and heteroscedastic autoregressive models whose residuals are martingale increments with conditional distributions that fulfill certain constraints. We treat two classes of constraints: residuals depending on the past through some function of the past observations only, and residuals that are invariant under some finite group of transformations. We determine the efficient ...