The purpose of this paper is to introduce and examine two alternative, although similar, approaches to the Moving Blocks and subsampling Bootstraps to bootstrapping the estimator of the parameters for time series regression models. More specifically, the first bootstrap is based on resampling from the normalised discrete Fourier transform of the residuals of the model, whereas the second is fro...

In examining the adequacy of a statistical model, an analysis of the residuals is often performed. This includes anything from performing a residual analysis in a simple linear regression to utilizing one of the portmanteau tests in time-series analysis. When modeling an autoregressive-moving average time series we typically use the Ljung-Box statistic on the residuals to see if our fitted mode...

We consider the problem of estimating quantile regression coefficients in errors-in-variables models. When the error variables for both the response and the manifest variables have a joint distribution that is spherically symmetric but is otherwise unknown, the regression quantile estimates based on orthogonal residuals are shown to be consistent and asymptotically normal. We also extend the wo...

This paper is devoted to convergence problems of the Gasser-MMller estima-tor for the regression function in a xed-design regression model. We prove the asymptotic normality and rates of uniform strong convergence for this type of estimators under the-mixing condition on the residuals. The proof of strong convergence is based on a Bernstein-type inequality which is very similar to that derived ...

Error density estimation in a nonparametric functional regression model with functional predictor and scalar response is considered. The unknown error density is approximated by a mixture of Gaussian densities with means being the individual residuals, and variance as a constant parameter. This proposed mixture error density has a form of a kernel density estimator of residuals, where the regre...

The following notes illustrate the problem of temporally autocorrelated regression residuals that may arise when using time-series data (and represent the most common violation of the independent-residual assumption in regression modeling). Here the Durbin-Watson statistic is shown to provide diagnostic tool for identifying temporal autocorrelation, and the method of two-stage least squares is ...

This paper addresses estimation of linear functionals of the error distribution in nonparametric regression models. It derives an i.i.d. representation for the empirical estimator based on residuals, using undersmoothed estimators for the regression curve. Asymptotic efficiency of the estimator is proved. Estimation of the error variance is discussed in detail. In this case, undersmoothing is n...

We introduce directed goodness-of-fit tests for Cox-type regression models in survival analysis. "Directed" means that one may choose against which alternatives the tests are particularly powerful. The tests are based on sums of weighted martingale residuals and their asymptotic distributions.We derive optimal tests against certain competing models which include Cox-type regression models with ...

A new search metric is discussed that may be used to better assess the predictive capability of different math term combinations during the optimization of a regression model of experimental data. The new search metric can be determined for each tested math term combination if the given experimental data set is split into two subsets. The first subset consists of data points that are only used ...