We consider a problem of estimation of parametric components in a partial linear model. Suppose that a finite set E of linear estimators is given. Our goal is to mimic the estimator in E that has the smallest risk. Using a second order expansion of the risk of linear estimators we propose a...

We consider a problem of estimation of parametric component in a partial linear model. Suppose that a finite set E of linear estimators is given. Our goal is to mimic the estimator in E that has the smallest risk. Using a second order expansion of the risk of linear estimators we propose a...

The problem of estimation of the finite dimensional parameter in a partial linear model is considered. We derive upper and lower bounds for the second minimax order risk and show that the second order minimax estimator is a penalized maximum likelihood estimator. It is well known that the...

Along with many others, we agree that a modern education in statistics needs to incorporate the practical analysis of real datasets, which are usually more complex than the common examples found in standard textbooks. The software used in the teaching of statistics includes standard spreadsheet...

This paper describes a method for testing a parametric model of the mean of a random variable <italic>Y</italic> conditional on a vector of explanatory variables <italic>X</italic> against a semiparametric alternative. The test is motivated by a conditional moment test against a parametric alternative and amounts to replacing...

We focus on the construction of confidence corridors for multivariate nonparametric generalized quantile regression functions. This construction is based on asymptotic results for the maximal deviation between a suitable nonparametric estimator and the true function of interest which follow...

Additive modelling has been widely used in nonparametric regression to circumvent the curse of dimensionality, by reducing the problem of estimating a multivariate regression function to the estimation of its univariate components. Estimation of these univariate functions, however, can suffer...

A major application of rescaled adjusted range analysis (RS analysis) is the study of price fluctuations in financial markets. There, the value of the Hurst constant, H, in a time series may be interpreted as an indicator of the irregularity of the price of a commodity, currency or similar...