A primary goal in modelling the dynamics of implied volatility surfaces (IVS) aims at reducing complexity. For this purpose one fits the IVS each day and applies a principal component analysis using a functional norm. This approach, however, neglects the degenerated string structure of the...

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...

One of the most difficult problems in applications of semiparametric generalized partially linear single-index model (GPLSIM) is the choice of pilot estimators and complexity parameters which may result in radically different estimators. Pilot estimators are often assumed to be root-n...

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...