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...

We propose marginal integration estimation and testing methods for the coefficients of varying coefficient multivariate regression model. Asymptotic distribution theory is developed for the estimation method which enjoys the same rate of convergence as univariate function estimation. For the...

Let a process SI , ... ,ST obey the conditionally heteroskedastic equation St = Vt Et whcrc Et is a random noise and Vt is the volatility coefficient which in turn obeys an autoregression type equation log v t = w + a S t- l + nt with an additional noise nt. We consider the situation which the...

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...

Models are studied where the response Y and covariates X, T are assumed to fulfill E(Y|X; T) = G{XT β + α + m1(T1) + … + md(Td)}. Here G is a known (link) function, β is an unknown parameter, and m1, …, md are unknown functions. In particular, we consider additive binary response models...

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...

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...