The article is devoted to the nonparametric estimation of the quadratic covariation of non-synchronously observed Itô processes in an additive microstructure noise model. In a high-frequency setting, we aim at establishing an asymptotic distribution theory for a generalized multiscale estimator...

Given a random sample from some unknown density f0 : R → [0;∞) we devise Haar wavelet estimators for fo with variable resolution levels constructed from localised test procedures (as in Lepski, Mammen, and Spokoiny (1997, Ann. Statist.)). We show that these estimators adapt to spatially...

In many applications, covariates are not observed but have to be estimated from data. We outline some regression-type models where such a situation occurs and discuss estimation of the regression function in this context.We review theoretical results on how asymptotic properties of nonparametric...

We deal with two kinds of Cox regression models with varying coefficients. The coefficients vary with time in one model. In the other model, there is an important random variable called an index variable and the coefficients vary with the variable. In both models, we have p-dimensional...

We estimate linear functionals in the classical deconvolution problem by kernel estimators. We obtain a uniform central limit theorem with square root n rate on the assumption that the smoothness of the functionals is larger than the ill-posedness of the problem, which is given by the polynomial...

We give an overview over smooth back tting type estimators in additive models. Moreover we illustrate their wide applicability in models closely related to additive models such as nonparametric regression with dependent error variables where the errors can be transformed to white noise by a...

Standard fixed symmetric kernel type density estimators are known to encounter problems for positive random variables with a large probability mass close to zero. We show that in such settings, alternatives of asymmetric gamma kernel estimators are superior but also differ in asymptotic and...

Equity basket correlation is an important risk factor. It characterizes the strength of linear dependence between assets and thus measures the degree of portfolio diversification. It can be estimated both under the physical measure from return series, and under the risk neutral measure from...

Price indices for heterogenous goods such as real estate or fine art constitute crucial information for institutional or private investors considering alternative investments in times of financial markets turmoil. Classical mean-variance analysis of alternative investments has been hampered by...