Let <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$\mathcal{M }_{\underline{i}}$$</EquationSource> </InlineEquation> be an exponential family of densities on <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$[0,1]$$</EquationSource> </InlineEquation> pertaining to a vector of orthonormal functions <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$$b_{\underline{i}}=(b_{i_1}(x),\ldots ,b_{i_p}(x))^\mathbf{T}$$</EquationSource> </InlineEquation> and consider a problem of estimating a density <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$$f$$</EquationSource> </InlineEquation> belonging to such family for...</equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation>

In this paper, we propose a nonparametric method to estimate the spatial density of a functional stationary random field. This latter is with values in some infinite dimensional normed space and admitted a density with respect to some reference measure. We study both the weak and strong...

Resampling for stationary sequences has been well studied in the last couple of decades. In the paper at hand, we focus on nonstationary time series data where the nonstationarity is due to a slowly-changing deterministic trend. We show that the local block bootstrap methodology is appropriate...