Data processing and source identification using lower dimensional hidden structure plays an essential role in many fields of applications, including image processing, neural networks, genome studies, signal processing and other areas where large datasets are often encountered. One of the common...

We suggest a new approach for forecasting energy demand at an intraday resolution. The demand in each intraday period is modeled using semiparametric regression smoothing to account for calendar and weather components. Residual serial dependence is captured by one of two multivariate stationary...

Abstract Many statistical estimation techniques for high-dimensional or functional data are based on a preliminary dimension reduction step, which consists in projecting the sample X 1 ,..., X n onto the first D eigenvectors of the Principal Component Analysis (PCA) associated with the empirical...

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We present two deconvolution estimators for the density function of a random variable X that is measured with error. The first estimates the density of X from the set of independent replicate measurements W[subscript r,j], where W[subscript r,j]=X[subscript x]+U[subscript r,j] for r=1,...,n and...

Denote the integer lattice points in the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$N$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>N</mi> </math> </EquationSource> </InlineEquation>-dimensional Euclidean space by <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$\mathbb {Z}^N$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msup> <mrow> <mi mathvariant="double-struck">Z</mi> </mrow> <mi>N</mi> </msup> </math> </EquationSource> </InlineEquation> and assume that <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$X_\mathbf{n}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi>X</mi> <mi mathvariant="bold">n</mi> </msub> </math> </EquationSource> </InlineEquation>, <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$\mathbf{n} \in \mathbb {Z}^N$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi mathvariant="bold">n</mi> <mo>∈</mo> <msup> <mrow> <mi mathvariant="double-struck">Z</mi> </mrow> <mi>N</mi> </msup> </mrow> </math> </EquationSource> </InlineEquation> is a linear random field. Sharp rates of convergence of histogram estimates...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

In this paper a k-nearest neighbor type estimator of the marginal density function for a random field which evolves with time is considered. Considering dependence, the consistency and asymptotic distribution are studied for the stationary and nonstationary cases. In particular, the parametric...

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 practical applications related to, for instance, machine learning, data mining and pattern recognition, one is commonly dealing with noisy data lying near some low-dimensional manifold. A well-established tool for extracting the intrinsically low-dimensional structure from such data is...