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...

The paper presents smooth estimation of densities utilizing penalized splines. The idea is to represent the unknown density by a convex mixture of basis densities, where the weights are estimated in a penalized form. The proposed method extends the work of Komárek and Lesaffre (Comput Stat Data...

In this note we show that the mathematical tools of cooperative game theory allow a successful approach to the statistical problem of estimating a density function. Specifically, any random sample of an absolutely continuous random variable determines a transferable utility game, the Shapley...

A parameter of an econometric model is identified if there is a one-to-one or many-to-one mapping from the population distribution of the available data to the parameter. Often, this mapping is obtained by inverting a mapping from the parameter to the population distribution. If the inverse...

We propose a flexible nonparametric density estimator for panel data. One possible areas of application is estimation of crop yield distributions whose data tend to be short panels from many geographical units. Taking into account the panel structure of the data can likely improve the efficiency...