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>

Statistical scientists have recently focused sharp attention on properties of iterated chaotic maps, with a view to employing such processes to model naturally occurring phenomena. In the present paper we treat the logistic map, which has earlier been studied in the context of modelling...