We enlarge the number of available functional depths by introducing the kernelized functional spatial depth (KFSD). KFSD is a local-oriented and kernel-based version of the recently proposed functional spatial depth (FSD) that may be useful for studying functional samples that require an...

The standard efficient testing procedures in the Generalized Inverse Gaussian (GIG) family (also known as Halphen Type A family) are likelihood ratio tests, and hence rely on Maximum Likelihood (ML) estimation of the three parameters of the GIG. The particular form of GIG densities, involving...

Calibration, the statistical consistency of forecast distributions and observations, is a central requirement for probabilistic predictions. Calibration of continuous forecasts has been widely discussed, and significance tests are commonly used to detect whether a prediction model is...

<Para ID="Par1">Given a location-scale family generated by a distribution with smooth positive density, the aim is to provide distribution-free tests and confidence intervals for a skewness coefficient determined by three quantiles. It is the Bowley–Hinkley ratio <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$S_r/R_r$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <msub> <mi>S</mi> <mi>r</mi> </msub> <mo stretchy="false">/</mo> <msub> <mi>R</mi> <mi>r</mi> </msub> </mrow> </math> </EquationSource> </InlineEquation>, where <InlineEquation ID="IEq2"> <EquationSource...</equationsource></inlineequation></equationsource></equationsource></inlineequation></para>

<Para ID="Par1">This article is divided into two parts. In the first part, we review and study the properties of single-stage cross-sectional and time series benchmarking procedures that have been proposed in the literature in the context of small area estimation. We compare cross-sectional and time series...</para>

The class of generalized autoregressive conditional heteroscedastic (GARCH) models has been proved to be particularly valuable in modeling financial data. This paper is devoted to study the empirical characteristic function process of the residuals. Specifically, it is shown that such process...