A comparison of the alr and ilr transformations for kernel density estimation of compositional data

In a seminal paper, Aitchison and Lauder (1985) introduced classical kernel densityestimation techniques in the context of compositional data analysis. Indeed, they gavetwo options for the choice of the kernel to be used in the kernel estimator. One ofthese kernels is based on the use the alr transformation on the simplex SD jointly withthe normal distribution on RD-1. However, these authors themselves recognized thatthis method has some deficiencies. A method for overcoming these dificulties based onrecent developments for compositional data analysis and multivariate kernel estimationtheory, combining the ilr transformation with the use of the normal density with a fullbandwidth matrix, was recently proposed in Martín-Fernández, Chacón and Mateu-Figueras (2006). Here we present an extensive simulation study that compares bothmethods in practice, thus exploring the finite-sample behaviour of both estimators

Transformation kernel density estimation of actuarial loss functions

[cat] Es presenta un estimador nucli transformat que és adequat per a distribucions de cua pesada. Utilitzant una transformació basada en la distribució de probabilitat Beta l’elecció del paràmetre de finestra és molt directa. Es presenta una aplicació a dades d’assegurances i es mostra com calcular el Valor en Risc.

Transformation kernel density estimation of actuarial loss functions

[cat] Es presenta un estimador nucli transformat que és adequat per a distribucions de cua pesada. Utilitzant una transformació basada en la distribució de probabilitat Beta l’elecció del paràmetre de finestra és molt directa. Es presenta una aplicació a dades d’assegurances i es mostra com calcular el Valor en Risc.

Estimation of parametric and nonparametric models for univariate claim severity distributions - an approach using R

This paper presents an analysis of motor vehicle insurance claims relating to vehicle damage and to associated medical expenses. We use univariate severity distributions estimated with parametric and non-parametric methods. The methods are implemented using the statistical package R. Parametric analysis is limited to estimation of normal and lognormal distributions for each of the two claim types. The nonparametric analysis presented involves kernel density estimation. We illustrate the benefits of applying transformations to data prior to employing kernel based methods. We use a log-transformation and an optimal transformation amongst a class of transformations that produces symmetry in the data. The central aim of this paper is to provide educators with material that can be used in the classroom to teach statistical estimation methods, goodness of fit analysis and importantly statistical computing in the context of insurance and risk management. To this end, we have included in the Appendix of this paper all the R code that has been used in the analysis so that readers, both students and educators, can fully explore the techniques described

Inequalities for a new data-based method for selecting nonparametric density estimates

We continue the development of a method for the selection of a bandwidth or a number of design parameters in density estimation. We provideexplicit non-asymptotic density-free inequalities that relate the $L_1$ error of the selected estimate with that of the best possible estimate,and study in particular the connection between the richness of the classof density estimates and the performance bound. For example, our methodallows one to pick the bandwidth and kernel order in the kernel estimatesimultaneously and still assure that for {\it all densities}, the $L_1$error of the corresponding kernel estimate is not larger than aboutthree times the error of the estimate with the optimal smoothing factor and kernel plus a constant times $\sqrt{\log n/n}$, where $n$ is the sample size, and the constant only depends on the complexity of the family of kernels used in the estimate. Further applications include multivariate kernel estimates, transformed kernel estimates, and variablekernel estimates.

An Introduction to parametric and non-parametric models for bivariate positive insurance claim severity distributions

We present a real data set of claims amounts where costs related to damage are recorded separately from those related to medical expenses. Only claims with positive costs are considered here. Two approaches to density estimation are presented: a classical parametric and a semi-parametric method, based on transformation kernel density estimation. We explore the data set with standard univariate methods. We also propose ways to select the bandwidth and transformation parameters in the univariate case based on Bayesian methods. We indicate how to compare the results of alternative methods both looking at the shape of the overall density domain and exploring the density estimates in the right tail.

Grain size analyses in tin-lead glazes based on 2d-sections

A problem in the archaeometric classification of Catalan Renaissance pottery is the fact, thatthe clay supply of the pottery workshops was centrally organized by guilds, and thereforeusually all potters of a single production centre produced chemically similar ceramics.However, analysing the glazes of the ware usually a large number of inclusions in the glaze isfound, which reveal technological differences between single workshops. These inclusionshave been used by the potters in order to opacify the transparent glaze and to achieve a whitebackground for further decoration.In order to distinguish different technological preparation procedures of the single workshops,at a Scanning Electron Microscope the chemical composition of those inclusions as well astheir size in the two-dimensional cut is recorded. Based on the latter, a frequency distributionof the apparent diameters is estimated for each sample and type of inclusion.Following an approach by S.D. Wicksell (1925), it is principally possible to transform thedistributions of the apparent 2D-diameters back to those of the true three-dimensional bodies.The applicability of this approach and its practical problems are examined using differentways of kernel density estimation and Monte-Carlo tests of the methodology. Finally, it istested in how far the obtained frequency distributions can be used to classify the pottery

A generalization of histogram type estimators

We introduce simple nonparametric density estimators that generalize theclassical histogram and frequency polygon. The new estimators are expressed as linear combination of density functions that are piecewisepolynomials, where the coefficients are optimally chosen in order to minimize the integrated square error of the estimator. We establish the asymptotic behaviour of the proposed estimators, and study theirperformance in a simulation study.

Variable Kernel estimates: On the impossibility of tuning the parameters

For the standard kernel density estimate, it is known that one can tune the bandwidth such that the expected L1 error is within a constant factor of the optimal L1 error (obtained when one is allowed to choose the bandwidth with knowledge of the density). In this paper, we pose the same problem for variable bandwidth kernel estimates where the bandwidths are allowed to depend upon the location. We show in particular that for positive kernels on the real line, for any data-based bandwidth, there exists a densityfor which the ratio of expected L1 error over optimal L1 error tends to infinity. Thus, the problem of tuning the variable bandwidth in an optimal manner is ``too hard''. Moreover, from the class of counterexamples exhibited in the paper, it appears thatplacing conditions on the densities (monotonicity, convexity, smoothness) does not help.

Interactive local bandwidth choice

A tool for user choice of the local bandwidth function for a kernel density estimate is developed using KDE, a graphical object-oriented package for interactive kernel density estimation written in LISP-STAT. The bandwidth function is a cubic spline, whose knots are manipulated by the user in one window, while the resulting estimate appears in another window. A real data illustration of this method raises concerns, because an extremely large family of estimates is available.

Variance reduction methods for simulation of densities on Wiener space

We develop a general error analysis framework for the Monte Carlo simulationof densities for functionals in Wiener space. We also study variancereduction methods with the help of Malliavin derivatives. For this, wegive some general heuristic principles which are applied to diffusionprocesses. A comparison with kernel density estimates is made.

Almost sure testability of classes of densities

Let a class $\F$ of densities be given. We draw an i.i.d.\ sample from a density $f$ which may or may not be in $\F$. After every $n$, one must make a guess whether $f \in \F$ or not. A class is almost surely testable if there exists such a testing sequence such that for any $f$, we make finitely many errors almost surely. In this paper, several results are given that allowone to decide whether a class is almost surely testable. For example, continuity and square integrability are not testable, but unimodality, log-concavity, and boundedness by a given constant are.

Hypernormal densities

We propose a new family of density functions that possess both flexibilityand closed form expressions for moments and anti-derivatives, makingthem particularly appealing for applications. We illustrate its usefulnessby applying our new family to obtain density forecasts of U.S. inflation.Our methods generate forecasts that improve on standard methods based on AR-ARCH models relying on normal or Student's t-distributional assumptions.

Changes in the enterocyte cytoskeleton in newborn rats exposed to ethanol in utero

BACKGROUND: Cytoskeletal changes after longterm exposure to ethanol have been described in a number of cell types in adult rat and humans. These changes can play a key part in the impairment of nutrient assimilation and postnatal growth retardation after prenatal damage of the intestinal epithelium produced by ethanol intake. AIMS: To determine, in the newborn rat, which cytoskeletal proteins are affected by longterm ethanol exposure in utero and to what extent. ANIMALS: The offspring of two experimental groups of female Wistar rats: ethanol treated group receiving up to 25% (w/v) of ethanol in the drinking fluid and control group receiving water as drinking fluid. METHODS: Single and double electron microscopy immunolocalisation and label density estimation of cytoskeletal proteins on sections of proximal small intestine incubated with monoclonal antibodies against actin, alpha-tubulin, cytokeratin (polypeptides 1, 5, 6, 7, 8, 10, 11, and 18), and with a polyclonal antibody anti-beta 1,4-galactosyl transferase as trans golgi (TG) or trans golgi network (TGN) marker, or both. SDS-PAGE technique was also performed on cytoskeletal enriched fractions from small intestine. Western blotting analysis was carried out by incubation with the same antibodies used for immunolocalisation. RESULTS: Intestinal epithelium of newborn rats from the ethanol treated group showed an overexpression of cytoskeletal polypeptides ranging from 39 to 54 kDa, affecting actin and some cytokeratins, but not tubulin. Furthermore, a cytokeratin related polypeptide of 28-29 kDa was identified together with an increase in free ubiquitin in the same group. It was noteworthy that actin and cytokeratin were abnormally located in the TG or the TGN, or both. CONCLUSIONS: Longterm exposure to ethanol in utero causes severe dysfunction in the cytoskeleton of the developing intestinal epithelium. Actin and cytokeratins, which are involved in cytoskeleton anchoring to plasma membrane and cell adhesion, are particularly affected, showing overexpression, impaired proteolysis, and mislocalisation.

Changes in the enterocyte cytoskeleton in newborn rats exposed to ethanol in utero

BACKGROUND: Cytoskeletal changes after longterm exposure to ethanol have been described in a number of cell types in adult rat and humans. These changes can play a key part in the impairment of nutrient assimilation and postnatal growth retardation after prenatal damage of the intestinal epithelium produced by ethanol intake. AIMS: To determine, in the newborn rat, which cytoskeletal proteins are affected by longterm ethanol exposure in utero and to what extent. ANIMALS: The offspring of two experimental groups of female Wistar rats: ethanol treated group receiving up to 25% (w/v) of ethanol in the drinking fluid and control group receiving water as drinking fluid. METHODS: Single and double electron microscopy immunolocalisation and label density estimation of cytoskeletal proteins on sections of proximal small intestine incubated with monoclonal antibodies against actin, alpha-tubulin, cytokeratin (polypeptides 1, 5, 6, 7, 8, 10, 11, and 18), and with a polyclonal antibody anti-beta 1,4-galactosyl transferase as trans golgi (TG) or trans golgi network (TGN) marker, or both. SDS-PAGE technique was also performed on cytoskeletal enriched fractions from small intestine. Western blotting analysis was carried out by incubation with the same antibodies used for immunolocalisation. RESULTS: Intestinal epithelium of newborn rats from the ethanol treated group showed an overexpression of cytoskeletal polypeptides ranging from 39 to 54 kDa, affecting actin and some cytokeratins, but not tubulin. Furthermore, a cytokeratin related polypeptide of 28-29 kDa was identified together with an increase in free ubiquitin in the same group. It was noteworthy that actin and cytokeratin were abnormally located in the TG or the TGN, or both. CONCLUSIONS: Longterm exposure to ethanol in utero causes severe dysfunction in the cytoskeleton of the developing intestinal epithelium. Actin and cytokeratins, which are involved in cytoskeleton anchoring to plasma membrane and cell adhesion, are particularly affected, showing overexpression, impaired proteolysis, and mislocalisation.