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.

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.

Growth of positive words and lower bounds of the growth rate for Thompson's group (F)p

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Parametric and semiparametric estimation of sample selection models: an empirical application to the female labour force in Portugal

This comment corrects the errors in the estimation process that appear in Martins (2001). The first error is in the parametric probit estimation, as the previously presented results do not maximize the log-likelihood function. In the global maximum more variables become significant. As for the semiparametric estimation method, the kernel function used in Martins (2001) can take on both positive and negative values, which implies that the participation probability estimates may be outside the interval [0,1]. We have solved the problem by applying local smoothing in the kernel estimation, as suggested by Klein and Spady (1993).

Elements of algebraic geometry and the positive theory of partially commutative groups

The first main result of the paper is a criterion for a partially commutative group G to be a domain. It allows us to reduce the study of algebraic sets over G to the study of irreducible algebraic sets, and reduce the elementary theory of G (of a coordinate group over G) to the elementary theories of the direct factors of G (to the elementary theory of coordinate groups of irreducible algebraic sets). Then we establish normal forms for quantifier-free formulas over a non-abelian directly indecomposable partially commutative group H. Analogously to the case of free groups, we introduce the notion of a generalised equation and prove that the positive theory of H has quantifier elimination and that arbitrary first-order formulas lift from H to H * F, where F is a free group of finite rank. As a consequence, the positive theory of an arbitrary partially commutative group is decidable.

Positive solutions of nonlinear problems involving the square root of the Laplacian

We consider nonlinear elliptic problems involving a nonlocal operator: the square root of the Laplacian in a bounded domain with zero Dirichlet boundary conditions. For positive solutions to problems with power nonlinearities, we establish existence and regularity results, as well as a priori estimates of Gidas-Spruck type. In addition, among other results, we prove a symmetry theorem of Gidas-Ni-Nirenberg type.

Two weight inequalities for discrete positive operators

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Beurling-Landau densities of weighted Fekete sets and correlation kernel estimates

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A new automated method versus continuous positive airway pressure method for measuring pressure-volume curves in patients with acute lung injury

Objective: To compare pressure–volume (P–V) curves obtained with the Galileo ventilator with those obtained with the CPAP method in patients with ALI or ARDS receiving mechanical ventilation. P–V curves were fitted to a sigmoidal equation with a mean R2 of 0.994 ± 0.003. Lower (LIP) and upper inflection (UIP), and deflation maximum curvature (PMC) points calculated from the fitted variables showed a good correlation between methods with high intraclass correlation coefficients. Bias and limits of agreement for LIP, UIP and PMC obtained with the two methods in the same patient were clinically acceptable.

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

Distribution of events of positive selection and population differentiation in a metabolic pathway: the case of asparagine N-glycosylation

Background: Asparagine N-Glycosylation is one of the most important forms of protein post-translational modification in eukaryotes. This metabolic pathway can be subdivided into two parts: an upstream sub-pathway required for achieving proper folding for most of the proteins synthesized in the secretory pathway, and a downstream sub-pathway required to give variability to trans-membrane proteins, and involved in adaptation to the environment andinnate immunity. Here we analyze the nucleotide variability of the genes of this pathway in human populations, identifying which genes show greater population differentiation and which genes show signatures of recent positive selection. We also compare how these signals are distributed between the upstream and the downstream parts of the pathway, with the aim of exploring how forces of population differentiation and positive selection vary among genes involved in the same metabolic pathway but subject to different functional constraints. Results:Our results show that genes in the downstream part of the pathway are more likely to show a signature of population differentiation, while events of positive selection are equally distributed among the two parts of the pathway. Moreover, events of positive selection arefrequent on genes that are known to be at bifurcation points, and that are identified as beingin key position by a network-level analysis such as MGAT3 and GCS1.Conclusions: These findings indicate that the upstream part of the Asparagine N-Glycosylation pathway has lower diversity among populations, while the downstream part is freer to tolerate diversity among populations. Moreover, the distribution of signatures of population differentiation and positive selection can change between parts of a pathway, especially between parts that are exposed to different functional constraints. Our results support the hypothesis that genes involved in constitutive processes can be expected to show lower population differentiation, while genes involved in traits related to the environment should show higher variability. Taken together, this work broadens our knowledge on how events of population differentiation and of positive selection are distributed among different parts of a metabolic pathway.

African signatures of recent positive selection in human FOXI1

Background: The human FOXI1 gene codes for a transcription factor involved in the physiology of the inner ear, testis, and kidney. Using three interspecies comparisons, it has been suggested that this may be a gene underhuman-specific selection. We sought to confirm this finding by using an extended set of orthologous sequences.Additionally, we explored for signals of natural selection within humans by sequencing the gene in 20 Europeans,20 East Asians and 20 Yorubas and by analysing SNP variation in a 2 Mb region centered on FOXI1 in 39worldwide human populations from the HGDP-CEPH diversity panel.Results: The genome sequences recently available from other primate and non-primate species showed that FOXI1divergence patterns are compatible with neutral evolution. Sequence-based neutrality tests were not significant inEuropeans, East Asians or Yorubas. However, the Long Range Haplotype (LRH) test, as well as the iHS and XP-Rsbstatistics revealed significantly extended tracks of homozygosity around FOXI1 in Africa, suggesting a recentepisode of positive selection acting on this gene. A functionally relevant SNP, as well as several SNPs either on theputatively selected core haplotypes or with significant iHS or XP-Rsb values, displayed allele frequencies stronglycorrelated with the absolute geographical latitude of the populations sampled.Conclusions: We present evidence for recent positive selection in the FOXI1 gene region in Africa. Climate mightbe related to this recent adaptive event in humans. Of the multiple functions of FOXI1, its role in kidney-mediatedwater-electrolyte homeostasis is the most obvious candidate for explaining a climate-related adaptation.

Asymmetric effects of monetary policy in the US: Positive vs. negative or big vs. small?

This paper reconsiders the empirical evidence on the asymmetricoutput effects of monetary policy. Asymmetric effects is a common feature ofmany theoretical models, and there are many different versions of suchasymmetries. We concentrate on the distinctions between positive andnegative money-supply changes, big and small changes in money-supply, andpossible combinations of the two asymmetries. Earlier research has foundempirical evidence in favor of the former of these in US data. Using M1 asthe monetary variable we find evidence in favor of neutrality of big shocksand non-neutrality of small shocks. The results may, however, be affected bystructual instability of M1 demand. Thus, we substitute M1 with the federalfunds rate. In these data we find that only small negative shocks affectreal aggregate activity. The results are interpreted in terms of menu-costmodels.

Weighted Kernel regression

In the fixed design regression model, additional weights areconsidered for the Nadaraya--Watson and Gasser--M\"uller kernel estimators.We study their asymptotic behavior and the relationships between new andclassical estimators. For a simple family of weights, and considering theIMSE as global loss criterion, we show some possible theoretical advantages.An empirical study illustrates the performance of the weighted estimatorsin finite samples.