Optimal Inverse Beta (3,3) Transformation in Kernel Density Estimation

A double transformation kernel density estimator that is suitable for heavy-tailed distributions is presented. Using a double transformation, an asymptotically optimal bandwidth parameter can be calculated when minimizing the expression of the asymptotic mean integrated squared error of the transformed variable. Simulation results are presented showing that this approach performs better than existing alternatives. An application to insurance claim cost data is included

Frequency and Severity Dependence in the Collective Risk Model: An Approach Based on Sarmanov Distribution

In actuarial mathematics, the claims of an insurance portfolio are often modeled using the collective risk model, which consists of a random number of claims of independent, identically distributed (i.i.d.) random variables (r.v.s) that represent cost per claim. To facilitate computations, there is a classical assumption of independence between the random number of such random variables (i.e., the claims frequency) and the random variables themselves (i.e., the claim severities). However, recent studies showed that, in practice, this assumption does not always hold, hence, introducing dependence in the collective model becomes a necessity. In this sense, one trend consists of assuming dependence between the number of claims and their average severity (...

Nonparametric Estimation of Extreme Quantiles with an Application to Longevity Risk

A new method to estimate longevity risk based on the kernel estimation of the extreme quantiles of truncated age-at-death distributions is proposed. Its theoretical properties are presented and a simulation study is reported. The flexible yet accurate estimation of extreme quantiles of age-at-death conditional on having survived a certain age is fundamental for evaluating the risk of lifetime insurance. Our proposal combines a parametric distributions with nonparametric sample information, leading to obtain an asymptotic unbiased estimator of extreme quantiles for alternative distributions with different right tail shape, i.e., heavy tail or exponential tail. A method for estimating the longevity risk of a continuous temporary annuity is also shown. We illustrate our proposal with an application to the official age-at-death statistics of the population in Spain

Retos para el análisis y la estimación de la distribución de probabilidad en Big-data

En este documento se describen los principales conceptos relacionados con el ajuste no paramétrico de la distribución de probabilidades cuando se dispone de datos masivos y estos poseen fuerte asimetría a la derecha. En concreto, se estudian datos que representan perdidas positivas, que son muy heterogéneos y, por tanto, que pueden ser muy reducidos, cercanos a cero, o muy elevados y, además, pueden proceder de distintas distribuciones de probabilidad. Además, se mostrará cómo, aún disponiendo de una gran cantidad de datos, el efecto de la censura y el truncamiento sigue siendo un problema de falta de información que provoca grandes sesgos en los valores estimados. También, se describirán algunos resultados relacionados con la estimación paramétrica desde la perspectiva del uso de datos masivos. Finalmente, se presentarán algunos estimadores tipo núcleo, que ya han sido propuestos en la literatura, y que abordan algunas dificultades de los estimadores núcleos más clásicos cuando en los datos existen valores muy extremos los cuales es necesario modelizar para la cuantificación del riesgo

Multivariate count data generalized linear models: Three approaches based on the Sarmanov distribution

Starting from the question: What is the accident risk of an insured individual?, we consider that the customer has contracted policies in different insurance lines: motor and home. Three models based on the multivariate Sarmanov distribution are analyzed. Driven by a real data set that takes into account three types of accident risks, two for motor and one for home, three trivariate Sarmanov distributions with generalized linear models (GLMs) for marginals are considered and fitted to the data. To estimate the parameters of these three models, we discuss a method for approaching the maximum likelihood (ML) estimators. Finally, the three models are compared numerically with the simpler trivariate Negative Binomial GLM and with elliptical copula based models

Offshoring and company characteristics: some evidence from the analysis of Spanish firm data

This article investigates firm characteristics associated with the probability of relocating activities in a foreign country. Using manufacturing firms micro data for the 1999-2005 period, we find evidence that cost-cutting objectives are the main determinants for offshoring production. The analysis reveals that firms that are larger and have higher productivity, more research and development activity and greater human capital intensity are more likely to relocate activity abroad. Thus, the best firms self-select to offshoring activities. We note the special prominence of foreign firms among those that engage in offshoring. Our results show that self-selection of the best firms are much more significant in foreign firms

Measuring Intermediary Determinants of Early Childhood Health: A Composite Index Comparing Colombian Departments

In recent years there has been growing interest in composite indicators as an efficient tool of analysis and a method of prioritizing policies. This paper presents a composite index of intermediary determinants of child health using a multivariate statistical approach. The index shows how specific determinants of child health vary across Colombian departments (administrative subdivisions). We used data collected from the 2010 Colombian Demographic and Health Survey (DHS) for 32 departments and the capital city, Bogotá. Adapting the conceptual framework of Commission on Social Determinants of Health (CSDH), five dimensions related to child health are represented in the index: material circumstances, behavioural factors, psychosocial factors, biological factors and the health system. In order to generate the weight of the variables, and taking into account the discrete nature of the data, principal component analysis (PCA) using polychoric correlations was employed in constructing the index. From this method five principal components were selected. The index was estimated using a weighted average of the retained components. A hierarchical cluster analysis was also carried out. The results show that the biggest differences in intermediary determinants of child health are associated with health care before and during delivery

International industry migration and firm characteristics: some evidence from the analysis of firm data

This article examines firm characteristics associated with the probability of relocating part of the activity in a foreign country. Using manufacturing firms’ micro data for the 1999-2005 period, we find evidence that cost-cutting objectives are the main determinants for offshoring production, that firms with lower profits are more likely to undertake in-house offshoring, and that imports from low-wage countries increase the likelihood that part of the activity will be relocated. We also find that most offshoring firms are foreign – nearly 76% of the total

Factors affecting hospital admission and recovery stay duration of in-patient motor victims in Spain

Hospital expenses are a major cost driver of healthcare systems in Europe, with motor injuries being the leading mechanism of hospitalizations. This paper investigates the injury characteristics which explain the hospitalization of victims of traffic accidents that took place in Spain. Using a motor insurance database with 16.081 observations a generalized Tobit regression model is applied to analyse the factors that influence both the likelihood of being admitted to hospital after a motor collision and the length of hospital stay in the event of admission. The consistency of Tobit estimates relies on the normality of perturbation terms. Here a semi-parametric regression model was fitted to test the consistency of estimates, concluding that a normal distribution of errors cannot be rejected. Among other results, it was found that older men with fractures and injuries located in the head and lower torso are more likely to be hospitalized after the collision, and that they also have a longer expected length of hospital recovery stay

Non-parametric 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 non-parametric methods. The methods are implemented using the statistical package R. 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