Most Likely Transformations

We propose and study properties of maximum likelihood estimators in the class of conditional transformation models. Based on a suitable explicit parameterisation of the unconditional or conditional transformation function, we establish a cascade of increasingly complex transformation models that can be estimated, compared and analysed in the maximum likelihood framework. Models for the unconditional or conditional distribution function of any univariate response variable can be set-up and estimated in the same theoretical and computational framework simply by choosing an appropriate transformation function and parameterisation thereof. The ability to evaluate the distribution function directly allows us to estimate models based on the exact likelihood, especially in the presence of random censoring or truncation. For discrete and continuous responses, we establish the asymptotic normality of the proposed estimators. A reference software implementation of maximum likelihood-based estimation for conditional transformation models allowing the same flexibility as the theory developed here was employed to illustrate the wide range of possible applications.Comment: Accepted for publication by the Scandinavian Journal of Statistics 2017-06-1

Adaptive Premiums for Evolutionary Claims in Non-Life Insurance

Rapid growth in heavy-tailed claim severity in commercial liability insurance requires insurer response by way of flexible mechanisms to update premiums. To this end in this paper a new premium principle is established for heavy-tailed claims, and its properties investigated. Risk-neutral premiums for heavy-tailed claims are consistently and unbiasedly estimated by the ratio of the first two extremes of the claims distribution. That is, the heavy-tailed risk-neutral premium has a Pareto distribution with the same tail-index as the claims distribution. Insurers must predicate premiums on larger tail-index values, if solvency is to be maintained. Additionally, the structure of heavy-tailed premiums is shown to lead to a natural model for tail-index imprecision (demonstrably inescapable in the sample sizes with which we deal). Premiums which compensate for tail-index uncertainty preserve the ratio structure of risk-neutral premiums, but make a 'prudent' adjustment which reflects the insurer's risk-profile. An example using Swiss Re's (1999) major disaster data is used to illustrate application of the methodology to the largest claims in any insurance class.Insurance Claims, Premiums, Tail-Index, Extreme Values

Direct modeling of the crude probability of cancer death and the number of life years lost due to cancer without the need of cause of death: a pseudo-observation approach in the relative survival setting.

In population-based cancer studies, net survival is a crucial measure for population comparison purposes. However, alternative measures, namely the crude probability of death (CPr) and the number of life years lost (LYL) due to death according to different causes, are useful as complementary measures for reflecting different dimensions in terms of prognosis, treatment choice, or development of a control strategy. When the cause of death (COD) information is available, both measures can be estimated in competing risks setting using either cause-specific or subdistribution hazard regression models or with the pseudo-observation approach through direct modeling. We extended the pseudo-observation approach in order to model the CPr and the LYL due to different causes when information on COD is unavailable or unreliable (i.e., in relative survival setting). In a simulation study, we assessed the performance of the proposed approach in estimating regression parameters and examined models with different link functions that can provide an easier interpretation of the parameters. We showed that the pseudo-observation approach performs well for both measures and we illustrated their use on cervical cancer data from the England population-based cancer registry. A tutorial showing how to implement the method in R software is also provided

Inference for the process performance index of products on the basis of power-normal distribution

[[abstract]]The process performance index (PPI) can be a simple metric to connect the conforming rate of products. The properties of the PPI have been well studied for the normal distribution and other widely used lifetime distributions, such as the Weibull, Gamma, and Pareto distributions. Assume that the quality characteristic of product follows power-normal distribution. Statistical inference procedures for the PPI are established. The maximum likelihood estimation method for the model parameters and PPI is investigated and the exact Fisher information matrix is derived. We discuss the drawbacks of using the exact Fisher information matrix to obtain the confidence interval of the model parameters. The parametric bootstrap percentile and bootstrap bias-corrected percentile methods are proposed to obtain approximate confidence intervals for the model parameters and PPI. Monte Carlo simulations are conducted to evaluate the performance of the proposed methods. One example about the flow width of the resist in the hard-bake process is used for illustration.[[notice]]補正完