Sequential Monte Carlo for rare event estimation

This paper discusses a novel strategy for simulating rare events and an associated Monte Carlo estimation of tail probabilities. Our method uses a system of interacting particles and exploits a Feynman-Kac representation of that system to analyze their fluctuations. Our precise analysis of the variance of a standard multilevel splitting algorithm reveals an opportunity for improvement. This leads to a novel method that relies on adaptive levels and produces, in the limit of an idealized version of the algorithm, estimates with optimal variance. The motivation for this theoretical work comes from problems occurring in watermarking and fingerprinting of digital contents, which represents a new field of applications of rare event simulation techniques. Some numerical results show performance close to the idealized version of our technique for these practical applications.     

A hierarchical model for ordinal matrix factorization

This paper proposes a hierarchical probabilistic model for ordinal matrix factorization. Unlike previous approaches, we model the ordinal nature of the data and take a principled approach to incorporating priors for the hidden variables. Two algorithms are presented for inference, one based on Gibbs sampling and one based on variational Bayes. Importantly, these algorithms may be implemented in the factorization of very large matrices with missing entries.     

Comparing aggregate and disaggregate forecasts of first order moving average models

This paper compares the performance of “aggregate” and “disaggregate” predictors in forecasting contemporaneously aggregated vector MA(1) processes. The necessary and sufficient condition for the equality of mean squared errors associated with the two competing predictors is provided in the bivariate MA(1) case. Furthermore, it is argued that the condition of equality of predictors as stated by Lütkepohl (Forecasting aggregated vector ARMA processes, Springer, Berlin, 1987) is only sufficient (not necessary) for the equality of mean squared errors. Finally, it is shown that the equality of forecasting accuracy for the two predictors can be achieved using specific assumptions on the parameters of the vector MA(1) structure.     

Multistate models in health insurance

We illustrate how multistate Markov and semi-Markov models can be used for the actuarial modeling of health insurance policies, focusing on health insurances that are pursued on a similar technical basis to that of life insurance. In the first part, we give an overview of the basic modeling frameworks that are commonly used and explain the calculation of prospective reserves and net premiums. In the second part, we discuss the biometric insurance risk, focusing on the calculation of implicit safety margins. We present new results on implicit margins in the semi-Markov model and on biometric estimation risk in the Markov model, and we explain why there is a need for future research concerning the systematic biometric risk.     

Generalized quasi-likelihood

The quasi-score function, as defined by Wedderburn (1974) and McCullagh (1983) and so on, is a linear function of observations. The generalized quasi-score function introduced in this paper is a linear function of some unbiased basis functions, where the unbiased basis functions may be some linear functions of the observations or not, and can be easily constructed by the meaning of the parameters such as mean and median and so on. The generalized quasi-likelihood estimate obtained by such a generalized quasi-score function is consistent and has an asymptotically normal distribution. As a result, the optimum generalized quasi-score is obtained and a method to construct the optimum unbiased basis function is introduced. In order to construct the potential function, a conservative generalized estimating function is defined. By conservative, a potential function for the projected score has many properties of a log-likelihood function. Finally, some examples are given to illustrate the theoretical results. This paper is supported by NNSF project (10371059) of China and Youth Teacher Foundation of Nankai University.     

A bias analysis of Weibull models under heaped data

Retrospectively collected duration data are often reported incorrectly. An important type of such an error is heaping—respondents tend to round-off or round-up the data according to some rule of thumb. For two special cases of the Weibull model we study the behaviour of the ‘naive estimators’, which simply ignore the measurement error due to heaping, and derive closed expressions for the asymptotic bias. These results give a formal justification of empirical evidence and simulation-based findings reported in the literature. Additionally, situations where a remarkable bias has to be expected can be identified, and an exact bias correction can be performed.     

A weighted polynomial regression method for local fitting of spatial data

Typically, parametric approaches to spatial problems require restrictive assumptions. On the other hand, in a wide variety of practical situations nonparametric bivariate smoothing techniques has been shown to be successfully employable for estimating small or large scale regularity factors, or even the signal content of spatial data taken as a whole.We propose a weighted local polynomial regression smoother suitable for fitting of spatial data. To account for spatial variability, we both insert a spatial contiguity index in the standard formulation, and construct a spatial-adaptive bandwidth selection rule. Our bandwidth selector depends on the Gearys local indicator of spatial association. As illustrative example, we provide a brief Monte Carlo study case on equally spaced data, the performances of our smoother and the standard polynomial regression procedure are compared.This note, though it is the result of a close collaboration, was specifically elaborated as follows: paragraphs 1 and 2 by T. Sclocco and the remainder by M. Di Marzio. The authors are grateful to the referees for constructive comments and suggestions.     

Some results on optimality in models with heteroscedastic errors from partial optimum designs

This paper studies optimum designs for linear models when the errors are heteroscedastic. Sufficient conditions are given in order to obtainD-, A- andE-optimum designs for a complete regression model from partial optimum designs for some sub-parameters. A result about optimality for a complete model from the optimality for the submodels is included. Supported by Junta de Andalucía, research group FQM244.     

Simple detection of outlying short time series

Sets of relatively short time series arise in many situations. One aspect of their analysis may be the detection of outlying series. We examine the performance of standard normal outlier tests applied to the means, or to simple functions of the means, of AR(1) series, not necessarily of equal lengths. Although unequal lengths of series implies that the means have unequal variances, that are only known approximately, it is shown that nominal significance levels hold good under most circumstances. Thus a standard outlier test can usefully be applied, avoiding the complication of estimating the time series' parameters. The test's power is affected by unequal lengths, being higher when the slippage occurs in one of the longer series