24,482 research outputs found

    Partially linear censored quantile regression

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    Censored regression quantile (CRQ) methods provide a powerful and flexible approach to the analysis of censored survival data when standard linear models are felt to be appropriate. In many cases however, greater flexibility is desired to go beyond the usual multiple regression paradigm. One area of common interest is that of partially linear models: one (or more) of the explanatory covariates are assumed to act on the response through a non-linear function. Here the CRQ approach of Portnoy (J Am Stat Assoc 98:1001–1012, 2003) is extended to this partially linear setting. Basic consistency results are presented. A simulation experiment and unemployment example justify the value of the partially linear approach over methods based on the Cox proportional hazards model and on methods not permitting nonlinearity

    Copulas in finance and insurance

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    Copulas provide a potential useful modeling tool to represent the dependence structure among variables and to generate joint distributions by combining given marginal distributions. Simulations play a relevant role in finance and insurance. They are used to replicate efficient frontiers or extremal values, to price options, to estimate joint risks, and so on. Using copulas, it is easy to construct and simulate from multivariate distributions based on almost any choice of marginals and any type of dependence structure. In this paper we outline recent contributions of statistical modeling using copulas in finance and insurance. We review issues related to the notion of copulas, copula families, copula-based dynamic and static dependence structure, copulas and latent factor models and simulation of copulas. Finally, we outline hot topics in copulas with a special focus on model selection and goodness-of-fit testing

    Joint Dispersion Model with a Flexible Link

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    The objective is to model longitudinal and survival data jointly taking into account the dependence between the two responses in a real HIV/AIDS dataset using a shared parameter approach inside a Bayesian framework. We propose a linear mixed effects dispersion model to adjust the CD4 longitudinal biomarker data with a between-individual heterogeneity in the mean and variance. In doing so we are relaxing the usual assumption of a common variance for the longitudinal residuals. A hazard regression model is considered in addition to model the time since HIV/AIDS diagnostic until failure, being the coefficients, accounting for the linking between the longitudinal and survival processes, time-varying. This flexibility is specified using Penalized Splines and allows the relationship to vary in time. Because heteroscedasticity may be related with the survival, the standard deviation is considered as a covariate in the hazard model, thus enabling to study the effect of the CD4 counts' stability on the survival. The proposed framework outperforms the most used joint models, highlighting the importance in correctly taking account the individual heterogeneity for the measurement errors variance and the evolution of the disease over time in bringing new insights to better understand this biomarker-survival relation.Comment: 27 pages, 3 figures, 2 table

    Bayesian Semiparametric Multi-State Models

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    Multi-state models provide a unified framework for the description of the evolution of discrete phenomena in continuous time. One particular example are Markov processes which can be characterised by a set of time-constant transition intensities between the states. In this paper, we will extend such parametric approaches to semiparametric models with flexible transition intensities based on Bayesian versions of penalised splines. The transition intensities will be modelled as smooth functions of time and can further be related to parametric as well as nonparametric covariate effects. Covariates with time-varying effects and frailty terms can be included in addition. Inference will be conducted either fully Bayesian using Markov chain Monte Carlo simulation techniques or empirically Bayesian based on a mixed model representation. A counting process representation of semiparametric multi-state models provides the likelihood formula and also forms the basis for model validation via martingale residual processes. As an application, we will consider human sleep data with a discrete set of sleep states such as REM and Non-REM phases. In this case, simple parametric approaches are inappropriate since the dynamics underlying human sleep are strongly varying throughout the night and individual-specific variation has to be accounted for using covariate information and frailty terms

    Bayesian Semiparametric Multi-State Models

    Get PDF
    Multi-state models provide a unified framework for the description of the evolution of discrete phenomena in continuous time. One particular example are Markov processes which can be characterised by a set of time-constant transition intensities between the states. In this paper, we will extend such parametric approaches to semiparametric models with flexible transition intensities based on Bayesian versions of penalised splines. The transition intensities will be modelled as smooth functions of time and can further be related to parametric as well as nonparametric covariate effects. Covariates with time-varying effects and frailty terms can be included in addition. Inference will be conducted either fully Bayesian using Markov chain Monte Carlo simulation techniques or empirically Bayesian based on a mixed model representation. A counting process representation of semiparametric multi-state models provides the likelihood formula and also forms the basis for model validation via martingale residual processes. As an application, we will consider human sleep data with a discrete set of sleep states such as REM and Non-REM phases. In this case, simple parametric approaches are inappropriate since the dynamics underlying human sleep are strongly varying throughout the night and individual-specific variation has to be accounted for using covariate information and frailty terms

    Time Series Cluster Kernel for Learning Similarities between Multivariate Time Series with Missing Data

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    Similarity-based approaches represent a promising direction for time series analysis. However, many such methods rely on parameter tuning, and some have shortcomings if the time series are multivariate (MTS), due to dependencies between attributes, or the time series contain missing data. In this paper, we address these challenges within the powerful context of kernel methods by proposing the robust \emph{time series cluster kernel} (TCK). The approach taken leverages the missing data handling properties of Gaussian mixture models (GMM) augmented with informative prior distributions. An ensemble learning approach is exploited to ensure robustness to parameters by combining the clustering results of many GMM to form the final kernel. We evaluate the TCK on synthetic and real data and compare to other state-of-the-art techniques. The experimental results demonstrate that the TCK is robust to parameter choices, provides competitive results for MTS without missing data and outstanding results for missing data.Comment: 23 pages, 6 figure

    Degradation modeling applied to residual lifetime prediction using functional data analysis

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    Sensor-based degradation signals measure the accumulation of damage of an engineering system using sensor technology. Degradation signals can be used to estimate, for example, the distribution of the remaining life of partially degraded systems and/or their components. In this paper we present a nonparametric degradation modeling framework for making inference on the evolution of degradation signals that are observed sparsely or over short intervals of times. Furthermore, an empirical Bayes approach is used to update the stochastic parameters of the degradation model in real-time using training degradation signals for online monitoring of components operating in the field. The primary application of this Bayesian framework is updating the residual lifetime up to a degradation threshold of partially degraded components. We validate our degradation modeling approach using a real-world crack growth data set as well as a case study of simulated degradation signals.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS448 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

    Copulas in finance and insurance

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    Copulas provide a potential useful modeling tool to represent the dependence structure among variables and to generate joint distributions by combining given marginal distributions. Simulations play a relevant role in finance and insurance. They are used to replicate efficient frontiers or extremal values, to price options, to estimate joint risks, and so on. Using copulas, it is easy to construct and simulate from multivariate distributions based on almost any choice of marginals and any type of dependence structure. In this paper we outline recent contributions of statistical modeling using copulas in finance and insurance. We review issues related to the notion of copulas, copula families, copula-based dynamic and static dependence structure, copulas and latent factor models and simulation of copulas. Finally, we outline hot topics in copulas with a special focus on model selection and goodness-of-fit testing.Dependence structure, Extremal values, Copula modeling, Copula review

    Estimating time-varying effects for overdispersed recurrent events data with treatment switching

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    In the analysis of multivariate event times, frailty models assuming time-independent regression coefficients are often considered, mainly due to their mathematical convenience. In practice, regression coefficients are often time dependent and the temporal effects are of clinical interest. Motivated by a phase III clinical trial in multiple sclerosis, we develop a semiparametric frailty modelling approach to estimate time-varying effects for overdispersed recurrent events data with treatment switching. The proposed model incorporates the treatment switching time in the time-varying coefficients. Theoretical properties of the proposed model are established and an efficient expectation-maximization algorithm is derived to obtain the maximum likelihood estimates. Simulation studies evaluate the numerical performance of the proposed model under various temporal treatment effect curves. The ideas in this paper can also be used for time-varying coefficient frailty models without treatment switching as well as for alternative models when the proportional hazard assumption is violated. A multiple sclerosis dataset is analysed to illustrate our methodology
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