3,134 research outputs found
Traces of symmetric Markov processes and their characterizations
Time change is one of the most basic and very useful transformations for
Markov processes. The time changed process can also be regarded as the trace of
the original process on the support of the Revuz measure used in the time
change. In this paper we give a complete characterization of time changed
processes of an arbitrary symmetric Markov process, in terms of the
Beurling--Deny decomposition of their associated Dirichlet forms and of Feller
measures of the process. In particular, we determine the jumping and killing
measure (or, equivalently, the L\'{e}vy system) for the time-changed process.
We further discuss when the trace Dirichlet form for the time changed process
can be characterized as the space of finite Douglas integrals defined by Feller
measures. Finally, we give a probabilistic characterization of Feller measures
in terms of the excursions of the base process.Comment: Published at http://dx.doi.org/10.1214/009117905000000657 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
On Additive Regression of Expectancy
Regression models have been important tools to study the association between outcome variables and their covariates. The traditional linear regression models usually specify such an association by the expectations of the outcome variables as function of the covariates and some parameters. In reality, however, interests often focus on their expectancies characterized by the conditional means. In this article, a new class of additive regression models is proposed to model the expectancies. The model parameters carry practical implication, which may allow the models to be useful in applications such as treatment assessment, resource planning or short-term forecasting. Moreover, the new model can be extended to include the outcome-dependent structure. Parametric and semiparametric methods are applied in the model estimation. Alternative models are discussed as well
Linear Regression of Censored Length-biased Lifetimes
Length-biased lifetimes may be collected in observational studies or sample surveys due to biased sampling scheme. In this article, we use a linear regression model, namely, the accelerated failure time model, for the population lifetime distributions in regression analysis of the length-biased lifetimes. It is discovered that the associated regression parameters are invariant under the length-biased sampling scheme. According to this discovery, we propose the quasi partial score estimating equations to estimate the population regression parameters. The proposed methodologies are evaluated and demonstrated by simulation studies and an application to actual data set
Semiparametric Quantitative-Trait-Locus Mapping: I. on Functional Growth Curves
The genetic study of certain quantitative traits in growth curves as a function of time has recently been of major scientific interest to explore the developmental evolution processes of biological subjects. Various parametric approaches in the statistical literature have been proposed to study the quantitative-trait-loci (QTL) mapping of the growth curves as multivariate outcomes. In this article, we view the growth curves as functional quantitative traits and propose some semiparametric models to relax the strong parametric assumptions which may not be always practical in reality. Appropriate inference procedures are developed to estimate the parameters of interest which characterise the possible QTLs of the growth curves in the models. Recently developed multiple comparison testing procedures are applied to locate the statistically meaningful QTLs. Numerical examples are presented with simulation studies and analysis of real data
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