Power Loss for Inhomogeneous Poisson Processes

In this work, based on a realization of an inhomogeneous Poisson process whose intensity function depends on a real parameter, we consider a simple null hypothesis against the composite one sided alternative. Under certain regularity conditions we will obtain the power loss of the score test which measures its performance with respect to the Neyman-Pearson test. We present the second-order approximation of the power of the score test under the close alternatives by specifying the explicit form of the next term after the Gaussian term.     

Characterization of Admissible Linear Estimators in Multivariate Linear Model with Respect to Inequality Constraints under Matrix Loss Function

In this article, we study the characterization of admissible linear estimators in a multivariate linear model with inequality constraint, under a matrix loss function. In the homogeneous class, we present several equivalent, necessary and sufficient conditions for a linear estimator of estimable functions to be admissible. In the inhomogeneous class, we find that the necessary and sufficient conditions depend on the rank of the matrix in the constraint. When the rank is greater than one, the necessary and sufficient conditions are obtained. When the rank is equal to one, we have necessary conditions and sufficient conditions separately. We also obtain the necessary and sufficient conditions for a linear estimator of inestimable function to be admissible in both classes.     

On minimum Lp-distance estimation for inhomogeneous Poisson processes

ABSTRACT

We consider the problem of parameter estimation by the observations of the inhomogeneous Poisson processes. We suppose that the intensity function of these processes is a smooth function of the unknown parameter and as a method of estimation we take the minimum distance approach. We are interested by the behavior of estimators in non Hilbertian situation and we define the minimum distance estimation (MDE) with the help of the L^p metrics. We show that (under regularity conditions) the MDE is consistent and we describe its limit distribution.     

Joint Modelling of Recurrent Infections and Antibody Response by Bayesian Data Augmentation

Abstract.  A joint dynamic model for the interdependence between infection, immunity and risk of disease is presented. Recurrent latent infections are modelled as realizations from a renewal process and antibody dynamics as a diffusion with a decreasing drift modified by the stimulating effect of the random infections. The augmented submodels are estimated simultaneously in one large Markov chain Monte Carlo algorithm. As an example, we consider the risk of recurrent ear infections when having only partially observed information on bacterial carriage and antibody concentrations.     

Sample Partitioning Estimation for Ergodic Diffusions

In this article, we present a new technique to obtain estimators for parameters of ergodic processes. When a diffusion is ergodic its transition density converges to the invariant density Durett (1996 Durett, R. (1996). Stochastic Calculus. A Practical Introduction. New York: CRC Press. [Google Scholar]). This convergence enabled us to introduce a sample partitioning technique that gives, in each subsample, observations that can be treated as independent and identically distributed. Within this framework, is possible the construction of estimators like maximum likelihood estimators or others.     

Laws of the iterated logarithm and large deviations for a class of diffusionl processes

We use the martingale approach to study large deviations and laws of the iterated logarithm for certain multidimensional diffusion processes. The criteria for the validity of these properties are expressed in terms of averaging properties of the coefficients of the infinitesimal generator. In particular we apply our results to diffusion processes with random coefficients.     

基于语言网络的语义韵研究

语言是一种复杂网络,语义韵是相似语义倾向的词同现连接关系体,因此更宜于采用词同现网络进行描写与研究。语义韵是一种客观存在的、相对稳定的两级网络结构, 有相应的两种语义弥散方式: 关键词节点与邻接词节点形成一种连接、发散状的密集核心,词节点之间较强的语义弥散产生了较为清晰、具体的基本语义;外围词节点通常形成集群,通过邻接词节点与关键词节点较弱地连接,弥散一种较为隐性的态度意义或交际目的,以延展、丰富基本语义。这一特征在更深层次上是一种认知与语用惯性,人类通常以关键词为注意点,以一种稳定、固化、相似的路径结构与方式认知语义韵。     

Asymptotic Inference for Jump Diffusions with State‐Dependent Intensity

We establish the local asymptotic normality property for a class of ergodic parametric jump‐diffusion processes with state‐dependent intensity and known volatility function sampled at high frequency. We prove that the inference problem about the drift and jump parameters is adaptive with respect to parameters in the volatility function that can be consistently estimated.     

A Note on Consistent Estimation of Multivariate Parameters in Ergodic Diffusion Models

Certain aspects of maximum likelihood estimation for ergodic diffusions are studied via recently developed empirical process theory for martingales. This approach enables us to remove some undesirable regularity conditions that usually appear in the statistical literature on ergodic diffusions. In particular, dimension dependent conditions for the existence of a continuous likelihood and for consistency of the maximum likelihood estimator turn out to be unnecessary.     

On Least Absolute Value Estimators for Poisson Processes

We consider the problem of parameter estimation for an inhomogeneous Poisson process observed on the time interval [0, τ]. We introduce the minimum L ₁-norm estimator of the unknown parameter and study the asymptotical behaviors of the estimates when the number of observations increases. It is established that this estimator is consistent and we show that the corresponding differences converge to certain variables. These limit variables are asymptotically normal as τ tends to infinity.