统计学系系列讲座之222-224期

统计学系系列讲座之222期

时间：2016年5月6日（周五）下午14:00-15:00

地点：史带楼301室

主持人：朱仲义教授复旦大学管理学院统计学系

主题：Analysis of Non-Gaussian Functional Data using Gaussian process priors

主讲人：Dr. Jian Qing Shi (Newcastle University)

简介：I will start the talk by discussing a Bayesian nonparametric regression model using a Gaussian process prior, and will then extend the idea to analyse the data with non-Gaussian functional response. This model offers a nonparametric generalized functional regression method for functional data with multi-dimensional covariates, and provides a natural framework on modelling common mean structure and covariance structure simultaneously for complex functional batch data. The mean structure provides an overall information about the observations, while the covariance structure can be used to catch up the characteristic of each individual batch. The prior specification of covariance kernel enables us to accommodate a wide class of nonlinear models. The definition of the model, the inference and implementation as well as its asymptotic properties will be discussed. Several applications and simulation studies with different non-Gaussian response variables are presented to illustrate the performance of the proposed models.

统计学系系列讲座之223期

时间：2016年5月6日（周五）下午15:00-16:00

地点：史带楼301室

主持人：朱仲义教授复旦大学管理学院统计学系

主题：Estimation Based on Jump Detection in Time-Varying Coefficient Regression Models and Empirical Applications

主讲人：林金官教授（东南大学数学系）

简介：The time-varying coefficient regression models are very important tools
to explore the hidden structure between the response variable and its predictors.
In certain applications, the underlying coefficient curve may have singularities,
including jumps at some unknown positions, representing structural changes of the
related process. Detection of such singularities is important for understanding
the structural changes. In this paper, an alternative jump detection procedure
is proposed based on first-order and second-order derivatives of the coefficient curves.
Using the detected jumps, a coefficient curve estimation procedure is also proposed,
which can preserve possible jumps reasonably well when the noise level is small.
Under some mild conditions, we not only establish the consistency and asymptotic normality for the estimators of the unknown coefficient functions, but also obtain the convergency of the proposed jump detection procedure and the consistency of the detected jumps based on the proposed jump detection procedure. Furthermore, the practical selection of procedure parameters is discussed. The methods and results are augmented by Monte Carlo simulated examples and illustrated by application to a real data example.

统计学系系列讲座之224期

时间：2016年5月6日（周五）下午16:00-17:00

地点：史带楼301室

主持人：朱仲义教授复旦大学管理学院统计学系

主题：Exponentially tilted likelihood inference on growing dimensional unconditional moment models

主讲人：唐年胜教授（云南大学数学与统计学院）

简介：Growing-dimensional data with likelihood unavailable are often encountered in various fields. This paper presents a penalized exponentially tilted likelihood (PETL) for variable selection and parameter estimation for growing dimensional unconditional moment models in the presence of correlation among variables and model misspecification. Under some regularity conditions, we investigate the consistent and oracle properties of the PETL estimators of parameters, and show that the constrainedly PETL ratio statistic for testing contrast hypothesis asymptotically follows the central chi-squared distribution. Theoretical results reveal that the PETL approach is robust to model misspecification. We also study high-order asymptotic properties of the proposed PETL estimators. Simulation studies are conducted to investigate the finite performance of the proposed methodologies. An example from the Boston Housing Study is illustrated.