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Event(s) on June 2014
- Friday, 20th June, 2014
Title: Partial Identification of Principal Stratum Treatment Effects Speaker: Dr. WU Jisong, Department of Economics, Indiana University-Purdue University Indianapolis, USA Time/Place: 11:00 - 12:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: Selection after randomization renders simple comparison procedures between the treated and control group outcomes commonly used to evaluate treatment effects invalid. Without strong assumptions on the selection procedure, policy parameters including average treatment effects and quantile treatment effects are only partially identified. In this paper, we explore different types of information to tighten existing bounds on treatment effects for the always selected group or principal stratum. The types of information we consider include: (i) baseline covariates; (ii) dependence structure between the counterfactual outcome and the selection indicator characterized by copula bounds; (iii) the presence of an instrumental variable or monotone instrumental variable in a threshold-crossing model for selection; and combinations of (i), (ii), and (iii). Numerical examples are provided to illustrate the power of each type of additional information in tightenting the bounds. An empirical application to HIV vaccine trial data is also provided. This is a joint work with Professors Yanqin Fan and Bryan Shepherd. - Friday, 20th June, 2014
Title: Segment recombinations and random sharing models Speaker: Prof. Sergei Zuyev, Department of Mathematical Science, Chalmers University of Technology, Sweden Time/Place: 14:30 - 15:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: Consider a renewal point process on the line and divide each of the segments it defines in a proportion given by i.i.d. realisations of a fixed distribution supported by [0,1]. Now recombine the obtained pieces of the segments by joining the neighbouring ones, so that the division points are now the separation points between the new segments. We ask ourselves for which renewal processes and which division distributions, the division points follow the same renewal process distribution? An evident case is that of equal length segments and a degenerate division distribution. Interestingly, the only other possible case is when the increments of the renewal process is Gamma and division points are Beta-distributed. In particular, the division points of a Poisson process is again Poisson, if the dividing distribution is Beta(r,1-r) for some 0<r<1. We show that a similar situation arrises in the random sharing model when a countable number of `households' exchange randomly distributed parts of their `wealth' with neighbours. More generally, a Dirichlet distribution arrises in these models as a fixed point distribution preserving independence of the wealths at each step. We also show that the fixed points of the random sharing are attractors meaning that starting with a non-equillibrium configuration distribution iterations will converge to the equilibrium. - Tuesday, 24th June, 2014
Title: Penalized Fixed Effect Model for Longitudinal Model with Unobserved Individual Effects Speaker: Dr. LU Ying, Department of Humanities and Social Sciences, New York University, USA Time/Place: 11:00 - 12:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: In longitudinal data, each subject is often observed for more than one episode. Observations that are belonged to the same individual are considered as subject to within-subject correlation due to unobserved individual heterogeneity. Traditionally, there are two ways of incorporating individual effects: treating unobserved individual effects as random effect; or incorporating the individual effects via fixed effect dummy variables. The fixed effect approach is criticized for producing in-efficient covariate estimates and being unable to include predictors whose values remain unchanged within individual. The random effect approach can address the shortcomings of the fixed effect approach, however the consistency of its estimators is based on an important assumption that the unobserved individual heterogeneity is uncorrelated with the observed covariates X. In this article, we propose a penalized fixed effect estimation approach that will ameliorate the inefficiency of the estimators under the fixed effect approach, this approach will also allow researchers to incorporate X variables with fixed values across individuals. When estimating fixed effect model for longitudinal data, a penalty term is applied to shrink the distance between adjacent values of fixed effect estimates of any two individuals. When the distance is small enough, one common fixed effect will be estimated for the two individuals. This model will lead to a much smaller number of individual fixed effects and also create enough cross-over so the X variable corresponding the same fixed effect will no longer to be constant and can be estimated. We will illustrate this approach using the National Longitudinal Survey of Youth 1988-2004. Theoretical results regarding the fixed effect covariates (with respect to X) and the penalized individual fixed effects will be discussed. - Monday, 30th June, 2014
Title: Tomography by Flat Tori Transform on Grassmannians and other Symmetric Spaces of Compact Type Speaker: Prof. Eric Grinberg, Department of Mathematics, University of Massachusetts Boston, USA Time/Place: 11:00 - 12:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: In a 1913 paper Paul Funk proved that a suitable function on the sphere S^2 is odd if and only if its integrals over great circles (closed geodesics) vanish, and that an even function is determined by such integrals. His motivation came from problems in differential geometry. This context of integral geometry is similar to that of the Radon transform and its cousins, is used in medical imaging (CAT scanners, MRI), and overlaps a number of subjects in mathematics, including but not restricted his to number theory. We replace the sphere S^2 by a symmetric space of compact type, e.g., a Grassmann manifold, and great circles by maximal totally geodesic flat tori, and consider the transform that integrates over these. We show that, when the symmetric space is the "universal covered space" in its class, the torus transform is injective, and otherwise the transform is non-injective, with a kernel that is directly linked to deck transformations of the appropriate symmetric covering space. This gives one of the direct extensions of Funk's transform and its injectivity properties. We also discuss other extensions and generalizations of the great circle transform, and propose conjectures and open problems.