USING TRAJECTORIES FROM A BIVARIATEGROWTH CURVE OF COVARIATES IN A COXMODEL ANALYSIS

In many maintenance treatment trials, patients are first enrolled into an open treatmentbefore they are randomized into treatment groups. During this period, patients are followedover time with their responses measured longitudinally. This design is very common intoday's public health studies of the prevention of many diseases. Using mixed model theory, onecan characterize these data using a wide array of across subject models. A state-spacerepresentation of the mixed model and use of the Kalman filter allow more fexibility inchoosing the within error correlation structure even in the presence of missing and unequallyspaced observations. Furthermore, using the state-space approach, one can avoid invertinglarge matrices resulting in eficient computations. Estimated trajectories from these models can be used as predictors in a survival analysis in judging the efacacy of the maintenance treatments. The statistical problem lies in accounting for the estimation error in these predictors. We considered a bivariate growth curve where the longitudinal responses were unequally spaced and assumed that the within subject errors followed a continuous firstorder autoregressive (CAR (1)) structure. A simulation study was conducted to validatethe model. We developed a method where estimated random effects for each subject froma bivariate growth curve were used as predictors in the Cox proportional hazards model,using the full likelihood based on the conditional expectation of covariates to adjust for the estimation errors in the predictor variables. Simulation studies indicated that error corrected estimators for model parameters are mostly less biased when compared with thenave regression without accounting for estimation errors. These results hold true in Coxmodels with one or two predictors. An illustrative example is provided with data from a maintenance treatment trial for major depression in an elderly population. A Visual Fortran 90 and a SAS IML program are developed

Institutions and efficiency in transition economies

This paper analyzes the effects of political and economic institutions on efficiency of transition economies over the 1995-2005 period. Perpetual Inventory Method is used to construct capital series for these countries, and then stochastic production frontier analysis is used to estimate the efficiency scores and effects of institutions at the same time. The empirical results show that better institutions are associated with higher efficiency. However, all else equal, the transition countries in East Asia are more efficient than Central and Eastern European or Former Soviet Union transition countries

Institutional determinants of investment in transition economies

Investment has been found to be a significant determinant of growth. This paper analyses the effects of institutions and transition progress on investment rates of transition economies since the collapse of the Socialist Bloc. Political institution is measured by the Freedom House’s Political Rights and Civil Liberties indexes; economic institution is proxied by the Index of Economic Freedom compiled by the Heritage Foundation; and transition progress is documented by the European Bank for Reconstruction and Development’s transition index. Panel data estimation techniques are applied and the results show that institutions and transition progress have expected and significant effect on investment rates of transition economies. However, it is the progress in all aspects of economic freedom that matters; just some individual economic freedom measures are significant marginally. Besides, as conditioning variables, growth, saving and financial development (liquid liabilities as % of GDP) are also found to have significant and positive effect on investment in transition economies. This paper highlights the indirect effect of institutions on economic growth via investment

Limits for circular Jacobi beta-ensembles

Bourgade, Nikeghbali and Rouault recently proposed a matrix model for the circular Jacobi $\beta$-ensemble, which is a generalization of the Dyson circular $\beta$-ensemble but equipped with an additional parameter $b$, and further studied its limiting spectral measure. We calculate the scaling limits for expected products of characteristic polynomials of circular Jacobi $\beta$-ensembles. For the fixed constant $b$, the resulting limit near the spectrum singularity is proven to be a new multivariate function. When $b=\beta Nd/2$, the scaling limits in the bulk and at the soft edge agree with those of the Hermite (Gaussian), Laguerre (Chiral) and Jacobi $\beta$-ensembles proved in the joint work with P Desrosiers "Asymptotics for products of characteristic polynomials in classical beta-ensembles", Constr. Approx. 39 (2014), arXiv:1112.1119v3. As corollaries, for even $\beta$ the scaling limits of point correlation functions for the ensemble are given. Besides, a transition from the spectrum singularity to the soft edge limit is observed as $b$ goes to infinity. The positivity of two special multivariate hypergeometric functions, which appear as one factor of the joint eigenvalue densities for spiked Jacobi/Wishart $\beta$-ensembles and Gaussian $\beta$-ensembles with source, will also be shown.Comment: 26 page

Degree growth for tame automorphisms of an affine quadric threefold

In this paper, we consider the degree sequences of the tame automorphisms preserving an affine quadric threefold. Using some valuatives estimates derived from the work of Shestakov-Umirbaev and the action of this group on a CAT(0), Gromov-hyperbolic square complex constructed by Bisi-Furter-Lamy, we prove that the dynamical degrees of tame elements avoid any value strictly between 1 and 4/3. As an application, these methods allow us to characterize when the growth exponent of the degree of a random product of finitely many tame automorphisms is positive.Comment: This paper is part of the author's PhD thesi