Oμιλίες Στατιστικής και Πιθανοτήτων
Πέμπτη 8 Ιουνίου 2017 (A303: 15.15-16.00, με τηλεδιάσκεψη)
Γεώργιος Αφένδρας
University at Buffalo
Τitle:
Uniform Integrability of the OLS Estimators, and the Convergence of their
Moments
Abstract:
The problem of convergence of moments of a sequence of random
variables to the moments of its asymptotic distribution is important
in many applications.
These include the determination of the optimal training sample size in the
cross validation estimation of the generalization error of computer algorithms,
and in the construction of graphical methods for studying dependence patterns between
two biomarkers. In this paper we prove the uniform integrability of the ordinary
least squares estimators of a linear regression model, under suitable assumptions on
the design matrix and the moments of the errors. Further, we prove the convergence
of the moments of the estimators to the corresponding moments of their asymptotic
distribution, and study the rate of the moment convergence. The canonical central
limit theorem corresponds to the simplest linear regression model. We investigate
the rate of the moment convergence in canonical central limit theorem proving a
sharp improvement of von Bahr’s (1965) theorem.
Σύνδεσμος
Πέμπτη 1 Ιουνίου 2017 (A303: 12.15-13.00)
Ιωάννης Καμαριανάκης
Arizona State University
Τitle:
Bayesian shrinkage estimates of logistic smooth transition autoregressions
Abstract:
The logistic smooth transition autoregressive (LSTAR) model is a regime-switching
nonlinear time series model that has been adopted in a wide variety of
applications. LSTAR is formulated as a weighted combination of two or more linear
autoregressive (AR) processes. In this work, LSTAR models are estimated using
Bayesian shrinkage (laplace and horseshoe) priors on the autoregressive
coefficients of each regime. Dirichlet priors are used to estimate composite
threshold variables in the transition function. The above specification provides
a flexible alternative to existing reversible jump Markov-chain Monte-Carlo
schemes for LSTAR model building, which can be implemented in existing Bayesian
software packages. A series of Monte Carlo experiments is presented to
demonstrate the efficacy of the proposed methodology. Application to a classic
nonlinear time series illustrates the ability to achieve superior forecasting
performance. Finally, the capability to handle multiple input exogenous time
series is exemplified through forecasting daily maximum water temperatures. For
31 Spanish rivers, Bayesian estimated linear and nonlinear river specific models
are evaluated on 7-step ahead forecast performance.
Προηγούμενες Ομιλίες