5,905 research outputs found
Variable Selection in Multivariable Regression Using SAS/IML
This paper introduces a SAS/IML program to select among the multivariate model candidates based on a few well-known multivariate model selection criteria. Stepwise regression and all-possible-regression are considered. The program is user friendly and requires the user to paste or read the data at the beginning of the module, include the names of the dependent and independent variables (the y's and the x's), and then run the module. The program produces the multivariate candidate models based on the following criteria: Forward Selection, Forward Stepwise Regression, Backward Elimination, Mean Square Error, Coefficient of Multiple Determination, Adjusted Coefficient of Multiple Determination, Akaike's Information Criterion, the Corrected Form of Akaike's Information Criterion, Hannan and Quinn Information Criterion, the Corrected Form of Hannan and Quinn (HQc) Information Criterion, Schwarz's Criterion, and Mallow's PC. The output also constitutes detailed as well as summarized results.
Model Selection Criteria in Multivariate Models with Multiple Structural Changes
This paper considers the issue of selecting the number of regressors and the number of structural breaks in multivariate regression models in the possible presence of mul- tiple structural changes. We develop a modified Akaike's information criterion (AIC), a modified Mallows' Cp criterion and a modified Bayesian information criterion (BIC). The penalty terms in these criteria are shown to be different from the usual terms. We prove that the modified BIC consistently selects the regressors and the number of breaks whereas the modified AIC and the modified Cp criterion tend to overly choose them with positive probability. The finite sample performance of these criteria is investigated through Monte Carlo simulations and it turns out that our modification is successful in comparison to the classical model selection criteria and the sequential testing procedure with the robust method.structural breaks, AIC, Mallows' Cp, BIC, information criteria
Characterizing Entanglement Sources
We discuss how to characterize entanglement sources with finite sets of
measurements. The measurements do not have to be tomographically complete, and
may consist of POVMs rather than von Neumann measurements. Our method yields a
probability that the source generates an entangled state as well as estimates
of any desired calculable entanglement measures, including their error bars. We
apply two criteria, namely Akaike's information criterion and the Bayesian
information criterion, to compare and assess different models (with different
numbers of parameters) describing entanglement-generating devices. We discuss
differences between standard entanglement-verificaton methods and our present
method of characterizing an entanglement source.Comment: This submission, together with the next one, supersedes
arXiv:0806.416
Empirical Information Criteria for Time Series Forecasting Model Selection
In this paper, we propose a new Empirical Information Criterion (EIC) for model selection which penalizes the likelihood of the data by a function of the number of parameters in the model. It is designed to be used where there are a large number of time series to be forecast. However, a bootstrap version of the EIC can be used where there is a single time series to be forecast. The EIC provides a data-driven model selection tool that can be tuned to the particular forecasting task. We compare the EIC with other model selection criteria including Akaike's Information Criterion (AIC) and Schwarz's Bayesian Information Criterion (BIC). The comparisons show that for the M3 forecasting competition data, the EIC outperforms both the AIC and BIC, particularly for longer forecast horizons. We also compare the criteria on simulated data and find that the EIC does better than existing criteria in that case also.Exponential smoothing; forecasting; information criteria; M3 competition; model selection.
A New Strategy of Quantum-State Estimation for Achieving the Cramer-Rao Bound
We experimentally analyzed the statistical errors in quantum-state estimation
and examined whether their lower bound, which is derived from the Cramer-Rao
inequality, can be truly attained or not. In the experiments, polarization
states of bi-photons produced via spontaneous parametric down-conversion were
estimated employing tomographic measurements. Using a new estimation strategy
based on Akaike's information criterion, we demonstrated that the errors
actually approach the lower bound, while they fail to approach it using the
conventional estimation strategy.Comment: 4 pages, 2 figure
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