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A bias correction to Akaike's information criterion (AIC) is derived for seemingly unrelated regressions models. The correction is of particular use when the sample size is not much larger than the number of fitted parameters. A…
The Akaike information criterion (AIC) has been used as a statistical criterion to compare the appropriateness of different dark energy candidate models underlying a particular data set. Under suitable conditions, the AIC is an indirect…
While the Bayesian Information Criterion (BIC) and Akaike Information Criterion (AIC) are powerful tools for model selection in linear regression, they are built on different prior assumptions and thereby apply to different data generation…
The Akaike information criterion (AIC) is commonly used to select a logistic regression model for optimal prediction of a binary response by a specified family of models. It however lacks a convincing method of prescribing a proper family…
In the information-based paradigm of inference, model selection is performed by selecting the candidate model with the best estimated predictive performance. The success of this approach depends on the accuracy of the estimate of the…
In the problem of selecting variables in a multivariate linear regression model, we derive new Bayesian information criteria based on a prior mixing a smooth distribution and a delta distribution. Each of them can be interpreted as a fusion…
The statistical regression technique is an extraordinarily essential data fitting tool to explore the potential possible generation mechanism of the random phenomenon. Therefore, the model selection or the variable selection is becoming…
Regression models fitted to data can be assessed on their goodness of fit, though models with many parameters should be disfavored to prevent over-fitting. Statisticians' tools for this are little known to physical scientists. These include…
Information criteria such as Akaike's (AIC) and Bayes' (BIC) are widely used for model selection in physics and beyond, quantifying the tradeoff between model complexity and goodness-of-fit to enforce parsimony. However, their derivation…
We introduce a new criterion to determine the order of an autoregressive model fitted to time series data. It has the benefits of the two well-known model selection techniques, the Akaike information criterion and the Bayesian information…
In statistical modeling area, the Akaike information criterion AIC, is a widely known and extensively used tool for model choice. The {\phi}-divergence test statistic is a recently developed tool for statistical model selection. The…
Effective model selection is critical in symbolic regression (SR) to identify mathematical expressions that balance accuracy and complexity, and have low expected error on unseen data. Many modern implementations of genetic programming (GP)…
Model selection is the problem of distinguishing competing models, perhaps featuring different numbers of parameters. The statistics literature contains two distinct sets of tools, those based on information theory such as the Akaike…
A popular model selection approach for generalized linear mixed-effects models is the Akaike information criterion, or AIC. Among others, \cite{vaida05} pointed out the distinction between the marginal and conditional inference depending on…
Given a random sample from a multivariate population, estimating the number of large eigenvalues of the population covariance matrix is an important problem in Statistics with wide applications in many areas. In the context of Principal…
Akaike's information criterion (AIC) is a measure of the quality of a statistical model for a given set of data. We can determine the best statistical model for a particular data set by the minimization of the AIC. Since we need to evaluate…
We develop an algorithm for model selection which allows for the consideration of a combinatorially large number of candidate models governing a dynamical system. The innovation circumvents a disadvantage of standard model selection which…
Model selection is of fundamental importance to high dimensional modeling featured in many contemporary applications. Classical principles of model selection include the Kullback-Leibler divergence principle and the Bayesian principle,…
Model selection and order selection problems frequently arise in statistical practice. A popular approach to addressing these problems in the frequentist setting involves information criteria based on penalised maxima of log-likelihoods for…
Unmeasured covariates constitute one of the important problems in causal inference. Even if there are some unmeasured covariates, some instrumental variable methods such as a two-stage residual inclusion (2SRI) estimator, or a…