scholarly journals Generalization of the order-restricted information criterion for multivariate normal linear models (pre-print )

2021 ◽  
Author(s):  
Rebecca M. Kuiper ◽  
Herbert Hoijtink
Keyword(s):  
Model Selection ◽  
Analysis Of Variance ◽  
Linear Models ◽  
Inequality Constraints ◽  
Information Criterion ◽  
Variance Model ◽  
Order Restrictions ◽  
Population Means ◽  
Order Restricted ◽  
The One

The Akaike information criterion for model selection presupposes that the parameter space is not subject to order restrictions or inequality constraints.Anraku (1999) proposed a modified version of this criterion, called the order-restricted information criterion, for model selection in the one-way analysis of variance model when the population means are monotonic.We propose a generalization of this to the case when the population means may be restricted by a mixture of linear equality and inequality constraints.If the model has no inequality constraints, then the generalized order-restricted information criterion coincides with the Akaike information criterion.Thus, the former extends the applicability of the latter to model selection in multi-way analysis of variance models when some models may have inequality constraints while others may not. Simulation shows that the information criterion proposed in this paper performs well in selecting the correct model.

scholarly journals An Akaike-type information criterion for model selection under inequality constraints (pre-print)

2021 ◽  
Author(s):  
Rebecca M. Kuiper ◽  
Herbert Hoijtink
Keyword(s):  
Model Selection ◽  
Analysis Of Variance ◽  
Akaike Information Criterion ◽  
Inequality Constraints ◽  
Information Criterion ◽  
Order Restrictions ◽  
Population Means ◽  
Equality And Inequality Constraints ◽  
Order Restricted ◽  
The One

The Akaike information criterion for model selection presupposes that the parameter space is not subject to order restrictions or inequality constraints. Anraku (1999) proposed a modified version of this criterion, called the order-restricted information criterion, for model selection in the one-way analysis of variance model when the population means are monotonic. We propose a generalization of this to the case when the population means may be restricted by a mixture of linear equality and inequality constraints. If the model has no inequality constraints, then the generalized order-restricted information criterion coincides with the Akaike information criterion. Thus, the former extends the applicability of the latter to model selection in multi-way analysis of variance models when some models may have inequality constraints while others may not. Simulation shows that the information criterion proposed in this paper performs well in selecting the correct model.

scholarly journals An Akaike-type information criterion for model selection under inequality constraints

Biometrika ◽  
2011 ◽  
Vol 98 (2) ◽  
pp. 495-501 ◽  
Author(s):  
R. M. Kuiper ◽  
H. Hoijtink ◽  
M. J. Silvapulle
Keyword(s):  
Model Selection ◽  
Analysis Of Variance ◽  
Akaike Information Criterion ◽  
Inequality Constraints ◽  
Information Criterion ◽  
Order Restrictions ◽  
Population Means ◽  
Equality And Inequality Constraints ◽  
Order Restricted ◽  
The One

Abstract The Akaike information criterion for model selection presupposes that the parameter space is not subject to order restrictions or inequality constraints. Anraku (1999) proposed a modified version of this criterion, called the order-restricted information criterion, for model selection in the one-way analysis of variance model when the population means are monotonic. We propose a generalization of this to the case when the population means may be restricted by a mixture of linear equality and inequality constraints. If the model has no inequality constraints, then the generalized order-restricted information criterion coincides with the Akaike information criterion. Thus, the former extends the applicability of the latter to model selection in multi-way analysis of variance models when some models may have inequality constraints while others may not. Simulation shows that the information criterion proposed in this paper performs well in selecting the correct model.

scholarly journals The Optimal Selection for Restricted Linear Models with Average Estimator

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Qichang Xie ◽  
Meng Du
Keyword(s):  
Model Selection ◽  
Linear Models ◽  
Weighted Average ◽  
Selection Procedure ◽  
Information Criterion ◽  
Optimal Weights ◽  
Model Average ◽  
Squared Error ◽  
Generalized Information Criterion ◽  
Risk Investment

The essential task of risk investment is to select an optimal tracking portfolio among various portfolios. Statistically, this process can be achieved by choosing an optimal restricted linear model. This paper develops a statistical procedure to do this, based on selecting appropriate weights for averaging approximately restricted models. The method of weighted average least squares is adopted to estimate the approximately restricted models under dependent error setting. The optimal weights are selected by minimizing ak-class generalized information criterion (k-GIC), which is an estimate of the average squared error from the model average fit. This model selection procedure is shown to be asymptotically optimal in the sense of obtaining the lowest possible average squared error. Monte Carlo simulations illustrate that the suggested method has comparable efficiency to some alternative model selection techniques.

Large-scale model selection in misspecified generalized linear models

Biometrika ◽  
2021 ◽  
Author(s):  
Emre Demirkaya ◽  
Yang Feng ◽  
Pallavi Basu ◽  
Jinchi Lv
Keyword(s):  
Model Selection ◽  
Generalized Linear Models ◽  
Large Scale ◽  
Linear Models ◽  
Information Criterion ◽  
Scale Model ◽  
High Dimensional ◽  
Model Selection Consistency ◽  
New Information ◽  
Large Scale Model

Summary Model selection is crucial both to high-dimensional learning and to inference for contemporary big data applications in pinpointing the best set of covariates among a sequence of candidate interpretable models. Most existing work assumes implicitly that the models are correctly specified or have fixed dimensionality, yet both are prevalent in practice. In this paper, we exploit the framework of model selection principles under the misspecified generalized linear models presented in Lv and Liu (2014) and investigate the asymptotic expansion of the posterior model probability in the setting of high-dimensional misspecified models.With a natural choice of prior probabilities that encourages interpretability and incorporates the Kullback–Leibler divergence, we suggest the high-dimensional generalized Bayesian information criterion with prior probability for large-scale model selection with misspecification. Our new information criterion characterizes the impacts of both model misspecification and high dimensionality on model selection. We further establish the consistency of covariance contrast matrix estimation and the model selection consistency of the new information criterion in ultra-high dimensions under some mild regularity conditions. The numerical studies demonstrate that our new method enjoys improved model selection consistency compared to its main competitors.

scholarly journals Proposals of non-linear models to adjust in vitro gas production at different incubation times in cassava genotypes

2021 ◽  
Vol 43 ◽  
pp. e22
Author(s):  
André Luiz Pinto dos Santos ◽  
Frank Sinatra Gomes da Silva ◽  
Guilherme Rocha Moreira ◽  
Cícero Carlos Ramos de Brito ◽  
Maria Lindomárcia Leonardo da Costa ◽  
...  
Keyword(s):  
Linear Models ◽  
Least Squares Method ◽  
Logistic Models ◽  
Information Criterion ◽  
Gas Production ◽  
Coefficient Of Determination ◽  
Absolute Deviation ◽  
In Vitro Gas Production ◽  
The One

The present study aimed to propose new two-compartment models from the combination of the Gompertz, Logistic and Von Bertalanffy models and to identify between Gompertz and Logistic models, in their uni and two-compartiment versions, the one that presents the highest quality of fit to cumulative gas production curves of five cassava genotypes: Brasília, Engana Ladrão, Dourada, Gema de Ovo e Amansa Burro. The gas production readings were 2, 4, 6, 8, 10, 12, 14, 17, 20, 24, 28, 32, 48, 72, and 96 hours after the start of the in vitro fermentation process. The estimation of the parameters for the models was made by the least squares method through the Gauss-Newton iterative process. The selection of the best model to describe the gas accumulation was based on the adjusted coefficient of determination, residual mean squares, mean absolute deviation, Akaike information criterion and Bayesian information criterion. Among the adjusted models, the proposed models were the best to describe the accumulation of gases over time according to the methodology and conditions under which this study was developed.

Analysing multiple variables per subject

2010 ◽  
pp. 393-445
Author(s):  
Janet L. Peacock ◽  
Philip J. Peacock
Keyword(s):  
Missing Data ◽  
Model Selection ◽  
Multiple Regression ◽  
Analysis Of Variance ◽  
Generalized Linear Models ◽  
Linear Models ◽  
Non Linear ◽  
Multiple Variables ◽  
Main Effects

Multiple variables per subject 394 Multifactorial methods: overview 396 Multifactorial methods: model selection 398 Multifactorial methods: challenges 400 Missing data 402 Generalized linear models 404 Multiple regression 406 Multiple regression: examples 408 Multiple regression and analysis of variance 412 Main effects and interactions 414 Linear and non-linear terms ...

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