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.

Comparison of Model Selection Method Using Data from Classical Designed Experiment

2013 ◽  
Vol 677 ◽  
pp. 357-362
Author(s):  
Natthasurang Yasungnoen ◽  
Patchanok Srisuradetchai
Keyword(s):  
Model Selection ◽  
Quantitative Research ◽  
Selection Procedure ◽  
Information Criterion ◽  
P Value ◽  
Selection Procedures ◽  
Final Model ◽  
Designed Experiment ◽  
Using Data ◽  
Selection Of

Model selection procedures play important role in many researches especially quantitative research. . In several area of sciences, the analysis and model selection of experiments are often used and often contains two fundamental goals associated with the experimental response of interest which are to determine the best model. The way to address these goals is to implement a model selection procedure. Then, the objectives of this research are to determine whether or not the final models selected are in agreement or differ substantially across the three approaches to model selection: using Akaike’s Information Criterion, using a p-value criterion, and using a stepwise procedure.. Generally, results from these three models are usually compare to each other. All selected models are based on the heredity principle to design the possible model for each design. The actual data from literature, consisting of the 2x3 and 32 and 3x4 factorial designs are used to determine the final model. The results show that the P-Value WH and Stepwise methods give the highest percentage of matched model.

scholarly journals On the Use of Entropy to Improve Model Selection Criteria

Entropy ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 394 ◽  
Author(s):  
Andrea Murari ◽  
Emmanuele Peluso ◽  
Francesco Cianfrani ◽  
Pasquale Gaudio ◽  
Michele Lungaroni
Keyword(s):  
Model Selection ◽  
Shannon Entropy ◽  
Selection Criteria ◽  
Mean Squared Error ◽  
Geodesic Distance ◽  
Information Criterion ◽  
Residual Distribution ◽  
Model Selection Criteria ◽  
Synthetic Indicators ◽  
Squared Error

The most widely used forms of model selection criteria, the Bayesian Information Criterion (BIC) and the Akaike Information Criterion (AIC), are expressed in terms of synthetic indicators of the residual distribution: the variance and the mean-squared error of the residuals respectively. In many applications in science, the noise affecting the data can be expected to have a Gaussian distribution. Therefore, at the same level of variance and mean-squared error, models, whose residuals are more uniformly distributed, should be favoured. The degree of uniformity of the residuals can be quantified by the Shannon entropy. Including the Shannon entropy in the BIC and AIC expressions improves significantly these criteria. The better performances have been demonstrated empirically with a series of simulations for various classes of functions and for different levels and statistics of the noise. In presence of outliers, a better treatment of the errors, using the Geodesic Distance, has proved essential.

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.

Improving data analysis in herpetology: using Akaike's Information Criterion (AIC) to assess the strength of biological hypotheses

2006 ◽  
Vol 27 (2) ◽  
pp. 169-180 ◽  
Author(s):  
Marc Mazerolle
Keyword(s):  
Model Selection ◽  
Observational Studies ◽  
Regression Models ◽  
Model Averaging ◽  
Weighted Average ◽  
Information Criterion ◽  
Data Sets ◽  
Data Set ◽  
Robust Estimates ◽  
Number Of Individuals

AbstractIn ecology, researchers frequently use observational studies to explain a given pattern, such as the number of individuals in a habitat patch, with a large number of explanatory (i.e., independent) variables. To elucidate such relationships, ecologists have long relied on hypothesis testing to include or exclude variables in regression models, although the conclusions often depend on the approach used (e.g., forward, backward, stepwise selection). Though better tools have surfaced in the mid 1970's, they are still underutilized in certain fields, particularly in herpetology. This is the case of the Akaike information criterion (AIC) which is remarkably superior in model selection (i.e., variable selection) than hypothesis-based approaches. It is simple to compute and easy to understand, but more importantly, for a given data set, it provides a measure of the strength of evidence for each model that represents a plausible biological hypothesis relative to the entire set of models considered. Using this approach, one can then compute a weighted average of the estimate and standard error for any given variable of interest across all the models considered. This procedure, termed model-averaging or multimodel inference, yields precise and robust estimates. In this paper, I illustrate the use of the AIC in model selection and inference, as well as the interpretation of results analysed in this framework with two real herpetological data sets. The AIC and measures derived from it is should be routinely adopted by herpetologists.

scholarly journals Upgrading Model Selection Criteria with Goodness of Fit Tests for Practical Applications

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 447
Author(s):  
Riccardo Rossi ◽  
Andrea Murari ◽  
Pasquale Gaudio ◽  
Michela Gelfusa
Keyword(s):  
Model Selection ◽  
Goodness Of Fit ◽  
Mean Squared Error ◽  
Information Criterion ◽  
Original Form ◽  
Residual Distribution ◽  
Practical Applications ◽  
Goodness Of Fit Tests ◽  
Squared Error ◽  
The Mean

The Bayesian information criterion (BIC), the Akaike information criterion (AIC), and some other indicators derived from them are widely used for model selection. In their original form, they contain the likelihood of the data given the models. Unfortunately, in many applications, it is practically impossible to calculate the likelihood, and, therefore, the criteria have been reformulated in terms of descriptive statistics of the residual distribution: the variance and the mean-squared error of the residuals. These alternative versions are strictly valid only in the presence of additive noise of Gaussian distribution, not a completely satisfactory assumption in many applications in science and engineering. Moreover, the variance and the mean-squared error are quite crude statistics of the residual distributions. More sophisticated statistical indicators, capable of better quantifying how close the residual distribution is to the noise, can be profitably used. In particular, specific goodness of fit tests have been included in the expressions of the traditional criteria and have proved to be very effective in improving their discriminating capability. These improved performances have been demonstrated with a systematic series of simulations using synthetic data for various classes of functions and different noise statistics.

Trading Variance Reduction with Unbiasedness: The Regularized Subspace Information Criterion for Robust Model Selection in Kernel Regression

2004 ◽  
Vol 16 (5) ◽  
pp. 1077-1104 ◽  
Author(s):  
Masashi Sugiyama ◽  
Motoaki Kawanabe ◽  
Klaus-Robert Müller
Keyword(s):  
Model Selection ◽  
Unbiased Estimator ◽  
Variance Reduction ◽  
Kernel Regression ◽  
Information Criterion ◽  
Parameter Estimates ◽  
Generalization Error ◽  
Squared Error ◽  
Robust Model ◽  
Robust Model Selection

A well-known result by Stein (1956) shows that in particular situations, biased estimators can yield better parameter estimates than their generally preferred unbiased counterparts. This letter follows the same spirit, as we will stabilize the unbiased generalization error estimates by regularization and finally obtain more robust model selection criteria for learning. We trade a small bias against a larger variance reduction, which has the beneficial effect of being more precise on a single training set. We focus on the subspace information criterion (SIC), which is an unbiased estimator of the expected generalization error measured by the reproducing kernel Hilbert space norm. SIC can be applied to the kernel regression, and it was shown in earlier experiments that a small regularization of SIC has a stabilization effect. However, it remained open how to appropriately determine the degree of regularization in SIC. In this article, we derive an unbiased estimator of the expected squared error, between SIC and the expected generalization error and propose determining the degree of regularization of SIC such that the estimator of the expected squared error is minimized. Computer simulations with artificial and real data sets illustrate that the proposed method works effectively for improving the precision of SIC, especially in the high-noise-level cases. We furthermore compare the proposed method to the original SIC, the cross-validation, and anempirical Bayesian method in ridge parameter selection, withgood results.

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 Model Selection in Continuous Test Norming With GAMLSS

Assessment ◽  
2017 ◽  
Vol 26 (7) ◽  
pp. 1329-1346 ◽  
Author(s):  
Lieke Voncken ◽  
Casper J. Albers ◽  
Marieke E. Timmerman
Keyword(s):  
Model Selection ◽  
Sample Size ◽  
Akaike Information Criterion ◽  
Reference Group ◽  
Generalized Additive Models ◽  
Selection Procedure ◽  
Information Criterion ◽  
Exponential Model ◽  
Additive Models ◽  
Model Selection Procedure

To compute norms from reference group test scores, continuous norming is preferred over traditional norming. A suitable continuous norming approach for continuous data is the use of the Box–Cox Power Exponential model, which is found in the generalized additive models for location, scale, and shape. Applying the Box–Cox Power Exponential model for test norming requires model selection, but it is unknown how well this can be done with an automatic selection procedure. In a simulation study, we compared the performance of two stepwise model selection procedures combined with four model-fit criteria (Akaike information criterion, Bayesian information criterion, generalized Akaike information criterion (3), cross-validation), varying data complexity, sampling design, and sample size in a fully crossed design. The new procedure combined with one of the generalized Akaike information criterion was the most efficient model selection procedure (i.e., required the smallest sample size). The advocated model selection procedure is illustrated with norming data of an intelligence test.

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