1,887,378 research outputs found
Simulation based selection of competing structural econometric models
This paper proposes a formal model selection test for choosing between two competing structural econometric models. The procedure is based on a novel lack-of-fit criterion, namely, the simulated mean squared error of predictions (SMSEP), taking into account the complexity of structural econometric models. It is asymptotically valid for any fixed number of simulations, and allows for any estimator which has a vn asymptotic normality or is superconsistent with a rate at n. The test is bi-directional and applicable to non-nested models which are both possibly misspecified. The asymptotic distribution of the test statistic is derived. The proposed test is general regardless of whether the optimization criteria for estimation of competing models are the same as the SMSEP criterion used for model selection. An empirical application using timber auction data from Oregon is used to illustrate the usefulness and generality of the proposed testing procedure.Lack-of-fit, Model selection tests, Non-nested models, Simulated mean squared error of predictions
Variable selection in semiparametric regression modeling
In this paper, we are concerned with how to select significant variables in
semiparametric modeling. Variable selection for semiparametric regression
models consists of two components: model selection for nonparametric components
and selection of significant variables for the parametric portion. Thus,
semiparametric variable selection is much more challenging than parametric
variable selection (e.g., linear and generalized linear models) because
traditional variable selection procedures including stepwise regression and the
best subset selection now require separate model selection for the
nonparametric components for each submodel. This leads to a very heavy
computational burden. In this paper, we propose a class of variable selection
procedures for semiparametric regression models using nonconcave penalized
likelihood. We establish the rate of convergence of the resulting estimate.
With proper choices of penalty functions and regularization parameters, we show
the asymptotic normality of the resulting estimate and further demonstrate that
the proposed procedures perform as well as an oracle procedure. A
semiparametric generalized likelihood ratio test is proposed to select
significant variables in the nonparametric component. We investigate the
asymptotic behavior of the proposed test and demonstrate that its limiting null
distribution follows a chi-square distribution which is independent of the
nuisance parameters. Extensive Monte Carlo simulation studies are conducted to
examine the finite sample performance of the proposed variable selection
procedures.Comment: Published in at http://dx.doi.org/10.1214/009053607000000604 the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Data driven smooth tests for composite hypotheses
The classical problem of testing goodness-of-fit of a parametric family is reconsidered. A new test for this problem is proposed and investigated. The new test statistic is a combination of the smooth test statistic and Schwarz's selection rule. More precisely, as the sample size increases, an increasing family of exponential models describing departures from the null model is introduced and Schwarz's selection rule is presented to select among them. Schwarz's rule provides the "right" dimension given by the data, while the smooth test in the "right" dimension finishes the job. Theoretical properties of the selection rules are derived under null and alternative hypotheses. They imply consistency of data driven smooth tests for composite hypotheses at essentially any alternative
Validating linear restrictions in linear regression models with general error structure
A new method for testing linear restrictions in linear regression models is suggested. It allows to validate the linear restriction, up to a specified approximation error and with a specified error probability. The test relies on asymptotic normality of the test statistic, and therefore normality of the errors in the regression model is not required. In a simulation study the performance of the suggested method for model selection purposes, as compared to standard model selection criteria and the t-test, is examined. As an illustration we analyze the US college spending data from 1994
Validation of nonlinear PCA
Linear principal component analysis (PCA) can be extended to a nonlinear PCA
by using artificial neural networks. But the benefit of curved components
requires a careful control of the model complexity. Moreover, standard
techniques for model selection, including cross-validation and more generally
the use of an independent test set, fail when applied to nonlinear PCA because
of its inherent unsupervised characteristics. This paper presents a new
approach for validating the complexity of nonlinear PCA models by using the
error in missing data estimation as a criterion for model selection. It is
motivated by the idea that only the model of optimal complexity is able to
predict missing values with the highest accuracy. While standard test set
validation usually favours over-fitted nonlinear PCA models, the proposed model
validation approach correctly selects the optimal model complexity.Comment: 12 pages, 5 figure
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