Parametric or nonparametric? A parametricness index for model selection

Parametric or Nonparametric? a Parametricness Index for Model Selection

In model selection literature two classes of criteria perform well asymptotically in different situations: Bayesian information criterion (BIC) (as a representative) is consistent in selection when the true model is finite dimensional (parametric scenario); Akaike’s information criterion (AIC) performs well in an asymptotic efficiency when the true model is infinite dimensional (nonparametric s...

To “ Parametric or Nonparametric ? a Parametricness Index for Model Selection ”

BIC is used to select the order of polynomial regression between 1 and 30. The estimated σ from the selected model is used to calculate the PI. Representative scatterplots at n = 200 with σ1 = 3, σ2 = 7 can be found in Figure 1. Note that the function estimate based on the selected model by BIC is visually more different from that based on the smaller model with one fewer term for the parametri...

Model Selection Error Rates in Nonparametric vs. Parametric Model Comparisons

Since the introduction of Akaike’s information criteria (AIC) in 1973, many information criteria have been developed and widely used in model selection. Many papers concerning the justification of criteria followed, particularly with respect to model selection error rates (the probability of selecting a wrong model). A model selection criterion is called consistent if the model selection error ...

Model Selection for Nonparametric Regression

Risk bounds are derived for regression estimation based on model selection over an unrestricted number of models. While a large list of models provides more flexibility, significant selection bias may occur with model selection criteria like AIC. We incorporate a model complexity penalty term in AIC to handle selection bias. Resulting estimators are shown to achieve a trade-off among approximat...

A Comparative Study Of Parametric And Nonparametric Regressions