Connection of the critical value for KS distance and model complexity
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I wonder about a correlation of the critical value for KS distance (with Lilliefor correction) and model complexity? The critical KS value is distribution-independant if we use the true model parameters. With estimated parameters the critical value needs to be lower. Isn't that reduction highly connected to the model flexibility? And when we compare this to model selection methods like AIC or BIC, isn't this KS critical value change a much better measure for model complexity than the pure number of parameters?
On the other hand, KS is not very sensitive to the tail behavior, so is there even a similar but better method to quantify model complexity? A simple example would be the Student-t distribution (with location and scale), it extends the normal model, but with keeping only one more parameter, we could further extend it to short-tail cases by using negative df parameters. Can we expect a certain law for KS critical value reduction against model complexity or number of parameters? Or at least for choosing a certain form of parameters (e.g. based on the distribution moments)?
statistics
asked Dec 12 '18 at 11:29
user32038user32038
184
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I wonder about a correlation of the critical value for KS distance (with Lilliefor correction) and model complexity? The critical KS value is distribution-independant if we use the true model parameters. With estimated parameters the critical value needs to be lower. Isn't that reduction highly connected to the model flexibility? And when we compare this to model selection methods like AIC or BIC, isn't this KS critical value change a much better measure for model complexity than the pure number of parameters?
On the other hand, KS is not very sensitive to the tail behavior, so is there even a similar but better method to quantify model complexity? A simple example would be the Student-t distribution (with location and scale), it extends the normal model, but with keeping only one more parameter, we could further extend it to short-tail cases by using negative df parameters. Can we expect a certain law for KS critical value reduction against model complexity or number of parameters? Or at least for choosing a certain form of parameters (e.g. based on the distribution moments)?
statistics
asked Dec 12 '18 at 11:29
user32038user32038
184
$endgroup$
add a comment |
$begingroup$
I wonder about a correlation of the critical value for KS distance (with Lilliefor correction) and model complexity? The critical KS value is distribution-independant if we use the true model parameters. With estimated parameters the critical value needs to be lower. Isn't that reduction highly connected to the model flexibility? And when we compare this to model selection methods like AIC or BIC, isn't this KS critical value change a much better measure for model complexity than the pure number of parameters?
On the other hand, KS is not very sensitive to the tail behavior, so is there even a similar but better method to quantify model complexity? A simple example would be the Student-t distribution (with location and scale), it extends the normal model, but with keeping only one more parameter, we could further extend it to short-tail cases by using negative df parameters. Can we expect a certain law for KS critical value reduction against model complexity or number of parameters? Or at least for choosing a certain form of parameters (e.g. based on the distribution moments)?
statistics
asked Dec 12 '18 at 11:29
user32038user32038
184
$endgroup$
I wonder about a correlation of the critical value for KS distance (with Lilliefor correction) and model complexity? The critical KS value is distribution-independant if we use the true model parameters. With estimated parameters the critical value needs to be lower. Isn't that reduction highly connected to the model flexibility? And when we compare this to model selection methods like AIC or BIC, isn't this KS critical value change a much better measure for model complexity than the pure number of parameters?
On the other hand, KS is not very sensitive to the tail behavior, so is there even a similar but better method to quantify model complexity? A simple example would be the Student-t distribution (with location and scale), it extends the normal model, but with keeping only one more parameter, we could further extend it to short-tail cases by using negative df parameters. Can we expect a certain law for KS critical value reduction against model complexity or number of parameters? Or at least for choosing a certain form of parameters (e.g. based on the distribution moments)?
statistics
statistics
asked Dec 12 '18 at 11:29
user32038user32038
184
asked Dec 12 '18 at 11:29
user32038user32038
184
asked Dec 12 '18 at 11:29
user32038user32038
184
asked Dec 12 '18 at 11:29
user32038user32038
184
asked Dec 12 '18 at 11:29
user32038user32038
184
184
add a comment |
add a comment |
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