compute_insample: In-Sample Error

In ygeunkim/youngtool: Research tools for academic writing

Description

This function computes training error, in-sample error, and optimism in MC simulation setting.

Usage

compute_insample(
  data,
  ny,
  fit,
  rand,
  mcname = "mc",
  xname = "x",
  yname = "y",
  fitname = "fx",
  pred_name = "pred",
  insample_name = "y",
  error = c("squared", "absolute"),
  distribution = FALSE,
  mod,
  formula,
  ...
)

Arguments

data	MC data set generated by mc_data.
ny	the number of response at each x point
fit	True model function with x-named argument.
rand	Random sample generator function for error term. By default, rnorm
mcname	column name of the MC sample. By default, "mc".
xname	column name of the data. By default, "x".
yname	column name of the response. By default, "y".
fitname	column name of the true fit. By default, "fx".
pred_name	column name of the predicted values. By default, "pred".
insample_name	multiple column names when computing insample error
error	Choice of loss function. See loss.
distribution	return the error for each MC sample? FALSE by default. If TRUE, it gives the data.table.
mod	Model function.
formula	an object of class formula.
...	Additional arguments for mod. If you wand argument for rand, define one.

Details

In-sample error differs from Expected test error in that it is computed in the same predictor values. Instead, it uses new response values at each predictor point.

Err_{in} = \frac{1}{N} ∑_{i = 1}^N E_{y_0} [L(Y_i^{(0)}, \hat{f}(x_i)) \mid T]

Optimism is the difference between the insample error and the training error.

Value

Training error, Insample error, Optimism

References

Hastie, T., Tibshirani, R.,, Friedman, J. (2001). The Elements of Statistical Learning. New York, NY, USA: Springer New York Inc..

ygeunkim/youngtool documentation built on Dec. 14, 2019, 7:42 p.m.