R: Confidence intervals for 'fLoss' estimators

check_CIbound {eshrink}

R Documentation

Confidence intervals for 'fLoss' estimators

Description

Compute confidence intervals by 'inverting the test' to determine if a given value should lie in the confidence region.

Usage

check_CIbound(
  testBeta,
  obsEst,
  type = c("ridge", "lasso"),
  postParam,
  lambdaseq,
  X,
  nPost,
  ind = 1,
  Bstar = 100,
  B = 500,
  loss = "fMBV",
  lowerBound = TRUE,
  reproducible = TRUE,
  alpha = 0.025,
  returnDist = FALSE,
  ...
)

invertTest(
  interval,
  type = "ridge",
  lower.interval = interval,
  upper.interval = interval,
  ...,
  tol = 0.005,
  fulldetail = FALSE
)

Arguments

`testBeta`	Candidate value of beta to test.
`obsEst`	Estimate of beta from the observed data for which a confidence interval is desired
`type`	String indicating "ridge" or "LASSO".
`postParam`	List of parameters for the posterior distribution of beta. See `samplePosterior` for expected names.
`lambdaseq`	Sequence of penalty values
`X`	deisgn matrix
`nPost`	Number of posterior samples to use.
`ind`	Index of parameter to test. Defaults to 1.
`Bstar`	Number of estimators to compute for comparison distribution. Larger values improve the precision of the procedure but increase computational cost.
`B`	Passed to `festLASSO`
`loss`	Either `"fMBV"` or `"fMSE"`.
`lowerBound`	Logical indicating that the test is for a lower bound
`reproducible`	Should the simulated datasets be reproducible?
`alpha`	Percentile of the distribution to compare against. See details.
`returnDist`	If TRUE, then distribution of estimates generated is returned instead of comparison against `alpha`
`...`	In `invertTest`, these are passed to `check_CIbound`. In `check_CIbound`, these arguments are passed to `samplePosterior`.
`interval`	Interval to check. Used for both upper and lower bound, if they are not provided
`lower.interval`, `upper.interval`	Bounding intervals over which to check for lower and upper endpoints of CI
`tol`	Passed to `uniroot`
`fulldetail`	If TRUE, then output from `uniroot` is included.

Details

This function is used as part of an 'inverting the test' approach to generate confidence intervals for estimators from festRidge. Bstar datasets are generated from slices of the posterior distribution of the model parameters where beta (or other parameter indicated by ind) is fixed at the value testBeta. For each dataset, beta is estimated via festRidge or festLASSO, and the resulting distribution of estimators is compared against the estimate from the observed data (obsEst).

The values of lambdaseq, X, nPost, and loss are passed to festRidge or festLASSO and typically match the values that were used to compute obsEst.

The computational cost of this function is most affected by the values of nPost and Bstar. Large values of the latter are important for adequately representing the distribution of parameter estimates. In some settings, nPost can be reduced without substantially impacting the results. However, each dataset is likely to be different.

Author(s)