Auction: Internal function to manage multiple experts.
In rai: Revisiting-Alpha-Investing for Polynomial Regression

runAuction is the workhorse of the rai package: it takes an initial expert list and runs the Revisiting Alpha-Investing algorithm to greedily fit (optional) polynomials and interactions to data. The term "auction" is the result of multiple experts bidding to perform the test which determines stepwise ordering. This function is not intended to be called directly, but through rai.

vif(res, y, X, x, n, p, m, TSS, lmFit)

runAuction(experts, gWealth, theData, y, alg, poly, searchType, m, sigma,
  omega, reuse, nMaxTest, verbose, save, lmFit)

`res`	residuals from current model.
`y`	the response as a single column matrix.
`X`	covariates in the current model.
`x`	covariate being tested for addition into the model.
`n`	number of observations.
`p`	number of predictors in the current model.
`m`	number of observations used in subsampling for variance inflation factor estimate of r.squared.
`TSS`	total sum of squares; considering current residuals to be the response.
`lmFit`	The core function that will be used to estimate linear model fits. The default is .lm.fit, but other alternatives are possible. Note that it does not use formula notation as this is costly. Another recommended option is fastLmPure from RcppEigen or related packages.
`experts`	list of expert objects. Each expert is the output of makeStepwiseExpert or makeScavengerExpert.
`gWealth`	global wealth object, output of gWealthStep.
`theData`	covariate matrix.
`alg`	algorithm can be one of "rai", "raiPlus", or "RH" (Revisiting Holm).
`poly`	logical. Should the algorithm look for higher-order polynomials?
`searchType`	A character string specifying the prioritization of higher-order polynomials. One of "breadth" (more base features) or "depth" (higher order).
`sigma`	type of error estimate used in gWealthStep; one of "ind" or "step".
`omega`	return from rejecting a test in Alpha-Investing.
`reuse`	logical. Should repeated tests of the same covariate be considered a test of the same hypothesis? Reusing wealth isn't implemented for RAI or RAIplus (effect is negligible).
`nMaxTest`	maximum number of tests
`verbose`	logical. Should auction output be printed?
`save`	logical. Should the auction results be saved? If TRUE, returns a summary matrix.

A list which includes the following components:

`formula`	final model formula.
`y`	response.
`X`	model matrix from final model.
`features`	list of interactions included in formula.
`summary`	included if save=TRUE; matrix where each row contains the summary information of a single test.