fsst: Conducts inference using the FSST procedure
In conroylau/lpinfer: An R Package for Inference in Linear Programs

View source: R/fsst.R

fsst	R Documentation

Conducts inference using the FSST procedure

Description

This module conducts inference in linear programs using the procedure by Fang, Santos, Shaikh and Torgovitsky (2020).

Usage

fsst(
  data = NULL,
  lpmodel,
  beta.tgt,
  R = 100,
  Rmulti = 1.25,
  lambda = NA,
  rho = 1e-04,
  n = NULL,
  weight.matrix = "diag",
  solver = NULL,
  progress = TRUE,
  sqrtm.method = function(m) pracma::sqrtm(m)$B,
  sqrtm.tol = .Machine$double.eps^(1/2),
  previous.output = NA
)

Arguments

`data`	An `data frame` or a `matrix`.
`lpmodel`	The `lpmodel` object.
`beta.tgt`	The value to be tested.
`R`	The number of bootstrap replications.
`Rmulti`	The multiplier for the number of bootstrap replications. The product of `Rmulti` and `R` refers to the maximum number of bootstrap replications to be conducted if there are errors.
`lambda`	Parameter used to obtain the restricted estimator \widehat{\bm{β}}^r_n. A data-driven parameter `lambda` can be included if `NA` is included as part of the vector for `lambda`. For instance, if `lambda` is set as `c(0.1, NA)`, then both 0.1 and the data-driven `lambda` will be applied in the `fsst` test. The default is to use the data-driven `lambda`.
`rho`	Parameter used in the studentization of matrices.
`n`	The sample size. This is only required if `data` is omitted in the input.
`weight.matrix`	The option used in the weighting matrix. There are three options available: `identity` — identity matrix `diag` — the diagonal matrix that takes the diagonal elements of the inverse of the variance matrix `avar` — inverse of the variance matrix
`solver`	The name of the linear and quadratic programming solver that is used to obtain the solution to linear and quadratic programs. The solvers supported by this package are `cplexAPI`, `gurobi`, `limSolve` and `Rcplex`.
`progress`	The boolean variable for whether the progress bars should be displayed. If it is set as `TRUE`, the progress bars will be displayed while the code is running.
`sqrtm.method`	The method used to obtain the matrix square root in the `fsst` procedure. This has to be a function that takes one argument that accepts a square matrix of size k x k and returns a square matrix of size k x k, where k can be the length of the β(P) vector, or the `beta.obs` component of the `lpinfer` object.
`sqrtm.tol`	The absolute tolerance used to check whether the matrix square root is correct. This is done by checking whether the Frobenius norm is smaller than the tolerance level, i.e., when A is the give matrix, B is the matrix square root obtained from the given `sqrtm.method` function, and ε is the tolerance level, the FSST test checks whether \|\|A - BB\|\|_F < ε. If this does not hold, the FSST test will use the `sqrtm` function from the `expm` package to obtain the matrix square root.
`previous.output`	The list of outputs obtained from the previous evaluation of the procedure. This is only used in the `fsst` test and when `previous.out` contains the studentized matrix `omega.i`. The rest of the arguments are ignored.

Details

The following components are required in the lpmodel for the fsst procedure:

A.tgt
A.obs
A.shp
beta.obs
beta.shp

Value

Returns the following information:

`pval`	A table of p-values.
`cv.table`	A table of sample and bootstrap Cone and Range test statistics.
`call`	The matched call.
`range`	The sample range test statistic.
`cone`	The sample cone test statistic.
`test`	The sample test statistic.
`cone.n.list`	The list of bootstrap cone test statistics.
`range.n.list`	The list of bootstrap range test statistics.
`solver.name`	Name of the solver used.
`rho`	The value of `rho` provided by the user.
`rhobar.i`	The regularization parameter used for the Cone studentization matrix.
`lambda.data`	The value of the data-driven `lambda` (if applicable).
`var.method`	The method used in obtaining the asymptotic variance of `beta.obs`.
`test.logical`	An indicator variable for whether the computation has been conducted. If `test.logical` is 1, it refers to the case where `beta.tgt` is inside the logical bound. If `test.logical` is 0, it refers to the case where `beta.tgt` is outside the logical bound.
`logical.lb`	Logical lower bound.
`logical.ub`	Logical upper bound.
`df.error`	A table showing the id of the bootstrap replication(s) with error(s) and the corresponding error message(s).
`R.succ`	The number of successful bootstrap replications.

Example

  source("./example/dgp_missingdata.R") # Change directory if necessary
  J <- 5
  N <- 1000
  data <- missingdata_draw(J = J, n = N, seed = 1, prob.obs = .5)
  lpm <- missingdata_lpm(J = J, info = "full", data = data)
  fsst(data = data,
       lpmodel = lpm,
       beta.tgt = .2,
       R = 100,
       lambda = .2,
       rho = 1e-4,
       weight.matrix = "identity",
       solver = "gurobi")