# cstaubest: Confidence sets for the tau-best In danielwilhelm/R-CS-ranks: Statistical Tools for Ranks

 cstaubest R Documentation

## Confidence sets for the tau-best

### Description

Computation of confidence sets for the identities of populations among the tau best.

### Usage

``````cstaubest(
x,
Sigma,
tau = 2,
coverage = 0.95,
stepdown = TRUE,
R = 1000,
na.rm = FALSE,
seed = NA
)

cstauworst(
x,
Sigma,
tau = 2,
coverage = 0.95,
stepdown = TRUE,
R = 1000,
na.rm = FALSE,
seed = NA
)
``````

### Arguments

 `x` vector of estimates containing estimated features by which the `length` populations are to be ranked. `Sigma` estimated covariance matrix of `x`. `tau` the confidence set contains indicators for the elements in `x` whose rank is less than or equal to `tau`. `coverage` nominal coverage of the confidence set. Default is 0.95. `stepdown` logical; if `TRUE` (default), stepwise procedure is used, otherwise single step procedure is used. See Details section for more. `R` number of bootstrap replications. Default is 1000. `na.rm` logical; if `TRUE`, then `NA`'s are removed from `x` and `Sigma` (if any). `seed` seed for bootstrap random variable draws. If set to `NA` (default), then seed is not set.

### Value

logical vector indicating which of the elements of `x` are in the confidence set for the tau-best.

### Functions

• `cstauworst()`: Confidence sets for the tau-worst

Equivalent to calling `cstaubest` with `-x`.

### Details

The function computes a confidence set containing indicators for the elements in `x` whose rank is less than or equal to `tau` with probability approximately equal to the nominal coverage (`coverage`).

The command implements the projection confidence set for the tau-best developed and described in more detail in Mogstad, Romano, Shaikh, and Wilhelm (2023).

### References

Mogstad, Romano, Shaikh, and Wilhelm (2023), "Inference for Ranks with Applications to Mobility across Neighborhoods and Academic Achievements across Countries", forthcoming at Review of Economic Studies cemmap working paper, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1093/restud/rdad006")}

### Examples

``````# simple simulated example:
n <- 100
p <- 10
X <- matrix(rep(1:p,n)/p, ncol=p, byrow=TRUE) + matrix(rnorm(n*p), 100, 10)
thetahat <- colMeans(X)
Sigmahat <- cov(X) / n

# confidence set for the populations that may be among the top-3 (with probability approximately 0.95):
cstaubest(thetahat, Sigmahat, tau=3)

# confidence set for the populations that may be among the bottom-3 (with probability approximately 0.95):
cstauworst(thetahat, Sigmahat, tau=3)

``````

danielwilhelm/R-CS-ranks documentation built on Sept. 25, 2023, 6:08 a.m.