argmin.HT.gupta {argminCS} | R Documentation |
Perform argmin hypothesis test using Gupta's method.
Description
Test whether a dimension is the argmin, using the method in (Gupta 1965).
Usage
argmin.HT.gupta(
data,
r,
sample.mean = NULL,
stds = NULL,
critical.val = NULL,
alpha = 0.05,
...
)
Arguments
data |
A n by p data matrix; each of its row is a p-dimensional sample. |
r |
The dimension of interest for hypothesis test. |
sample.mean |
The sample mean of the n samples in data; defaults to NULL. It can be calculated via colMeans(data).
If performing multiple tests across dimensions, pre-computing |
stds |
A vector of the same (population) standard deviations for all dimensions; defaults to a vector of 1's. These are used to standardize the sample means. |
critical.val |
The quantile for the hypothesis test; defaults to NULL. It can be calculated via get.quantile.gupta.selection. If your experiment involves hypothesis testing over more than one dimension, pass a quantile to speed up computation. |
alpha |
The significance level of the hypothesis test; defaults to 0.05. |
... |
Additional argument to get.quantile.gupta.selection. A correct argument name needs to be specified if it is used. |
Value
A list containing:
test.stat | The test statistic |
. critical.value | The critical value for the hypothesis test. Being greater than it leads to a rejection. |
ans | 'Reject' or 'Accept' |
Note
This method requires independence among the dimensions.
References
Gupta SS (1965). “On Some Multiple Decision (Selection and Ranking) Rules.” Technometrics, 7(2), 225–245. doi:10.1080/00401706.1965.10490251.
Futschik A, Pflug G (1995). “Confidence Sets for Discrete Stochastic Optimization.” Annals of Operations Research, 56(1), 95–108. doi:10.1007/BF02031702.