argmin.HT.nonsplit

Test if a dimension may be argmin without any splitting.

Provides methods to construct frequentist confidence sets with valid marginal
coverage for identifying the population-level argmin or argmax based on IID data.
For instance, given an n by p loss matrix—where n is the sample size and p is the
number of models—the CS.argmin() method produces a discrete confidence set that contains
the model with the minimal (best) expected risk with desired probability. The argmin.HT()
method helps check if a specific model should be included in such a confidence set. The main
implemented method is proposed by Tianyu Zhang, Hao Lee and Jing Lei (2024)
"Winners with confidence: Discrete argmin inference with an application to model selection".

Hao Lee

argminCS

Argmin Inference over a Discrete Candidate Set

Tianyu Zhang

Jing Lei

argmin.HT.nonsplit function

<dl><dt>difference.matrix</dt>
<dd>A n by (p-1) difference data matrix (reference dimension - the rest);
each of its row is a (p-1)-dimensional vector of differences.</dd>
<dt>lambda</dt>
<dd>The real-valued tuning parameter for exponential weightings (the calculation of softmin).</dd>
<dt>sample.mean</dt>
<dd>The sample mean of differences; defaults to NULL. It can be calculated via colMeans(difference.matrix).</dd>
<dt>alpha</dt>
<dd>The significance level of the hypothesis test; defaults to 0.05.</dd>
<dt>scale.input</dt>
<dd>A boolean variable specifying whether the input difference matrix should be standardized defaults to TRUE</dd></dl>

Arguments

Perform argmin hypothesis test. — argmin.HT.nonsplit

<dl>

<dt>difference.matrix</dt>
<dd>A n by (p-1) difference data matrix (reference dimension - the rest);
each of its row is a (p-1)-dimensional vector of differences.</dd>


<dt>lambda</dt>
<dd>The real-valued tuning parameter for exponential weightings (the calculation of softmin).</dd>


<dt>sample.mean</dt>
<dd>The sample mean of differences; defaults to NULL. It can be calculated via colMeans(difference.matrix).</dd>


<dt>alpha</dt>
<dd>The significance level of the hypothesis test; defaults to 0.05.</dd>


<dt>scale.input</dt>
<dd>A boolean variable specifying whether the input difference matrix should be standardized defaults to TRUE</dd>

</dl>

`test.stat.scale`	The scaled test statistic

. `critical.value`	The critical value for the hypothesis test. Being greater than it leads to a rejection.

`std`	The standard deviation estimate.

`ans`	'Reject' or 'Accept'

argmin.HT.nonsplit: Perform argmin hypothesis test.

Description

Usage

Value

Arguments

Details