Helper function for monotonicity test.

internal

Provides functions to nonparametrically assess assumptions necessary to prevent the surrogate paradox through hypothesis tests of stochastic dominance, monotonicity of regression functions, and non-negative residual treatment effects. More details are available in Hsiao et al 2025 (under review). A tutorial for this package can be found at <https://laylaparast.com/home/SurrogateParadoxTest.html>.

Emily Hsiao

SurrogateParadoxTest

Empirical Testing of Surrogate Paradox Assumptions

S function

<dl> <dt>a</dt>
<dd>Value of a (regression coefficient)</dd> <dt>b</dt>
<dd>Value of b (regression coefficient)</dd> <dt>r</dt>
<dd>Index to start summation</dd> <dt>s</dt>
<dd>Index to end summation</dd> <dt>X</dt>
<dd>Vector of X values</dd> <dt>Y</dt>
<dd>Vector of Y values</dd></dl>

Arguments

Author

Helper function — S

<dl>

 <dt>a</dt>
<dd>Value of a (regression coefficient)</dd>

 <dt>b</dt>
<dd>Value of b (regression coefficient)</dd>

 <dt>r</dt>
<dd>Index to start summation</dd>

 <dt>s</dt>
<dd>Index to end summation</dd>

 <dt>X</dt>
<dd>Vector of X values</dd>

 <dt>Y</dt>
<dd>Vector of Y values</dd>

</dl>

S: Helper function

Description

Usage

Value

Arguments

Author