verify_mean

Draws n i.i.d. N(0, I_m) latent factors, applies g component-wise,
and checks whether |E[g(x)]| &lt; tol on every coordinate.

Implements general unilateral loading estimator for two-layer latent factor models with smooth, element-wise factor transformations. We provide data simulation, loading estimation,finite-sample error bounds, and diagnostic tools for zero-mean and sub-Gaussian assumptions. A unified interface is given for evaluating estimation accuracy and cosine similarity. The philosophy of the package is described in Guo G. (2026) <doi:10.1016/j.apm.2025.116280>.

Guangbao Guo

GulFM

General Unilateral Load Estimator for Two-Layer Latent Factor
Models

verify_mean function

<dl><dt>g_fun</dt>
<dd>vectorised map g: R -&gt; R</dd>
<dt>m</dt>
<dd>latent dimension</dd>
<dt>n</dt>
<dd>Monte-Carlo sample size</dd>
<dt>tol</dt>
<dd>numerical tolerance (default 1e-3)</dd></dl>

Arguments

Verify zero-mean preservation (Theorem 10 assumption 2a) — verify_mean

<dl>

<dt>g_fun</dt>
<dd>vectorised map g: R -&gt; R</dd>


<dt>m</dt>
<dd>latent dimension</dd>


<dt>n</dt>
<dd>Monte-Carlo sample size</dd>


<dt>tol</dt>
<dd>numerical tolerance (default 1e-3)</dd>

</dl>

verify_mean: Verify zero-mean preservation (Theorem 10 assumption 2a)

Description

Usage

Value

Arguments

Examples