g_theorem

One Monte-Carlo replicate; returns empirical error, exceedance indicator,
theoretical bounds, and assumption-check flags.

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

g_theorem function

<dl><dt>n</dt>
<dd>sample size</dd>
<dt>p</dt>
<dd>number of observed variables</dd>
<dt>m</dt>
<dd>number of latent factors</dd>
<dt>g_type</dt>
<dd>character: "linear", "weak_nonlinear", "strong_nonlinear"</dd>
<dt>epsilon</dt>
<dd>error threshold</dd>
<dt>zero_tol</dt>
<dd>zero-mean tolerance (default 0.02)</dd></dl>

Arguments

Simulation wrapper for Theorems 9 &amp; 10 — g_theorem

<dl>

<dt>n</dt>
<dd>sample size</dd>


<dt>p</dt>
<dd>number of observed variables</dd>


<dt>m</dt>
<dd>number of latent factors</dd>


<dt>g_type</dt>
<dd>character: "linear", "weak_nonlinear", "strong_nonlinear"</dd>


<dt>epsilon</dt>
<dd>error threshold</dd>


<dt>zero_tol</dt>
<dd>zero-mean tolerance (default 0.02)</dd>

</dl>

g_theorem: Simulation wrapper for Theorems 9 & 10

Description

Usage

Value

Arguments

Examples