pSAVE

The partial-SAVE model. This model is correct only under very strong
assumptions, the solution is used as the initial value in the <code>orthoDr</code>
optimization.

Utilize an orthogonality constrained optimization algorithm of
Wen & Yin (2013) <DOI:10.1007/s10107-012-0584-1> to solve a variety of
dimension reduction problems in the semiparametric framework, such as
Ma & Zhu (2012) <DOI:10.1080/01621459.2011.646925>, Ma & Zhu (2013)
<DOI:10.1214/12-AOS1072>, Sun, Zhu, Wang & Zeng (2019) <DOI:10.1093/biomet/asy064>
and Zhou, Zhu & Zeng (2021) <DOI:10.1093/biomet/asaa087>. The package also
implements some existing dimension reduction methods such as hMave by Xia, Zhang,
& Xu (2010) <DOI:10.1198/jasa.2009.tm09372> and partial SAVE by Feng, Wen & Zhu (2013)
<DOI:10.1080/01621459.2012.746065>. It also serves as a general purpose
optimization solver for problems with orthogonality constraints, i.e., in Stiefel
manifold. Parallel computing for approximating the gradient is enabled through 'OpenMP'.

Ruoqing Zhu

orthoDr

Semi-Parametric Dimension Reduction Models Using Orthogonality
Constrained Optimization

Ruilin Zhao

Jiyang Zhang

Wenzhuo Zhou

Peng Xu

James Joseph Balamuta

pSAVE function

<dl><dt>x</dt>
<dd>A <code>matrix</code> for features (continuous only).</dd>
<dt>a</dt>
<dd>A <code>vector</code> of observed dose levels (continuous only).</dd>
<dt>r</dt>
<dd>A <code>vector</code> of reward (outcome).</dd>
<dt>ndr</dt>
<dd>The dimension structure</dd>
<dt>nslices0</dt>
<dd>Number of slides used for save</dd></dl>

Arguments

Partial Sliced Averaged Variance Estimation — pSAVE

<dl>

<dt>x</dt>
<dd>A <code>matrix</code> for features (continuous only).</dd>


<dt>a</dt>
<dd>A <code>vector</code> of observed dose levels (continuous only).</dd>


<dt>r</dt>
<dd>A <code>vector</code> of reward (outcome).</dd>


<dt>ndr</dt>
<dd>The dimension structure</dd>


<dt>nslices0</dt>
<dd>Number of slides used for save</dd>

</dl>

pSAVE: Partial Sliced Averaged Variance Estimation

Description

Usage

Value

Arguments

References