fista.nuclear

Function to estimate low-rank matrix using FISTA algorithm

internal

Implementations of Thresholded Block Segmentation Scheme (TBSS) and Low-rank plus Sparse Two Step Procedure (LSTSP) algorithms for detecting multiple changes in structural VAR models. The package aims to address the problem of change point detection in piece-wise stationary VAR models, under different settings regarding the structure of their transition matrices (autoregressive dynamics); specifically, the following cases are included: (i) (weakly) sparse, (ii) structured sparse, and (iii) low rank plus sparse. It includes multiple algorithms and related extensions from Safikhani and Shojaie (2020) <doi:10.1080/01621459.2020.1770097> and Bai, Safikhani and Michailidis (2020) <doi:10.1109/TSP.2020.2993145>.

Yue Bai

VARDetect

Multiple Change Point Detection in Structural VAR Models

Peiliang Bai

Abolfazl Safikhani

George Michailidis

fista.nuclear function

<dl><dt>A</dt>
<dd>A n by p design matrix</dd>
<dt>b</dt>
<dd>A correspond vector, or a matrix</dd>
<dt>lambda</dt>
<dd>tuning parameter</dd>
<dt>d</dt>
<dd>model dimension</dd>
<dt>niter</dt>
<dd>the maximum number of iterations required for applying FISTA algorithm</dd>
<dt>backtracking</dt>
<dd>a boolean argument, indicate whether use backtracking or not</dd>
<dt>phi.true</dt>
<dd>true model parameter, only available for simulations</dd></dl>

Arguments

A helper function for implementing FISTA algorithm to estimate low-rank matrix — fista.nuclear

<dl>

<dt>A</dt>
<dd>A n by p design matrix</dd>


<dt>b</dt>
<dd>A correspond vector, or a matrix</dd>


<dt>lambda</dt>
<dd>tuning parameter</dd>


<dt>d</dt>
<dd>model dimension</dd>


<dt>niter</dt>
<dd>the maximum number of iterations required for applying FISTA algorithm</dd>


<dt>backtracking</dt>
<dd>a boolean argument, indicate whether use backtracking or not</dd>


<dt>phi.true</dt>
<dd>true model parameter, only available for simulations</dd>

</dl>

fista.nuclear: A helper function for implementing FISTA algorithm to estimate low-rank matrix

Description

Usage

Value

Arguments