VARMLE

Sparse estimation of transtion matrix in vector autoregression given conditional autocovariance matrices.

The model is high-dimensional vector autoregression with measurement error, also known as linear gaussian state-space model. Provable sparse expectation-maximization algorithm is provided for the estimation of transition matrix and noise variances. Global and simultaneous testings are implemented for transition matrix with false discovery rate control. For more information, see the accompanying paper: Lyu, X., Kang, J., & Li, L. (2023). "Statistical inference for high-dimensional vector autoregression with measurement error", Statistica Sinica.

Xiang Lyu

hdiVAR

Statistical Inference for Noisy Vector Autoregression

Jian Kang

Lexin Li

VARMLE function

<dl><dt>S0</dt>
<dd>a p by p matrix; average (over time points) of conditional expectation of \(x_t x_t^\top\) on \(y_1, \ldots, y_T\) and parameter estimates, obtained from expectation step.</dd>
<dt>S1</dt>
<dd>a p by p matrix; average (over time points) of conditional expectation of \(x_t x_{t+1}^\top\)on \(y_1, \ldots, y_T\) and parameter estimates, obtained from expectation step.</dd>
<dt>tol</dt>
<dd>tolerance parameter in Dantzig selector.</dd></dl>

Arguments

Author

generalized Dantzig selector for transition matrix update in maximization step — VARMLE

<dl>

<dt>S0</dt>
<dd>a p by p matrix; average (over time points) of conditional expectation of \(x_t x_t^\top\) on \(y_1, \ldots, y_T\) and parameter estimates, obtained from expectation step.</dd>


<dt>S1</dt>
<dd>a p by p matrix; average (over time points) of conditional expectation of \(x_t x_{t+1}^\top\)on \(y_1, \ldots, y_T\) and parameter estimates, obtained from expectation step.</dd>


<dt>tol</dt>
<dd>tolerance parameter in Dantzig selector.</dd>

</dl>

VARMLE: generalized Dantzig selector for transition matrix update in maximization step

Description

Usage

Value

Arguments

Author