CV_VARMLE

Tune the tolerance parameter of generalized Dantzig selector and hard thresholding
level via prediction error in test data.

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

CV_VARMLE function

<dl><dt>tol_seq</dt>
<dd>vector; grid of tolerance parameter in Dantzig selector for cross-validation.</dd>
<dt>ht_seq</dt>
<dd>vector; grid of hard-thresholding levels for transition matrix estimate.
To avoid hard thresholding, set <code>ht_seq=0</code>.</dd>
<dt>S0_train</dt>
<dd>a p by p matrix; average (over time points in training data) 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_train</dt>
<dd>a p by p matrix; average (over time points in training data) 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>Y_test</dt>
<dd>a p by T_test matrix; observations of time series in test set.</dd>
<dt>is_echo</dt>
<dd>logical; if true, display the information of CV-optimal (tol, ht).</dd></dl>

Arguments

Author

cross-validation for transition matrix update in maximization step — CV_VARMLE

<dl>

<dt>tol_seq</dt>
<dd>vector; grid of tolerance parameter in Dantzig selector for cross-validation.</dd>


<dt>ht_seq</dt>
<dd>vector; grid of hard-thresholding levels for transition matrix estimate.
To avoid hard thresholding, set <code>ht_seq=0</code>.</dd>


<dt>S0_train</dt>
<dd>a p by p matrix; average (over time points in training data) 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_train</dt>
<dd>a p by p matrix; average (over time points in training data) 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>Y_test</dt>
<dd>a p by T_test matrix; observations of time series in test set.</dd>


<dt>is_echo</dt>
<dd>logical; if true, display the information of CV-optimal (tol, ht).</dd>

</dl>

`tol_min`	CV-optimal tolerance parameter in Dantzig selector.
`ht_min`	CV-optimal hard thresholding level for the output of Dantzig selector.
`test_loss`	a matrix of prediction error in test data; columns match `tol_seq`, and rows match `ht_seq`.

CV_VARMLE: cross-validation for transition matrix update in maximization step

Description

Usage

Value

Arguments

Author