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.

Testing homogeneity of k multivariate distributions is a classical and challenging problem in
             statistics, and this becomes even more challenging when the dimension of the data exceeds the sample size.
             We construct some tests for this purpose which are exact level (size) alpha tests based on clustering. 
             These tests are easy to implement and distribution-free in finite sample situations. Under appropriate 
             regularity conditions, these tests have the consistency property in HDLSS asymptotic regime, where the 
             dimension of data grows to infinity while the sample size remains fixed. We also consider a multiscale 
             approach, where the results for different number of partitions are aggregated judiciously. Details are in 
             Biplab Paul, Shyamal K De and Anil K Ghosh (2021) <doi:10.1016/j.jmva.2021.104897>; Soham Sarkar and Anil K Ghosh (2019) 
             <doi:10.1109/TPAMI.2019.2912599>; William M Rand (1971) <doi:10.1080/01621459.1971.10482356>;  
             Cyrus R Mehta and Nitin R Patel (1983) <doi:10.2307/2288652>; Joseph C Dunn (1973) 
             <doi:10.1080/01969727308546046>; Sture Holm (1979) <doi:10.2307/4615733>; 
             Yoav Benjamini and Yosef Hochberg (1995) <doi: 10.2307/2346101>.

Implementation of selected high-dimensional statistical and
    econometric methods for estimation and inference. Efficient estimators and
    uniformly valid confidence intervals for various low-dimensional causal/
    structural parameters are provided which appear in high-dimensional
    approximately sparse models. Including functions for fitting heteroscedastic
    robust Lasso regressions with non-Gaussian errors and for instrumental variable
    (IV) and treatment effect estimation in a high-dimensional setting. Moreover,
    the methods enable valid post-selection inference and rely on a theoretically
    grounded, data-driven choice of the penalty.
    Chernozhukov, Hansen, Spindler (2016) <arXiv:1603.01700>.