Usage

The package contains two functions that compute the non-parametric estimators presented in Appendix C of Rose, Schellenberg, and Shem-Tov (2022).

The first, ustat.varcovar(), estimates the variance-covariance, taking in two matrices as inputs:

import ustat_var as ustat
import numpy as np

# Seed and data
np.random.seed(18341)
X,Y = ustat.generate_test_data.generate_data(n_teachers = 10, n_time = 5, n_arrays = 2, var_fixed = 1, var_noise = 1.0, cov_factor = 0.5)

# Variance-covariance
ustat.varcovar(X, X) # Var(X)
ustat.varcovar(X, Y) # Cov(X, Y)

The second, ustat_samp_covar, estimates the sampling variance/covariance of varcovar. It takes four matrices as inputs, where ustat_samp_covar(A, B, C, D) yields \(\hat{\operatorname{Cov}}(\hat{\operatorname{Cov}}(A, B) − \operatorname{Cov}(A, B), \hat{\operatorname{Cov}} (C,D) − \operatorname{Cov}(C,D))\) . For example, using the \(X,Y\) generated above:

# Base implementation through ustat_samp_covar.ustat_samp_covar() functions:
ustat.ustat_samp_covar.ustat_samp_covar(X, X, X, X) # Sampling variance of Var(X)
ustat.ustat_samp_covar.ustat_samp_covar(X, Y, X, Y) # Sampling variance of Cov(X, Y)

# Faster implementation available in ustat_samp_covar.ustat_samp_covar_fast() function
ustat.ustat_samp_covar.ustat_samp_covar_fast(X, X, X, X) # Also computes sampling variance of Var(X), but faster than above
ustat.ustat_samp_covar.ustat_samp_covar_fast(X, Y, X, Y) # Also computes sampling variance of Cov(X, Y), but faster than above

For further details about these two functions and the required empirical setup, please see the user manual.