Helper function to determine \(\beta\) estimates for MLE regression with patterning.

Generates \(\beta\) estimates for MLE using a conditioning approach with patterning support.

bsm.fit(x, y, z, pattern)

Arguments

x: An \(N \times (P + F)\) design matrix, where \(F\) is the number of columns conditioned on. This is equivalent to the multiplication of \(xyzb\).
y: The \(N \times (Q - F)\) matrix of observations, where \(F\) is the number of columns conditioned on. This is equivalent to the multiplication of \(Yz_a\).
z: A \((Q - F) \times L\) design matrix, where \(F\) is the number of columns conditioned on.
pattern: An optional \(N-F x F\) matrix of 0's and 1's indicating which elements of \(\beta\) are allowed to be nonzero.

A list with the following components:

Beta: The least-squares estimate of \(\beta\).
SE: The \((P+F)\times L\) matrix with the \(ij\)th element being the standard error of \(\hat{\beta}_ij\).
T: The \((P+F)\times L\) matrix with the \(ij\)th element being the t-statistic based on \(\hat{\beta}_ij\).
Covbeta: The estimated covariance matrix of the \(\hat{\beta}_ij\)'s.
df: A \(p\)-dimensional vector of the degrees of freedom for the \(t\)-statistics, where the \(j\)th component contains the degrees of freedom for the \(j\)th column of \(\hat{\beta}\).
Sigmaz: The \((Q - F) \times (Q - F)\) matrix \(\hat{\Sigma}_z\).
Cx: The \(Q \times Q\) residual sum of squares and crossproducts matrix.

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