Constructs confidence intervals (CIs), based on the difference in \(X^2\) statistic, for estimands in contingency tables subject to equality constraints.
The program may stop because of a non-convergence issue.
diff_Xsq_nr(y, strata, fixed.strata, h0.fct, h0.fct.deriv,
S0.fct, S0.fct.deriv, max.mph.iter, step,
change.step.after, y.eps, iter.orig, norm.diff.conv,
norm.score.conv, max.score.diff.iter, S.space.H0,
tol.psi, tol, max.iter, cut.off, delta)Observed table counts in the contingency table(s), in vector form.
Vector of the same length as y that gives the stratum membership
identifier.
The object that gives information on which stratum (strata) has (have) fixed sample sizes.
The constraint function \(h_{0}(\cdot)\) with respect to \(m\), where \(m = E(Y)\), the vector of expected table counts.
The R function object that computes analytic derivative of the
transpose of the constraint function \(h_{0}(\cdot)\) with
respect to \(m\). If h0.fct.deriv is not specified or
h0.fct.deriv = NULL, numerical derivatives will be used.
The estimand function \(S_{0}(\cdot)\) with respect to \(m\).
The R function object that computes analytic derivative of the
estimand function \(S_{0}(\cdot)\) with
respect to \(m\). If S0.fct.deriv is not
specified or S0.fct.deriv = NULL, numerical derivatives
will be used.
The parameters used in mph.fit.
Restricted estimand space of \(S(\cdot)\) under \(H_{0}\), i.e. subject to the imposed equality constraints along with sampling constraints.
The parameters used in the three stopping criteria in solving for the roots to the test-inversion equation.
qchisq(cc, 1). i.e. The chi-square cutoff, with \(1\)
df, based on the significance level 1-cc.
The constant \(\delta\) that is in expressions of the moving critical values within each sliding quadratic step.
Provided that diff_Xsq_nr does not stop,
it returns a \(1\)-by-\(2\) matrix which displays two endpoints of the confidence interval based on the difference in \(X^2\) statistic.
Zhu, Q. (2020) "On improved confidence intervals for parameters of discrete distributions." PhD dissertation, University of Iowa.