Constructs confidence intervals (CIs), based on the difference in power-divergence statistic, for estimands in contingency tables subject to equality constraints.
diff_PD_robust(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, pdlambda,
adj.epsilon, iter.robust.max, iter.robust.eff)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.
The index parameter \(\lambda\) in the power-divergence statistic.
The parameters used in the robustifying procedure.
diff_PD_robust returns a list, which includes two objects. The first object is a \(1\)-by-\(2\) matrix which displays two endpoints of the confidence interval based on the difference in power-divergence statistic. For the second object, it includes the warning message that occurs during construction of the confidence
interval if the robustifying procedure is evoked: "diff.PD.CI: Adjustment used. Not on original data.\n". If the robustifying procedure is not evoked, the second object is NULL.
Zhu, Q. (2020) "On improved confidence intervals for parameters of discrete distributions." PhD dissertation, University of Iowa.