nested_Xsq_robust: Nested X-Squared Statistic Based CIs (Robust)
In cta: Contingency Table Analysis Based on ML Fitting of MPH Models

Description Usage Arguments Value Author(s) References See Also

Constructs confidence intervals (CIs), based on the nested X^2 statistic, for estimands in contingency tables subject to equality constraints.

nested_Xsq_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, adj.epsilon,
                  iter.robust.max, iter.robust.eff)

`y`	Observed table counts in the contingency table(s), in vector form.
`strata`	Vector of the same length as `y` that gives the stratum membership identifier.
`fixed.strata`	The object that gives information on which stratum (strata) has (have) fixed sample sizes.
`h0.fct`	The constraint function h_{0}(\cdot) with respect to m, where m = E(Y), the vector of expected table counts.
`h0.fct.deriv`	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.
`S0.fct`	The estimand function S_{0}(\cdot) with respect to m.
`S0.fct.deriv`	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.
`max.mph.iter, step, change.step.after, y.eps, iter.orig, norm.diff.conv, norm.score.conv, max.score.diff.iter`	The parameters used in `mph.fit`.
`S.space.H0`	Restricted estimand space of S(\cdot) under H_{0}, i.e. subject to the imposed equality constraints along with sampling constraints.
`tol.psi, tol, max.iter`	The parameters used in the three stopping criteria in solving for the roots to the test-inversion equation.
`cut.off`	`qchisq(cc, 1)`. i.e. The chi-square cutoff, with 1 df, based on the significance level `1-cc`.
`delta`	The constant δ that is in expressions of the moving critical values within each sliding quadratic step.
`adj.epsilon, iter.robust.max, iter.robust.eff`	The parameters used in the robustifying procedure.

nested_Xsq_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 nested X^2 statistic. For the second object, it includes the warning message that occurs during construction of the confidence interval if the robustifying procedure is evoked: "nested.Xsq.CI: Adjustment used. Not on original data.\n". If the robustifying procedure is not evoked, the second object is NULL.

Qiansheng Zhu

Zhu, Q. (2020) "On improved confidence intervals for parameters of discrete distributions." PhD dissertation, University of Iowa.

nested_Xsq_nr, f.psi, ci.table

cta documentation built on Aug. 24, 2021, 1:06 a.m.