R: Nested X-Squared Statistic Based CIs (Non-Robust)

nested_Xsq_nr {cta}

R Documentation

Nested `X`-Squared Statistic Based CIs (Non-Robust)

Description

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

The program may stop because of a non-convergence issue.

Usage

nested_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)

Arguments

`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 `\delta` that is in expressions of the moving critical values within each sliding quadratic step.

Value

Provided that nested_Xsq_nr does not stop, it returns a 1-by-2 matrix which displays two endpoints of the confidence interval based on the nested X^2 statistic.

Author(s)

Qiansheng Zhu

References

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

Nested X-Squared Statistic Based CIs (Non-Robust)