R: Wald-Type CIs (Non-Robust)

Wald_trans.Wald_nr {cta}

R Documentation

Wald-Type CIs (Non-Robust)

Description

Constructs non-transformed and transformed (if the transformation g is specified) Wald confidence intervals (CIs) for estimands in contingency tables subject to equality constraints.

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

Usage

Wald_trans.Wald_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, cut.off,
                   S.space.H0, trans.g, trans.g.deriv, trans.g.inv)

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`.
`cut.off`	`qchisq(cc, 1)`. i.e. The chi-square cutoff, with `1` df, based on the significance level `1-cc`.
`S.space.H0`	Restricted estimand space of `S(\cdot)` under `H_{0}`, i.e. subject to the imposed equality constraints along with sampling constraints.
`trans.g`	The transformation `g` used in the transformed Wald confidence interval.
`trans.g.deriv`	The derivative function of the transformation `g`, i.e. `d g(w) / d w`. If it is specified, it should be an R function, even if the derivative function is a constant function.
`trans.g.inv`	`g^{-1}` function used in back-transformation step in construction of the transformed Wald confidence interval.

Value

Provided that Wald_trans.Wald_nr does not stop,

either it returns a 1-by-2 matrix which displays two endpoints of the non-transformed Wald confidence interval, if the transformation g is not specified;
or it returns a 2-by-2 matrix, whose first row displays two endpoints of the non-transformed Wald confidence interval, and whose second row displays two endpoints of the transformed Wald confidence interval, if the transformation g is specified.

Author(s)

Qiansheng Zhu

References

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