diff_PD_nr {cta}R Documentation

Difference in Power-Divergence Statistic Based CIs (Non-Robust)

Description

Constructs confidence intervals (CIs), based on the difference in power-divergence statistic, for estimands in contingency tables subject to equality constraints.

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

Usage

diff_PD_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, pdlambda)

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.

pdlambda

The index parameter \lambda in the power-divergence statistic.

Value

Provided that diff_PD_nr does not stop, it returns a 1-by-2 matrix which displays two endpoints of the confidence interval based on the difference in power-divergence statistic.

Author(s)

Qiansheng Zhu

References

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

See Also

diff_PD_robust, f.psi, ci.table


[Package cta version 1.3.0 Index]