compute_cons_MLE_ase {cta}

Constrained MLE and ASE

Description

Computes the constrained MLE of S_{0}(m) subject to equality constraints h_{0}(m) = 0 under the specified strata and fixed.strata configuration, and its associated asymptotic standard error. Here m is the vector of expected table counts, i.e. m = E(Y).

Usage

compute_cons_MLE_ase(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)

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.

Value

compute_cons_MLE_ase returns a vector of length two. The first element S0.fct.m_H0 is the constrained MLE of S_{0}(m) subject to equality constraints h_{0}(m) = 0, and the second element ase.S0.fct.m_H0 is the associated asymptotic standard error.

Author(s)

Qiansheng Zhu

References

Lang, J. B. (2004) Multinomial-Poisson homogeneous models for contingency tables, Annals of Statistics, 32, 340–383.

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

See Also

ci.table