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Use the \e... estimator macros instead of raw \hat in _sec_poisson_dx.qmd #1144

Description

@d-morrison

_subfiles/count-regression/_sec_poisson_dx.qmd hand-expands estimator notation that latex-macros/macros.qmd already provides:

6:  $$e \eqdef y - \hat y$$
10: $$r \eqdef \frac{e}{\hse{e}} \approx \frac{e}{\sqrt{\hat y}}$$
20: d_k \eqdef \signt(y - \hat y)
21:   \left\{\sqrt{2[\ell_{\text{full}}(y) - \ell(\hat\beta; y)]}\right\}

\ey (\def\ey{\est{y}}) and \eb (\def\eb{\est{\beta}}, macros.qmd:658) cover all four sites. Per CLAUDE.md, new content should prefer the \e... estimator-indirection family over applying \hat directly, so that changing the estimator glyph later is a one-line edit to \est.

Why this is a separate issue

Raised during review of #1132, which fixed three genuinely new instances of this class (\hat{\vec{\beta}} at two sites and \hat{\theta}). These four are different: they are pre-existing on main and that PR only reflowed the lines around them (= to \eqdef, plus one line split). Converting one of the four inside #1132 would have been an inconsistent partial sweep of untouched content, so it was reverted there and filed here instead.

Scope

Worth doing as a file-level or chapter-level sweep rather than four spot edits — a grep for \\hat across _subfiles/count-regression/ and chapters/count-regression.qmd will find whether other sites share the pattern. Purely notational: the rendered output is unchanged, so this needs a render check but no mathematical review.

Filed by Claude Code (AI agent).

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