Estimate variance from replicate weights

[vahid-ahmadi]

Adds variance and standard error estimation from replicate weights for scalar statistics, including weighted means, counts, Gini coefficients and quantiles. The API recomputes the statistic with each replicate's weights and preserves the source values' dtype, index and name, including categorical, Boolean, nullable and exact large-integer data.

replicate_variance, replicate_standard_error and MicroSeries.replicate_standard_error accept the keyword-only centering argument. "full-sample" remains the default and uses the full-sample estimate; "replicate-mean" uses the mean of the replicate estimates. Both choices retain the same method factors, where R counts replicate columns:

Method	Factor
Unstratified JK1 / common-factor delete-group jackknife	(R - 1) / R
Balanced repeated replication (BRR)	1 / R
Fay's BRR	1 / (R * (1 - fay_k)**2)
Bootstrap	1 / R
Successive-difference replication	4 / R

The survey's replication design determines the appropriate factor and centering convention. Statistical validity also depends on the statistic: nonsmooth quantiles can require an appropriate replication method or smoothing of replicate estimates. This API applies the supplied statistic directly and supports common-factor schemes; arbitrary stratified jackknife and averaged-bootstrap schemes that require additional or replicate-specific factors remain outside its scope. Replicate-weight rows must follow the source series' row order; DataFrame index labels do not realign them.

Changing main weights without corresponding design-consistent adjustments to replicate weights invalidates the original replicates. Calibration can remain valid when the required calibration is repeated appropriately for every replicate.

Reference-relative centering and scaled accumulation preserve representable variances at extreme magnitudes without depending on platform-specific extended precision. BRR replicates alternating between 0 and 2e154 now return variance 1e308 and standard error 1e154; identical replicate estimates of 1e308 return zero. Replicate-mean centering retains a variance of 1 for estimates alternating between 2**53 and 2**53 + 2. Full-sample centering continues to use the callback's returned estimate, and nonfinite callback results retain their existing propagation.

Regression tests cover dtype preservation, metadata and input integrity, both centering conventions through all public entry points, each method's factor, default compatibility, invalid centering and positional weight rows. Exact nonlinear examples distinguish the two centers without relying on stochastic agreement. The 118 added numerical cases cover finite extreme results, small common-offset differences, representable subnormal variances, Fay amplification of tiny deviations, true overflow and nonfinite behavior.

The full-sample callback receives an independent copy of the source. A statistic that normalizes values or changes weights in place cannot contaminate subsequent replicate inputs or the caller's data, including when it raises an exception. The reported in-place normalization case now returns variance 3,600 and standard error 60, matching the functional callback.

Validation: 566 full-suite tests passed on each of pandas 2.3.1 and 3.0.5, including 24 callback-isolation regressions. Independent verification passed 63 diagnostics per environment across all three entry points and both centering modes, including mutation and exception cases.

Combined with #321 and #323, 817 full-suite tests, 35 repair acceptance cases and 180 exact-arithmetic interaction cases pass on each pandas version. Formatting, lint and changelog drafts pass.

Closes #319.

[vahid-ahmadi]

Paper side updated in #315: the State of the Field table now reads "Replicate weights" rather than "No" under design-based variance, and the scope paragraph says what this does and does not do — replicate weights yes, variance from a stratum/PSU design specification no, and not valid on calibrated weights.

Worth merging this before the paper, so the table describes what ships.

[vahid-ahmadi]

Lint is clean on the files this PR adds. The remaining failures in that job are pre-existing on main — 141 errors there before this branch, which is #305 / #307.