Result · DS-PROJECTED-K-REQUIREMENT

The projected problem needs fewer cells

Proved herepublication: internal

Meaning

Efficient-score projection reduces the relevant rank requirement to the number of parameters of interest.

Statement

When nuisance information is supplied externally via full-data efficient-score projection, the lower-dimensional projected D problem structurally requires only K>=d_ψ+1.

Where it stops

This is a different statistical formulation from full in-bin nuisance profiling.

Relationships

Rests on

The full chain beneath it

Open next door

Local graph

Prerequisites to the left, what it enables or raises to the right, boundary cases below. Open in the map.

Proof

DS9. The $K\le d$ feasibility split

For the full in-bin profiled formulation, $I_q$ is singular when $K\le d$ , so ordinary full-block $D_s$ profiling is not identifiable.

The projected efficient-score problem only needs enough categories to identify the $d_\psi$ -dimensional efficient score, i.e. structurally $K\ge d_\psi+1$ , if nuisance information is supplied externally.

These are different statistical problems and must be exposed separately.

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