CV-TMLE of the fold-local learned-rule value at exceptional and weak-blip laws

This study reads the interval of LearnedRuleValue at two laws that the gated study does not claim. The estimator, the learners, the size, the truth rule and the oracle SE are those of the gated study. Only the laws differ.

The study publishes under the reporting policy, and it declares no property cell. A study with no property cells is not a validation row, as adding a method row states. The validation grid therefore does not list it. Each red verdict enters the red-cell ledger with the owner F27.

No canonical implementation is compared. The gated study gives the comparator survey. A zero-row equivalence artifact records the absence of a comparator.

What was tested

setting	declaration
law, fit, learners, truth and oracle SE	as in the gated study
primary budget	6,000 replications for each law, at n = 2,000
verdicts	the gated study’s primary verdicts on the error, under publication_policy="reporting"
reading	the declared reading table of the Reading section, read from the top
seeds	seed=20263003 and resampling_seed=20263004
policy	reporting

law	\(b(W)\)	\(d_0\) treats	limit blip of the learner	\(\Psi_{d_0}(P_0)\)	condition C3
exceptional	\(0\)	no unit	\(0\), so no fixed limit rule exists	0.512179	fails. Every rule has the value 0.512179
weak_blip	\(0.15 W_1\)	\(W_1 > 0\)	\(0.15 W_1\)	0.521047	holds. Equation (5) and Theorem 6 of van der Laan and Luedtke (2015) apply

At exceptional the truth of every replication is 0.512179, because the effect is zero for every unit. At weak_blip the truth varies with the fitted rules.

The RM30 record names the commit that holds the declaration. That declaration fixed the laws, the budget, the seeds and the reading table before any run.

Accuracy against known truth

law	estimand	what was tested	implementation	bias (99% interval)	coverage	SE ratio	result
learned-rule law with the blip 0, no treatment effect for any unit	ey_learned_rule[learned rule]	fold average of the value of the rule learned on each fold’s training rows from its outcome regression	cleverly fold-evaluated CV-TMLE of the learned-rule value	-0.000748 to 0.000535	0.8938	0.8211	fail
learned-rule law with the weak blip 0.15 W1	ey_learned_rule[learned rule]	fold average of the value of the rule learned on each fold’s training rows from its outcome regression	cleverly fold-evaluated CV-TMLE of the learned-rule value	-0.000514 to 0.000732	0.8948	0.8314	fail

Both laws pass the bias verdict and the SE-ratio screen. Both laws fail the coverage floor, so each truth row is red.

Reading

The declared table takes each law’s 99% Clopper-Pearson coverage interval. The first condition that holds names the reading.

reading, for each law	condition
under-covers at the <law> law	the interval’s upper end is below 0.95
no under-coverage resolved at the declared budget	the interval’s lower end is at or above 0.90
unresolved	otherwise

The reading unresolved cannot occur at 6,000 replications. It needs an interval that reaches below 0.90 and above 0.95, so it is at least 0.05 wide. At 6,000 replications the 99% Clopper-Pearson interval is at most 0.0334 wide.

law	coverage	99% interval	reading
exceptional	0.8938	0.8832 to 0.9038	under-covers at the exceptional law
weak_blip	0.8948	0.8842 to 0.9048	under-covers at the weak_blip law

reading.csv holds each reading. The Measured values section gates every number in this table.

What the readings show

law	what the reading shows	source of the interpretation
exceptional	the interval under-covers where condition C3 fails. The effect is zero for every unit, so the fold rules have no fixed limit and do not stabilize	Luedtke and van der Laan (2016), Annals of Statistics, Section 4.1, expect the rule estimate “to fluctuate randomly” where the blip is zero. Section 4.2 names the tools that avoid a fixed limit, and no reviewed source applies them to this target (F27)
weak_blip	the interval under-covers at n = 2,000 on a law within C3. Theorem 6 gives nominal coverage asymptotically. The study reads the red cell as a finite-sample limit, which one size does not establish. The mean reported SE agrees with the mean oracle SE of the fixed fold rules, 0.0156 against 0.0155, while the SD of the error is 0.0187. That agreement supports the reading	van der Laan and Luedtke (2015), Equation (5) and Theorem 6, cover this law. F27 states that no published result is missing for it

At both laws the mean reported SE is smaller than the SD of the error. The SE ratio is 0.8211 at exceptional and 0.8314 at weak_blip. The table gives the three spreads. The oracle SE is the standard error that the influence curves of the fold rules give under \(P_0\), with each rule held fixed. It is a descriptive column of harness.csv.gz, and no rule reads it.

law	mean reported SE	mean oracle SE	SD of the error
exceptional	0.0158	0.0158	0.0193
weak_blip	0.0156	0.0155	0.0187

The readings do not show the items in this list.

• The cause of the smaller SE. The study does not separate the instability of the rules from other finite-sample effects.

• The size at which weak_blip reaches nominal coverage. The study runs one size.

• The coverage at other laws, learners or fold counts.

• A defect in cleverly. The gated study validates the interval at two laws that meet C3.

Measured values

Names beginning margin: are thresholds declared before the run. Everything else is measured from the committed results and checked at the precision printed.

quantity	value	source
replicates	6000	primary replications per law
n	2000	observations per primary replication
independent_tests_total	2	law tests against the replication truth
independent_tests_passed	0	of those, passing
paired_tests_total	0	external comparisons declared
paired_tests_passed	0	external comparisons passing
property_cells_total	0	repeated-sampling property cells, none declared
property_cells_passed	0	of those, passing
max_standardized_bias	0.0058	largest absolute primary bias in error SDs
min_coverage	0.8938	lowest measured primary coverage
min_coverage_ci_lower	0.8832	lowest exact 99% primary coverage endpoint, against 0.90
min_se_ratio_ci_lower	0.8017	lowest bootstrap primary SE-ratio endpoint, against 0.80
max_se_ratio_ci_upper	0.8519	highest bootstrap primary SE-ratio endpoint
performance[cleverly-learned-rule-cvtmle/exceptional/ey_learned_rule[learned rule]]:coverage	0.8938	coverage at exceptional
performance[cleverly-learned-rule-cvtmle/exceptional/ey_learned_rule[learned rule]]:coverage_ci_lower	0.8832	its 99% lower endpoint
performance[cleverly-learned-rule-cvtmle/exceptional/ey_learned_rule[learned rule]]:coverage_ci_upper	0.9038	its 99% upper endpoint, against 0.95
performance[cleverly-learned-rule-cvtmle/exceptional/ey_learned_rule[learned rule]]:se_ratio	0.8211	SE ratio at exceptional
performance[cleverly-learned-rule-cvtmle/weak_blip/ey_learned_rule[learned rule]]:coverage	0.8948	coverage at weak_blip
performance[cleverly-learned-rule-cvtmle/weak_blip/ey_learned_rule[learned rule]]:coverage_ci_lower	0.8842	its 99% lower endpoint
performance[cleverly-learned-rule-cvtmle/weak_blip/ey_learned_rule[learned rule]]:coverage_ci_upper	0.9048	its 99% upper endpoint, against 0.95
performance[cleverly-learned-rule-cvtmle/weak_blip/ey_learned_rule[learned rule]]:se_ratio	0.8314	SE ratio at weak_blip
summary[cleverly-learned-rule-cvtmle/exceptional/ey_learned_rule[learned rule]]:mean_std_error	0.0158	mean reported SE at exceptional
summary[cleverly-learned-rule-cvtmle/exceptional/ey_learned_rule[learned rule]]:empirical_se	0.0193	SD of the error at exceptional
summary[cleverly-learned-rule-cvtmle/weak_blip/ey_learned_rule[learned rule]]:mean_std_error	0.0156	mean reported SE at weak_blip
summary[cleverly-learned-rule-cvtmle/weak_blip/ey_learned_rule[learned rule]]:empirical_se	0.0187	SD of the error at weak_blip
mean_oracle_se_exceptional	0.0158	mean oracle SE of the fixed fold rules at exceptional, from harness.csv.gz. No rule reads it
mean_oracle_se_weak_blip	0.0155	mean oracle SE at weak_blip
margin:confidence_level	0.9900	confidence level of every Monte Carlo interval
margin:alpha	0.0500	nominal size of the reported intervals
margin:nominal_coverage	0.9500	nominal coverage those intervals claim
margin:bootstrap_replicates	10000	resamples behind every bootstrap interval
margin:standardized_bias	0.2500	bias equivalence margin, in error SDs
margin:coverage_floor	0.9000	validity floor the coverage lower endpoint must clear
margin:over_coverage_ceiling	0.9900	above this, coverage is conservative rather than invalid
margin:se_ratio_sanity_lower	0.8000	SE-ratio screen, lower limit
margin:se_ratio_sanity_upper	1.2000	SE-ratio screen, upper limit
margin:calibration_se_ratio_lower	0.9300	calibration-cell SE-ratio band, lower limit. The study declares no calibration cell
margin:calibration_se_ratio_upper	1.0700	calibration-cell SE-ratio band, upper limit
margin:calibration_coverage_lower	0.9200	calibration-cell coverage band, lower limit
margin:calibration_coverage_upper	0.9800	calibration-cell coverage band, upper limit
margin:type_i_ceiling	0.1000	largest size a one-sided type-I bound may establish
margin:paired_difference	0.1500	paired similarity margin, in pooled empirical SDs
margin:rmse_noninferiority	1.1000	largest external-comparison RMSE ratio bound
margin:coverage_noninferiority	-0.0250	smallest external-comparison coverage difference bound
margin:calibration_noninferiority	0.0500	largest external-comparison calibration excess bound
margin:minimum_power	0.8000	rejection lower bound a power control must clear
margin:root_n_slope	-0.5000	contraction rate root-n asymptotics predict
margin:root_n_slope_lower	-0.6250	accepted root-n slope band, lower limit
margin:root_n_slope_upper	-0.3750	accepted root-n slope band, upper limit
margin:excluded_slope	-0.2500	slower rate a root-n interval must exclude

Limitations

limitation	what it means for use
The row publishes under the reporting policy	Both truth rows are red, and the policy publishes them. The fast tier recomputes each verdict and does not fail on a red one
No property cell	The study is not a validation row, and the validation grid does not list it
There is no cross-implementation evidence	No maintained package fits this construction
Two laws, one size, one learner class	The readings hold for the declared laws at n = 2,000 with the gated study’s logistic learners
The gated study’s other limits apply	A binary treatment and outcome, equal folds, and no weights, clusters, missing outcomes, repeats, full-refit bootstrap or strata
A red cell is not a defect	A red exceptional cell marks the boundary of condition C3. A red weak_blip cell is a finite-sample limit at n = 2,000 inside C3

Reproduction

The fixture README gives the run command and the run form. The manifest records the seeds, the margins, the estimator configuration, the source hashes and the result hashes. The run log records the commit, the clean tree, the runtime and the wall time. The replications, the harness columns and the readings carry every published row.