# Question 18174: Withholding Statistical Claims Does Not Prove Their Negations [Return to catalogue page 91](https://ocme.evemisslab.com/en/questions/page/91/) [← Question derivation index](https://ocme.evemisslab.com/en/questions/) · [Original question batch](https://ocme.evemisslab.com/en/practice/batch-20261014-advance-20261104-r04-statistical-estimator-foundations/#q-20261014-advance-20261104-r04-statistical-estimator-0099) This teaching derivation has second-context AI mathematical and bilingual semantic review, limited to the model and assumptions stated in this question. It has no human review or new Lean proof and does not promote the original question or MKO to Canonical truth. R0035-18174 · q-20261014-advance-20261104-r04-statistical-estimator-0099 ## Original question and givens Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/27, 1/27, 25/27], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 24, 48] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary). - G001 — Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/27, 1/27, 25/27], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 24, 48] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary). ## Definition and scope Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate. - [mko-statistical-estimator](https://ocme.evemisslab.com/en/mko/mko-statistical-estimator/) ## Step-by-step derivation S001 · impliesBefore source operation=estimator-property-nonconclusion;original snapshot and mathematics retained After explicit ordered source output fields=[statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary] Conditions: none Keep the historical interface marker in the original snapshot while giving ordered fields here,without JavaScript or an external table.Labels are not mathematical evidence,and each No marker retains the operation's claim scope. Step identifiers and dependenciesRule: source_ordered_interface_explicit_without_javascript · Uses: G001 S002 · calculationBefore estimator parameter0 complete law sum := sum(1/27, 1/27, 25/27) After estimator parameter0 complete law sum = 1 Conditions: none Compute exactly from original roles and established intermediates,retaining indices,denominators,signs and the relevant carrier. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S001 S003 · impliesBefore original parameter=0;SAME outcome carrier Fin(3);aligned reduced candidate law=[1/27, 1/27, 25/27] After sum=1;nonnegative=Yes;law qualified=Yes Conditions: none Every model row must be nonnegative and total1.Invalid candidate rows retain false flags;a total statistic does not repair a probability model. Step identifiers and dependenciesRule: estimator_complete_laws_separate_from_total_statistic · Uses: G001, S002 S004 · calculationBefore estimator parameter1 complete law sum := sum(1/2, 1/3, 1/6) After estimator parameter1 complete law sum = 1 Conditions: none Compute exactly from original roles and established intermediates,retaining indices,denominators,signs and the relevant carrier. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S003 S005 · impliesBefore original parameter=1;SAME outcome carrier Fin(3);aligned reduced candidate law=[1/2, 1/3, 1/6] After sum=1;nonnegative=Yes;law qualified=Yes Conditions: none Every model row must be nonnegative and total1.Invalid candidate rows retain false flags;a total statistic does not repair a probability model. Step identifiers and dependenciesRule: estimator_complete_laws_separate_from_total_statistic · Uses: G001, S004 S006 · impliesBefore original parameter carrier Fin(2);common outcome carrier Fin(3);ONE original statistic array=[0, 24, 48] After all model laws qualified=Yes;one value per outcome=Yes;SAME statistic map T(o) at EVERY parameter Conditions: none The statistic definition takes an observation index,not the unknown parameter.This is functional parameter-independence,not a claim that the law or expectation of T(X) is parameter-free.No estimand,prior or posterior has been supplied. Step identifiers and dependenciesRule: estimator_definition_parameter_independence_not_distribution_free · Uses: G001, S005 S007 · impliesBefore single total statistic=[0, 24, 48];model qualified=Yes;no estimand/prior/asymptotic sampling sequence supplied After four literal No markers WITHHOLD claims;not four failed tests;no_unbiased_consistent_sufficient_identifiable_or_posterior_claim Conditions: none The four No values withhold definition-level claims;they do not prove bias,inconsistency or other negated properties.Without an estimand and asymptotic sampling setup,do not invent and decide those questions. Step identifiers and dependenciesRule: estimator_property_nonconclusions_not_negations · Uses: G001, S006 ## Reverse checks - S007 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S006 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S005 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S004 · premise_and_result_audit — Recompute estimator parameter1 complete law sum with exact rational arithmetic, not rounded decimals. - S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S002 · premise_and_result_audit — Recompute estimator parameter0 complete law sum with exact rational arithmetic, not rounded decimals. - S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. ## Result ([0, 24, 48], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim) The full substitutions and premise checks give the original answer; source identity,format and status are unchanged. ## This question review and source binding Review date: 2026-10-26 Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof. Source hashes and review receipts - input commit: 0f7be61e2c22317a4075561dc822c87d881a50db - original question SHA-256: d07ee134707802c31fd3db0ffb13d1db578caced383afbabf9288e8a6685be92 - candidate record SHA-256: 2f91d7bec4decf84255104de0aafd248236e5879519c312e6b5549598ef2c335 - semantic review receipt SHA-256: 713db6309b22bf8b31f0253d4aaa7aca9011ab908587ae0e9d4a365edce1f9bc - question-first witness SHA-256: 0338a3db344ab237113fc63be29153c3684da96e388109e9dcd913a0a693aed2 - Lean: NOT_RUN · human review: NOT_PERFORMED [Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261014-advance-20261104-r04-statistical-estimator-0099.json)