Completion checkpoints

Reference catalog of completion targets and optional practice

This catalog is a reference across the guides. It is not an assignment to finish every topic before continuing. Each page labels its completion checkpoint, gives a readiness standard, and separates Additional practice (optional). A checkpoint in a specialized extension assesses that topic when you study it.

Try the task before opening the hint or solution. Explain the objects, assumptions, and reasoning, then attempt its transfer question. The guide overview states the one or two outcomes that these tasks build toward.

Research questions, study design, and estimands

• ID-01 — Separate definition, identification, and estimation. Ready when you can show nonidentification by constructing different compatible targets, rather than describing it only as a software difficulty.
• DES-02 — Choose a unit, weighting, and resampling design. Ready when you can connect target weights and independent records to estimation, derive the grand-mean variance, and choose an uncertainty and validation unit.
• DES-03 — Separate a target from a procedure’s limit. Ready when you can distinguish target mismatch, sampling uncertainty, finite-sample bias, and nonidentification.
• MIS-01 — Identify the target under an observation process. Ready when you can distinguish a complete-case target, an identified full-population target, and a genuinely unidentified component.

Estimation and uncertainty

• LS-01 — Interpret consistency and a limiting law. Ready when you can distinguish concentration near a target, a limiting law for scaled errors, and convergence along almost every sample path.
• LS-02 — Expand empirical and population expectations. Ready when you can expand the expectation shorthand, identify its distribution, and distinguish averaging transformed observations from transforming an average.
• LS-03 — Separate measurement spread from mean uncertainty. Ready when you can calculate the variance and SE of a sample mean and explain why averaging reduces estimation uncertainty without reducing population heterogeneity.
• LS-04 — Combine theorems and check a remainder. Ready when you can justify studentization with the core theorems and distinguish a negligible root-n remainder from an error that changes the limiting law.
• SP-01 — Complete a smooth estimating-equation argument. Ready when you can connect the population root to consistency, a negligible remainder, a CLT, and an estimated standard error.
• INF-01 — Interpret a standard error, interval, and test. Ready when you can connect a sampling approximation to an interval and test without confusing measurement variability, coverage, null probability, and target alignment.
• CL-01 — Derive the cluster contribution for the chosen target. Ready when you can derive both cluster-level contributions and connect target weighting to the independent-unit variance.
• CL-02 — Construct a valid fold and variance argument. Ready when you can account for the shared component and preserve the independent unit in training, uncertainty, and resampling.
• BOOT-01 — Derive what the bootstrap mean approximates. Ready when you can connect the empirical resampling law, the target error distribution, and the independent unit without confusing sampling error with Monte Carlo error.
• BOOT-02 — Prove an ordinary bootstrap failure. Ready when you can diagnose a failure of the resampling approximation separately from limited replicate precision and an incorrect sampling unit.

Statistical models, influence functions, and efficiency

• SP-03 — Build a valid path and calculate its score. Ready when you can verify that a proposed perturbation is a probability distribution and relate its score to the target derivative.
• SP-02 — Prove the projection property. Ready when you can derive the decomposition, justify the vanishing cross term, and state uniqueness up to almost-sure equality.
• SP-04 — Derive mean and variance influence functions. Ready when you can differentiate both functionals, center their contributions, and explain the moment assumptions.
• SP-05 — Differentiate a ratio of means. Ready when you can combine the two mean contributions, state the denominator condition, and interpret the correct population target.
• SP-07 — Remove a nuisance score and compute the bound. Ready when you can carry the same nuisance projection through to information and estimator variance, with its model assumptions stated.
• SP-09 — Compare information with known and unknown variance. Ready when you can show why adding a nuisance parameter may leave the target information unchanged, rather than assuming information always decreases strictly.
• SP-08 — Prove the efficient-gradient variance comparison. Ready when you can identify both the object and the projection space, prove the variance comparison, and state what remains to show for an estimator to attain it.
• SP-06 — Derive the quantile expansion and influence function. Ready when you can distinguish the population derivative from the stochastic increment and obtain both the expansion and pathwise representation.

Semiparametric estimation with learned nuisance functions

• SP-11 — Bound the nuisance-bias remainder. Ready when you can derive the exact product remainder, distinguish big-O from little-o, and identify the additional empirical and variance arguments needed for inference.
• SP-10 — Derive a nuisance rate and assess its dimension requirement. Ready when you can distinguish squared error from its square root and translate a smoothness/dimension assumption into a sufficient inferential condition.
• SP-12 — Control the cross-fitted empirical-process term. Ready when you can show exactly which random term cross-fitting controls and what it does not control.
• SP-13 — Complete the missing-outcome mean capstone. Ready when you can reproduce the chain from target and assumptions through estimator, proof, uncertainty, and interpretation.
• SP-14 — Distinguish identification, variance, and remainder failures. Ready when you can name the failed condition or term instead of treating every problem as insufficient sample size.

Omics data and measurement

• OM-02 — Reconstruct the statistical observation. Ready when you can reconstruct the sampling unit and identify a scale/measurement gap before fitting a model.
• PRE-01 — Name the target after each processing decision. Ready when you can separate a scale definition, selection, biological adjustment, and causal/measurement assumptions.
• OM-01 — Identify measurements and biological replication. Ready when you can distinguish measurement units from replication and describe the information needed to interpret the matrix.
• PROT-01 — Reconstruct a protein-level claim. Ready when you can separate biological replication, aggregation, observation, and calibration assumptions.
• MET-01 — Separate a molecular quantity from its assay response. Ready when you can connect response correction, identification resolution, and acquisition design to the scope of a group contrast.
• MIC-01 — Demonstrate scale nonidentification and name the reference. Ready when you can exhibit observationally equivalent absolute communities and distinguish reference-specific relative changes from absolute changes.
• METH-01 — Distinguish scale and mixture effects. Ready when you can calculate scale and composition effects and state the extra information needed for a stronger biological interpretation.

Omics analysis problems

• DE-01 — Write an estimable contrast. Ready when you can connect a design/contrast calculation to its population interpretation and check rank and confounding.
• DE-02 — Explain what variance moderation changes. Ready when you can separate the target contrast, variance borrowing, hierarchical calibration, and the independent-unit/weighting assumptions.
• MT-01 — Specify the family and error guarantee. Ready when you can state the family, distinguish an expectation from a realized fraction, execute the BH step-up rule, and identify the p-value and dependence assumptions.
• MT-02 — Separate permutation resolution from validity and precision. Ready when you can distinguish a valid Monte Carlo p-value, its resolution, tail precision, and the error-rate summary being estimated.
• NET-01 — Identify the association represented by an edge. Ready when you can distinguish marginal and residual targets and describe what the edge does and does not establish.
• DES-01 — Separate the scientific target from a pooled association. Ready when you can name the population target and derive the procedure’s limit without treating a pooled quantity as intrinsically wrong.
• PV-01 — Verify the linear pseudo-value case. Ready when you can derive the identity and explain why it does not make every pseudo-value a raw biological measurement.
• COV-01 — Separate nuisance bias from held-out fluctuation. Ready when you can derive the covariance nuisance-bias remainder and distinguish its rate requirement from cross-fitting and variance consistency.
• MV-01 — Match the permutation to the design and null. Ready when you can identify the randomization unit, preserve its dependent measurements, and limit the interpretation of an omnibus result.
• CASE-01 — Specify and identify the expression contrast. Ready when you can distinguish the standardized target from a complete-case crude contrast, a constant regression coefficient, and a causal effect.
• CASE-02 — Reconstruct the estimator and its remainder. Ready when you can connect every correction and condition to an observed-data quantity and explain what double-robust consistency does and does not establish.
• CASE-03 — Interpret discoveries and uncertainty correctly. Ready when you can label each uncertainty quantity and error criterion, including the conditions multiplicity adjustment cannot repair.
• CASE-04 — Reproduce and challenge the complete analysis. Ready when you can rebuild the result, trace a claim to its inputs and assumptions, and diagnose a failed condition without silently discarding failures.
• NETCASE-01 — Derive the residual-edge contrast and its contribution. Ready when you can connect the edge definition, centering, nuisance cancellation, and remainder to the estimator actually implemented.
• NETCASE-02 — Audit uncertainty and reproduce a failure case. Ready when you can trace each conclusion to its target, inputs, conditions, and evaluation record rather than relying on a plot of discoveries.

Developing and evaluating methods

• EVAL-01 — Separate target bias from uncertainty calibration. Ready when you can distinguish the target, the procedure’s limit, sampling uncertainty, and Monte Carlo uncertainty, and compute a paired performance difference.
• SENS-01 — Separate unidentified variation from sampling uncertainty. Ready when you can construct compatible missing-data worlds, calculate a sensitivity curve, and label the identification and sampling uncertainties separately.
• SENS-02 — Name what each robustness check changes. Ready when you can keep the estimand explicit while distinguishing an estimator choice, an assumption departure, and a changed population or measurement.
• SIM-01 — Write a target-based simulation protocol. Ready when another reader could implement your protocol and distinguish the scientific null, the procedure’s target, and simulation uncertainty.

Research practice and reproducibility

• REP-01 — Specify a complete rerun contract. Ready when another reader can identify the inputs, configuration, environment, entry point, and expected outputs, and you can verify a rerun without your interactive workspace.
• PROV-01 — Audit a join and its population consequences. Ready when you can reconstruct the joins and exclusions and distinguish the retained-data target from the original eligible-population target.
• WRITE-01 — Rewrite a claim to match its evidence. Ready when you can state what the reported evidence supports and identify the missing target, assumptions, uncertainty, or validation needed for each stronger claim.

Additional practice is optional

Variations, extra simulations, and optional research extensions do not silently become extra completion requirements. The quantile page supplies its empirical-CDF lemma; a full general proof is additional theory. The survival extension is relevant to projects using that model.