{"id":"d989d59d-7d30-4c22-a5a3-b872518fac13","arxiv_id":"2606.20930","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":5.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":1,"one_line_summary":"kNN estimators for vector parameter and nonparametric operator in partial linear model with functional covariate and missing-at-random responses, plus initial asymptotic results.","lead":"This paper proposes three kNN-based estimators for the linear parameter and nonparametric operator in a semi-functional partial linear regression model where the scalar response is missing at random. A smart generalist might read it for methods handling mixed vector and functional covariates with incomplete data in statistical modeling.","discovery_kind":"unclear","skeptic_critique":{"model":"grok-4.3","headline":"No significant objection identified","rationale":"The reader's UNVERDICTED verdict stems from abstract-only access. With no full derivations or equations available to inspect for technical gaps, no load-bearing concern is identified and the verdict is left unchanged.","tokens_in":1553,"tokens_out":194,"duration_ms":14311,"concrete_test":"Re-derive the consistency rate for the vector-parameter estimator from the kNN weights and the MAR correction term; confirm it matches the stated asymptotic result under the paper's bandwidth conditions.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that three kNN-based estimators are proposed for the finite-dimensional parameter and the nonparametric operator in the semi-functional partial linear model with MAR missing responses, together with initial asymptotic results. No internal inconsistency, hidden assumption in a derivation, or weakest link in the construction can be located from the provided description of the claim.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript considers a semi-functional partial linear regression model with scalar response missing at random, a finite-dimensional covariate X with linear effect, and an infinite-dimensional functional covariate Χ with nonparametric effect. Three kNN-based estimators are proposed for the vector parameter and the nonparametric operator, together with initial asymptotic results.","tokens_in":1606,"tokens_out":264,"duration_ms":16628,"significance":"If the asymptotic results hold under the stated conditions, the work provides practical kNN estimators for mixed-dimensional regression with MAR missingness, extending existing functional data methods. The explicit construction of multiple estimators and the derivation of asymptotics constitute a concrete contribution, though the scope is described as preliminary.","major_comments":[],"minor_comments":[{"comment":"Abstract: the description of the three estimators remains high-level; a brief indication of how the kNN weights are combined for the linear and nonparametric components would improve clarity for readers.","section":"Abstract"},{"comment":"The paper should include a short simulation study or real-data illustration to demonstrate finite-sample behavior of the three estimators, as the asymptotics alone leave practical performance unexamined.","section":null}],"recommendation":"minor_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for their review of our manuscript on kNN estimation in semi-functional partial linear regression with missing responses at random. The report provides a concise summary and recommends minor revision, but lists no specific major comments.","responses":[],"tokens_in":1017,"tokens_out":63,"duration_ms":8494,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The new piece is the asymptotic theory for kNN in this exact setup: scalar response missing at random, linear effect from a vector covariate, and nonparametric effect from a functional covariate. They give three variants of the estimator for both the finite-dimensional parameter and the operator, which extends prior kNN work in functional regression to the partial linear case with missingness.\n\nThe approach looks standard and externally grounded. kNN is a natural fit for the functional part, and handling MAR via inverse probability weighting or similar is a reasonable step. The abstract indicates the derivations follow the usual nonparametric rates, so the central claim holds up on its face.\n\nThe main limitation is that the abstract gives no detail on how k is chosen in practice or on finite-sample behavior, and the conditions for the asymptotics are not visible here. If the full proofs require unusually strong smoothness or bandwidth restrictions, that would narrow the result. No circularity or internal contradiction shows up from the description.\n\nThis is for researchers already working in functional data analysis and missing-data nonparametric regression. A reader in that niche gets a concrete extension with rates they can build on. It is narrow enough that it will not change broader practice, but the claim of first asymptotics is enough to warrant referee time rather than a desk reject.","headline":"This paper supplies the first asymptotic results for three kNN estimators in a semi-functional partial linear model with MAR missing responses.","tokens_in":2062,"tokens_out":329,"would_cite":false,"duration_ms":15315,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Three kNN estimators are introduced for the linear coefficient and nonparametric operator in a semi-functional partial linear model when responses are missing at random.","keywords":["kNN estimation","partial linear regression","functional data","missing at random","semi-functional model","asymptotic properties","nonparametric estimation"],"falsifier":"Simulate data exactly from the partial linear model with known beta and m, impose the missing-at-random mechanism, apply the three kNN estimators, and check whether their empirical convergence rates match the paper's stated asymptotic orders.","tokens_in":2447,"feed_emoji":"","tokens_out":649,"duration_ms":9255,"temperature":0.7,"pith_summary":"The paper addresses estimation in a regression setup that mixes a vector covariate acting linearly with a functional covariate acting nonparametrically, where the scalar response is observed only with probability that depends on the covariates. It constructs three separate kNN procedures that target the finite-dimensional parameter and the infinite-dimensional operator, then derives initial asymptotic properties for these estimators. A reader would care because many real datasets combine low-dimensional measurements with curve or image data and suffer from incomplete responses, so practical methods that respect both features are needed.","feed_headline":"kNN estimators target linear and functional parts under missing responses","feed_subtitle":"Three nearest-neighbor procedures are built for the vector coefficient and the nonparametric operator in a mixed-dimensional regression mode","key_machinery":"kNN estimators adapted to the semi-functional partial linear structure, using nearest-neighbor averaging in the functional metric to handle the nonparametric component while isolating the linear effect of the vector covariate.","core_discovery":"In the model Y = X^T beta + m(X) + epsilon with P(response observed | X, X) = p(X, X) > 0, three kNN-based estimators are proposed: one for beta that uses local averaging after nonparametric adjustment, one for the operator m that averages over nearest neighbors in the functional space, and a combined procedure; first asymptotic results establish consistency or rates for these estimators under the stated missing-at-random mechanism.","pith_inferences":["If the functional metric used for nearest neighbors is misspecified, the rates for the nonparametric part would degrade while the linear part might remain consistent.","The estimators could be paired with cross-validation to choose the number of neighbors without altering the asymptotic claims.","Extensions to prediction intervals would require additional variance estimation steps not addressed here."],"forward_implications":["The estimators remain well-defined and can be computed when only a subset of responses is observed.","Asymptotic results supply rates that separate the linear and functional contributions.","The same kNN machinery targets both the finite-dimensional beta and the operator m simultaneously.","The approach covers the case where the functional covariate lives in an infinite-dimensional space."],"fun_headline_variants":["kNN targets linear beta and nonparametric m with missing responses","kNN estimation in semi-functional PLR under random missingness","Nearest neighbor methods for mixed regression with missing scalar response","kNN estimators for beta and m in partial linear model with MAR data"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The data truly follow a partial linear structure with exactly one linear vector effect and one nonparametric functional effect, and the probability of observing the response depends only on the observed covariates.","fun_headline_variants_meta":{"raw":{"variants":["kNN targets linear beta and nonparametric m with missing responses","kNN estimation in semi-functional PLR under random missingness","Nearest neighbor methods for mixed regression with missing scalar response","kNN estimators for beta and m in partial linear model with MAR data"]},"model":"grok-4.3","cost_usd":0.004325,"raw_usage":{"total_tokens":2022,"prompt_tokens":530,"num_sources_used":0,"completion_tokens":68,"cost_in_usd_ticks":43253000,"prompt_tokens_details":{"text_tokens":530,"audio_tokens":0,"image_tokens":0,"cached_tokens":64},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1424,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":530,"tokens_out":68,"duration_ms":8068,"temperature":1.0,"reasoning_tokens":1424,"cache_read_input_tokens":64,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-26T15:49:06.716816+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Simulate data exactly from the partial linear model with known beta and m, impose the missing-at-random mechanism, apply the three kNN estimators, and check whether their empirical convergence rates match the paper's stated asymptotic orders.","supporting_citations":[],"review_version":1}