{
  "abstract": "We study bias-corrected empirical-likelihood inference for single-index expectile regression when responses are missing at random. Local-linear expectile estimation is combined with conditional centering to construct three procedures based on complete cases, inverse-probability weighting, and cross-fitted imputation. The expectile score is continuous and globally Lipschitz, which permits the bias-correction argument without further smoothing of the score. Under the stated conditions, the index estimators are asymptotically normal and each empirical-likelihood ratio has a standard chi-squared limit. Joint confidence regions can therefore be formed without estimating the limiting covariance matrix. For the imputation construction considered here, I-BCEL and CC-BCEL have the same first-order limiting covariance. In the simulations, the estimation error decreases with sample size; differences among the incomplete-data methods are more apparent when the missing-response rate is 40%, where small-sample undercoverage also remains. An analysis of the New York air-quality data illustrates the three procedures with naturally missing responses.",
  "abstract_shown": true,
  "affiliations": [
    "School of Science, Xi’an Polytechnic University, Xi’an 710048, China"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Pingping Liu"
    },
    {
      "affs": [
        0
      ],
      "name": "Shuanghua Luo",
      "orcid": "0000-0002-1473-8458"
    },
    {
      "affs": [
        0
      ],
      "name": "Junxiang Lu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3egtspkes8mqq.bib",
  "cited_by": 0,
  "doi": "10.3390/axioms15110816",
  "fulltext_url": null,
  "id": "3egtspkes8mqq",
  "issns": [
    "2075-1680"
  ],
  "landing_url": "https://www.mdpi.com/2075-1680/15/11/816",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/3egtspkes8mqq.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T12:20:59Z",
      "native_id": "10.3390/axioms15110816",
      "source": "crossref",
      "url": "https://www.mdpi.com/2075-1680/15/11/816"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "journal-openalex:F26",
      "subfield": "general"
    }
  ],
  "title": "Bias-Corrected Empirical-Likelihood Inference for Single-Index Expectile Regression Under Missing-at-Random Responses",
  "title_text": "Bias-Corrected Empirical-Likelihood Inference for Single-Index Expectile Regression Under Missing-at-Random Responses",
  "type": "peer-reviewed",
  "updated_at": "2026-11-06T00:21:06Z",
  "url": "https://research.draconitic.com/paper/3egtspkes8mqq",
  "venue": "Axioms",
  "versions": []
}