English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Conducting valid statistical analyses is challenging in the presence ofmissing-not-at-random (MNAR) data, where the missingness mechanism is dependenton the missing values themselves even conditioned on the observed data. Here,we consider a MNAR model that generalizes several prior popular MNAR models intwo ways: first, it is less restrictive in terms of statistical independenceassumptions imposed on the underlying joint data distribution, and second, itallows for all variables in the observed sample to have missing values. ThisMNAR model corresponds to a so-called criss-cross structure considered in theliterature on graphical models of missing data that prevents nonparametricidentification of the entire missing data model. Nonetheless, part of thecomplete-data distribution remains nonparametrically identifiable. Byexploiting this fact and considering a rich class of exponential familydistributions, we establish sufficient conditions for identification of thecomplete-data distribution as well as the entire missingness mechanism. We thenpropose methods for testing the independence restrictions encoded in suchmodels using odds ratio as our parameter of interest. We adopt twosemiparametric approaches for estimating the odds ratio parameter and establishthe corresponding asymptotic theories: one involves maximizing a conditionallikelihood with order statistics and the other uses estimating equations. Theutility of our methods is illustrated via simulation studies.

Sufficient Identification Conditions and Semiparametric Estimation under Missing Not at Random Mechanisms