{"paper":{"title":"Parametric Estimation from Approximate Data: Non-Gaussian Diffusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ilya Timofeyev, Peng Ren, Robert Azencott","submitted_at":"2015-01-22T02:05:54Z","abstract_excerpt":"We study the problem of parameters estimation in Indirect Observability contexts, where $X_t \\in R^r$ is an unobservable stationary process parametrized by a vector of unknown parameters and all observable data are generated by an approximating process $Y^{\\varepsilon}_t$ which is close to $X_t$ in $L^4$ norm. We construct consistent parameter estimators which are smooth functions of the sub-sampled empirical mean and empirical lagged covariance matrices computed from the observable data. We derive explicit optimal sub-sampling schemes specifying the best paired choices of sub-sampling time-st"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05370","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}