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copulas","primary_cat":"math.ST","submitted_at":"2026-05-13T15:57:05+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"A functional central limit theorem for pattern frequencies in 2D samples enables nonparametric goodness-of-fit, two-sample, and symmetry tests for copulas, with bootstrap critical values and parametric examples.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"in the situation considered here. The (lengthy) proof requires some additional technical arguments and will be part of a separate, more general project. Also, similar statements can be derived for the related one sided testing problem𝐻 0 :𝜃≤𝜃 0 against 𝐻+ :𝜃 > 𝜃 0, and the two-sided testing problem𝐻 0 :𝜃=𝜃 0 against𝐻 1 :𝜃≠𝜃 0. Finally, we refer to [31], [32] and [49] for general results on the coincidence of different efficiency approaches. 6. Implementation and simulations In this section we consider computational aspects, and we provide an experimental comparison of our procedures with traditional tests in the important special case of testing for independence. 6.1. Exact enumeration and Monte Carlo approximation"},{"citing_arxiv_id":"2604.16283","ref_index":18,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Boson correlations are spurious for classical states","primary_cat":"quant-ph","submitted_at":"2026-04-17T17:45:19+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"Boson correlations for states with well-behaved Glauber-Sudarshan P-representations are spurious statistical correlations due to Simpson's paradox from symmetry-breaking in ensemble averages over varying geometries.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null}],"limit":50,"offset":0}