{
  "annotation_id": "6253269b-4e26-4e42-b20a-7bf1fa358fdc",
  "date_created": "2026-03-02T18:01:11.445000Z",
  "date_modified": "2026-03-02T18:01:11.445000Z",
  "file_hash": "04b7bdc198d097017e23084875f4666f8d6dcfd3edf7f2d0bc8c93dda6559cc3",
  "private": false,
  "record": {
    "abstract": "We suggest a class of direct sample estimates for the two-point quadratic\nstatistical functions of multidimensional data, which includes: estimates of\nthe sample autocovariance function (AcF), sample mean square increment (also,\nstructure) function, and the estimate of the power spectrum. The central\nestimate for the class is the sample AcF, which is constructed as to represent\nthe finite Fourier transform of the periodogram estimate of the spectrum and is\npositive semidefinite. The estimate explicitly account for the anisotropy of\nthe fields in all spatial directions and is illustrated on two examples: the\nmorphology of the Grab nebula and the surface roughness generated as a solution\nof the anisotropic Kardar-Parisi-Zhang equation. We also provide an expression\nof the covariance of the sample AcF in the case of data assumed to be drawn\nfrom a two-dimensional Gaussian field with a known mean.",
    "arxiv_id": "physics/0609082",
    "authors": [
      "Ivailo S. Atanasov",
      "Oleg I. Yordanov"
    ],
    "categories": [
      "physics.data-an",
      "cond-mat.stat-mech"
    ],
    "title": "Direct sample estimates of multidimensional quadratic statistical   functions: application to the anisotropic KPZ equation",
    "url": "https://arxiv.org/abs/physics/0609082"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "1a42833f-815a-4dab-a1b0-a5546c0a1146",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}