Parametric Model - Regular Parametric Model

Let μ be a fixed σ-finite measure on a probability space (Ω, ℱ), and the collection of all probability measures dominated by μ. Then we will call a regular parametric model if the following requirements are met:

  1. Θ is an open subset of Rk.
  2. The map
    from Θ to L2(μ) is Fréchet differentiable: there exists a vector such that
    \lVert s(\theta+h) - s(\theta) - \dot{s}(\theta)'h \rVert = o(|h|)\ \ \text{as }h \to 0,
    where ′ denotes matrix transpose.
  3. The map (defined above) is continuous on Θ.
  4. The k×k Fisher information matrix
    is non-singular.

Read more about this topic:  Parametric Model

Famous quotes containing the words regular and/or model:

    “My attitude toward punctuation is that it ought to be as conventional as possible. The game of golf would lose a good deal if croquet mallets and billiard cues were allowed on the putting green. You ought to be able to show that you can do it a good deal better than anyone else with the regular tools before you have a license to bring in your own improvements.”
    —Ernest Hemingway (1899–1961)

    “... if we look around us in social life and note down who are the faithful wives, the most patient and careful mothers, the most exemplary housekeepers, the model sisters, the wisest philanthropists, and the women of the most social influence, we will have to admit that most frequently they are women of cultivated minds, without which even warm hearts and good intentions are but partial influences.”
    —Mrs. H. O. Ward (1824–1899)