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:

    ““I couldn’t afford to learn it,” said the Mock Turtle with a sigh. “I only took the regular course.”
    “What was that?” inquired Alice.
    “Reeling and Writhing, of course, to begin with,” the Mock Turtle replied; “and then the different branches of Arithmetic—Ambition, Distraction, Uglification, and Derision.”
    “I never heard of ‘Uglification,’” Alice ventured to say.”
    —Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)

    “AIDS occupies such a large part in our awareness because of what it has been taken to represent. It seems the very model of all the catastrophes privileged populations feel await them.”
    —Susan Sontag (b. 1933)