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)

    “...that absolutely everything beloved and cherished of the bourgeoisie, the conservative, the cowardly, and the impotent—the State, family life, secular art and science—was consciously or unconsciously hostile to the religious idea, to the Church, whose innate tendency and permanent aim was the dissolution of all existing worldly orders, and the reconstitution of society after the model of the ideal, the communistic City of God.”
    —Thomas Mann (1875–1955)