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:

    “While you’re playing cards with a regular guy or having a bite to eat with him, he seems a peaceable, good-humoured and not entirely dense person. But just begin a conversation with him about something inedible, politics or science, for instance, and he ends up in a deadend or starts in on such an obtuse and base philosophy that you can only wave your hand and leave.”
    —Anton Pavlovich Chekhov (1860–1904)

    “One of the most important things we adults can do for young children is to model the kind of person we would like them to be.”
    —Carol B. Hillman (20th century)