Asymptotic Theory of Nonlinear Regression

1997
ISBN: 978-0-7923-4335-6
Verlag: Springer Netherlands

Buch, Englisch, Band 389, 330 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 1440 g

Reihe: Mathematics and Its Applications

Let us assume that an observation Xi is a random variable (r.v.) with values in 1 1 (1R1, 8 ) and distribution Pi (1R1 is the real line, and 8 is the cr-algebra of its Borel subsets). Let us also assume that the unknown distribution Pi belongs to a 1 certain parametric family {Pi(), () E e}. We call the triple £i = {1R1, 8, Pi(), () E e} a statistical experiment generated by the observation Xi. n We shall say that a statistical experiment £n = {lRn, 8, P; ,() E e} is the product of the statistical experiments £i, i = 1,. ,n if PO' = P () X. X P () (IRn 1 n n is the n-dimensional Euclidean space, and 8 is the cr-algebra of its Borel subsets). In this manner the experiment £n is generated by n independent observations X = (X1,. ,Xn). In this book we study the statistical experiments £n generated by observations of the form j = 1,. ,n. (0.1) Xj = g(j, (}) + cj, c c In (0.1) g(j, (}) is a non-random function defined on e, where e is the closure in IRq of the open set e ~ IRq, and C j are independent r. v.-s with common distribution function (dJ.) P not depending on ().

Zielgruppe

Research

Autoren/Hrsg.

Ivanov, A. A.

Fachgebiete

• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Datenanalyse, Datenverarbeitung
• Mathematik | Informatik Mathematik Mathematische Analysis Variationsrechnung
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik

Inhaltsverzeichnis

1 Consistency.- 2 Approximation by a Normal Distribution.- 3 Asymptotic Expansions Related to the Least Squares Estimator.- 4 Geometric Properties of Asymptotic Expansions.- I Subsidiary Facts.- II List of Principal Notations.- Commentary.- 1.- 2.- 3.- 4.