# Asymptotic Theory of Nonlinear Regression

Part of the Mathematics and Its Applications book series (MAIA, volume 389)

Advertisement

Part of the Mathematics and Its Applications book series (MAIA, volume 389)

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 ().

Estimator Parameter Power Probability theory linear regression modeling normal distribution regression systems theory

- DOI https://doi.org/10.1007/978-94-015-8877-5
- Copyright Information Springer Science+Business Media B.V. 1997
- Publisher Name Springer, Dordrecht
- eBook Packages Springer Book Archive
- Print ISBN 978-90-481-4775-5
- Online ISBN 978-94-015-8877-5
- Buy this book on publisher's site