 # Asymptotic Theory of Nonlinear Regression

• Alexander V. Ivanov Book

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

1. Front Matter
Pages i-vi
2. Alexander V. Ivanov
Pages 1-3
3. Alexander V. Ivanov
Pages 5-78
4. Alexander V. Ivanov
Pages 79-153
5. Alexander V. Ivanov
Pages 155-250
6. Alexander V. Ivanov
Pages 251-288
7. Back Matter
Pages 289-330

### Introduction

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 ().

### Keywords

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

#### Authors and affiliations

• Alexander V. Ivanov
• 1
1. 1.Glushkov Institute for CyberneticsKievUkraine

### Bibliographic information

• DOI https://doi.org/10.1007/978-94-015-8877-5