Conditional Expectations

Chaohua Dong and Jiti Gao ()
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Chaohua Dong: Zhongnan University of Economics and Law
Jiti Gao: Monash University

Chapter Chapter 2 in Modern Series Methods in Econometrics and Statistics, 2025, pp 15-41 from Springer

Abstract: Abstract This chapter explores the main sources of unknown functional relationships in econometrics and statistics, viz., conditional expectations. In doing so, starting from the basic notion like probability space, random variables and their expectations, we discuss in detail the definition of conditional expectations given discrete variable, continuous variable and more generally Sigma fields. We also summarize their properties and proofs that are used frequently in existing studies. In addition, we discuss the conditional expectation from a projection point of view. One crucial theorem is shown when the conditional expectation of Y given X is linear in X that lays a theoretical foundation for linear regression models. Several examples are used to help the reader grasp conditional expectations and their applications.

Date: 2025
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DOI: 10.1007/978-981-96-2822-3_2

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