Conditionally Expected Value
A Conditionally Expected Value is an expected value for a conditional random variable.
- AKA: Conditional Mean.
- Context:
- It can (typically) be produced by a Conditional Expectation Function.
- It can range from being a Bivariate Expected Value (bivariate expectation) to being ...
- Example(s):
- …
- Counter-Example(s):
- See: Fitted Conditional Expectation, Conditional Probability, Conditional Distribution, Probability Space.
References
2015
- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/conditional_expectation Retrieved:2015-5-13.
- In probability theory, the conditional expectation of a random variable is another random variable equal to the average of the former over each possible "condition". In the case when the random variable is defined over a discrete probability space, the "conditions" are a partition of this probability space. This definition is then generalized to any probability space using measure theory.
Conditional expectation is also known as conditional expected value or conditional mean.
In modern probability theory the concept of conditional probability is defined in terms of conditional expectation.
- In probability theory, the conditional expectation of a random variable is another random variable equal to the average of the former over each possible "condition". In the case when the random variable is defined over a discrete probability space, the "conditions" are a partition of this probability space. This definition is then generalized to any probability space using measure theory.
- http://www.math.uah.edu/stat/expect/Conditional.html
- QUOTE: As usual, our starting point is a random experiment with probability measure P on a sample space Ω. Suppose that X is a random variable taking values in a set S and that Y is a random variable taking values in T⊆R. In this section, we will study the conditional expected value of Y given X, a concept of fundamental importance in probability. As we will see, the expected value of Y given X is the function of X that best approximates Y in the mean square sense. Note that X is a general random variable, not necessarily real-valued. In this section, we will assume that all expected values that are mentioned exist (as real numbers).
2002
- (Acerbi & Tasche, 2002) ⇒ Carlo Acerbi, and Dirk Tasche. (2002). “Expected Shortfall: A Natural Coherent Alternative to Value at Risk." Economic notes 31, no. 2
- QUOTE: … It is not difficult to understand that, if the distribution function of the portfolio is continuous, then the statistic which answers the above question is simply given by a conditional expected value below the quantile or 'tail conditional expectation' (Artzner et al., 1997). …
1961
- (Muth, 1961) ⇒ John F. Muth. (1961). “Rational Expectations and the Theory of Price Movements." Econometrica: Journal of the Econometric Society
- QUOTE: … If the shock is observable, then the conditional expected value or its regression estimate may be found directly. If the shock is not observable, it must be estimated from the past history of variables that can be measured. …