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In probability theory, the conditional expectation, conditional expected value, or conditional mean of a random variable is its expected value evaluated with respect to the conditional probability distribution. If the random variable can take on only a finite number of values, the "conditions" are that the variable can only take on a subset of ...
Thus, we postulate that the conditional expectation of given is a simple linear function of , {} = +, where the measurement is a random vector, is a matrix and is a vector. This can be seen as the first order Taylor approximation of E { x ∣ y } {\displaystyle \operatorname {E} \{x\mid y\}} .
The Heckman correction is a statistical technique to correct bias from non-randomly selected samples or otherwise incidentally truncated dependent variables, a pervasive issue in quantitative social sciences when using observational data. [1]
In statistics, kernel regression is a non-parametric technique to estimate the conditional expectation of a random variable.The objective is to find a non-linear relation between a pair of random variables X and Y.
Conditional probabilities, conditional expectations, and conditional probability distributions are treated on three levels: discrete probabilities, probability density functions, and measure theory. Conditioning leads to a non-random result if the condition is completely specified; otherwise, if the condition is left random, the result of ...
The gambler's conditional expected fortune after the next game, given the history, is equal to his present fortune. This sequence is thus a martingale. Let Y n = X n 2 − n where X n is the gambler's fortune from the prior example. Then the sequence {Y n : n = 1, 2, 3, ... } is a martingale.
To do this, instead of computing the conditional probability of failure, the algorithm computes the conditional expectation of Q and proceeds accordingly: at each interior node, there is some child whose conditional expectation is at most (at least) the node's conditional expectation; the algorithm moves from the current node to such a child ...
Sufficiency finds a useful application in the Rao–Blackwell theorem, which states that if g(X) is any kind of estimator of θ, then typically the conditional expectation of g(X) given sufficient statistic T(X) is a better (in the sense of having lower variance) estimator of θ, and is never worse.