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A VAR with p lags can always be equivalently rewritten as a VAR with only one lag by appropriately redefining the dependent variable. The transformation amounts to stacking the lags of the VAR(p) variable in the new VAR(1) dependent variable and appending identities to complete the precise number of equations. For example, the VAR(2) model
This implies that in a weighted sum of variables, the variable with the largest weight will have a disproportionally large weight in the variance of the total. For example, if X and Y are uncorrelated and the weight of X is two times the weight of Y, then the weight of the variance of X will be four times the weight of the variance of Y.
In probability and statistics, a mixture distribution is the probability distribution of a random variable that is derived from a collection of other random variables as follows: first, a random variable is selected by chance from the collection according to given probabilities of selection, and then the value of the selected random variable is realized.
Let Y be a random variable and X another random variable on the same probability space. The law of total variance can be understood by noting: The law of total variance can be understood by noting: Var ( Y ∣ X ) {\displaystyle \operatorname {Var} (Y\mid X)} measures how much Y varies around its conditional mean E [ Y ∣ X ...
The canonical tail value at risk is the left-tail (large negative values) in some disciplines and the right-tail (large positive values) in other, such as actuarial science.
A main assumption in linear regression is constant variance or (homoscedasticity), meaning that different response variables have the same variance in their errors, at every predictor level. This assumption works well when the response variable and the predictor variable are jointly normal. As we will see later, the variance function in the ...
Interaction effect of education and ideology on concern about sea level rise. In statistics, an interaction may arise when considering the relationship among three or more variables, and describes a situation in which the effect of one causal variable on an outcome depends on the state of a second causal variable (that is, when effects of the two causes are not additive).
Here, as usual, stands for the conditional expectation of Y given X, which we may recall, is a random variable itself (a function of X, determined up to probability one). As a result, Var ( Y ∣ X ) {\displaystyle \operatorname {Var} (Y\mid X)} itself is a random variable (and is a function of X ).