Search results
Results From The WOW.Com Content Network
This theorem follows from the fact that if X n converges in distribution to X and Y n converges in probability to a constant c, then the joint vector (X n, Y n) converges in distribution to (X, c) . Next we apply the continuous mapping theorem , recognizing the functions g ( x , y ) = x + y , g ( x , y ) = xy , and g ( x , y ) = x y −1 are ...
Print/export Download as PDF; Printable version; In other projects ... By Slutsky's theorem and continuous mapping theorem these results can be combined to establish ...
Proof of the theorem: Recall that in order to prove convergence in distribution, one must show that the sequence of cumulative distribution functions converges to the F X at every point where F X is continuous. Let a be such a point. For every ε > 0, due to the preceding lemma, we have:
There are two parts of the Slutsky equation, namely the substitution effect and income effect. In general, the substitution effect is negative. Slutsky derived this formula to explore a consumer's response as the price of a commodity changes. When the price increases, the budget set moves inward, which also causes the quantity demanded to decrease.
The proof can be found in Page 126 (Theorem 5.3.4) of the book by Kai Lai Chung. [13] However, for a sequence of mutually independent random variables, convergence in probability does not imply almost sure convergence. [14] The dominated convergence theorem gives sufficient conditions for almost sure convergence to imply L 1-convergence:
Print/export Download as PDF; Printable version; In other projects Wikidata item; Appearance. move to sidebar hide. ... Slutsky's theorem; Stein's lemma; V.
Background Chlorine and caustic soda are produced at chlor-alkali plants using mercury cells or the increasingly popular membrane technology that is mercury free and more energy-
Download as PDF; Printable version; In other projects ... , by the central limit theorem, the law of large numbers, and the Slutsky's theorem, the estimator ...