Statements (21)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
random variables
|
| gptkbp:category |
probability theorems
statistical theorems |
| gptkbp:describes |
convergence in probability
convergence in distribution |
| gptkbp:field |
gptkb:probability_theory
statistics |
| https://www.w3.org/2000/01/rdf-schema#label |
Slutsky's theorem
|
| gptkbp:namedAfter |
Evgeny Slutsky
|
| gptkbp:publishedIn |
1925
|
| gptkbp:relatedTo |
gptkb:central_limit_theorem
gptkb:law_of_large_numbers |
| gptkbp:state |
If X_n converges in distribution to X and Y_n converges in probability to a constant c, then X_n + Y_n converges in distribution to X + c.
If X_n converges in distribution to X and Y_n converges in probability to c ≠ 0, then X_n / Y_n converges in distribution to X / c. If X_n converges in distribution to X and Y_n converges in probability to c, then X_n Y_n converges in distribution to Xc. |
| gptkbp:usedIn |
statistical inference
asymptotic analysis |
| gptkbp:bfsParent |
gptkb:Eugen_Slutsky
gptkb:Mathematical_Statistics |
| gptkbp:bfsLayer |
8
|