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Grigori
  • Member for 9 months
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revised
Uniform distribution as argument for copula likelihood
added 22 characters in body
asked
Uniform distribution as argument for copula likelihood
revised
Formalization of sample convergence
edited body
asked
Formalization of sample convergence
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Convergence of probabilities imply convergence of joint probability
Indeed, @IosifPinelis, thank you for saying that :) I think simple triangle inequality will solve everything here.
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Convergence of probabilities imply convergence of joint probability
@tsnao, fair point. I assume now that these RV are defined on the same space. I also added the "dependence vanishing condition". Would it help somehow?
revised
Convergence of probabilities imply convergence of joint probability
added 260 characters in body
comment
Convergence of probabilities imply convergence of joint probability
@ChristianRemling, thank you, I misunderstood you. I know something about the dependence of $X_n$ and $Y_n$, I will add it to the question.
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Convergence of probabilities imply convergence of joint probability
@ChristianRemling, but in this case there won't be convergence of $|P(X_n \in A) - P(\tilde{X}_n \in A)| \to 0$.
awarded
 Editor
comment
Convergence of probabilities imply convergence of joint probability
@tsnao, thank you for the comment, I corrected the question, there was a typo: $X_n$ and $Y_n$ could be dependent, but $\tilde{X}_n$ and $\tilde{Y}_n$ are independent for any $n$.
revised
Convergence of probabilities imply convergence of joint probability
edited body
awarded
 Supporter
asked
Convergence of probabilities imply convergence of joint probability
awarded
 Scholar
awarded
 Student
accepted
Difference of probabilities of two random vectors lying in the same set
asked
Difference of probabilities of two random vectors lying in the same set