Timeline for Which is the relation between population/probability space/sampling?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Mar 6, 2018 at 8:28 | history | bounty ended | Star | ||
| Mar 6, 2018 at 8:28 | vote | accept | Star | ||
| Mar 5, 2018 at 17:04 | comment | added | David Dale | (1) I suspect there is a modification of LLN for the case of "weakly dependent" observations. However, asking for consistency means "increase sample size indefinitely and look at the distribution of your estimator", and with sampling from finite population w/o replacement it is plainly impossible. Thus, notion of consistency is inapplicable here. (2) Exactly so! | |
| Mar 5, 2018 at 16:55 | comment | added | Star | Thanks. Last points I would like to clarify before accepting your answer: let's imagine that I sample from a FINITE population without replacement; (1) in this case the i.i.d. hypothesis fails and I cannot apply L.L.N. to show consistency. Actually, in that case, consistency as usually meant does not make a lot of sense. Correct? (2) If, instead, I sample from a finite population with replacement, I'm back to i.i.d., LLN, and usual notion of consistency. Correct? | |
| Mar 1, 2018 at 19:40 | comment | added | David Dale | No, it doesn't change. The most popular distribution is normal, which indeed has pdf strictly positive everywhere, and it is frequently used to approximate discrete distributions, e.g. binomial. | |
| Mar 1, 2018 at 18:50 | comment | added | Star | Thanks. Regarding sub-question 4: I am a bit confused also reading the answer below. Suppose that I assume not only that $U_m$ is a continuous random variable, but also that it has a STRICTLY positive pdf on the entire real line. Does your conclusion change? | |
| Mar 1, 2018 at 15:17 | history | answered | David Dale | CC BY-SA 3.0 |