All Questions
Tagged with confidence-interval variance
110
questions
2
votes
2
answers
132
views
Computing the confidence interval for two samples but getting slightly different answers
Consider two samples $X_1,..,X_k$ and $Y_1,..,Y_m$ where $X_i \sim \mathcal{N}(\mu_x,\,\sigma^{2})\,$ and $Y_i \sim \mathcal{N}(\mu_y,\,\sigma^{2})\,.$ Say $k=m=100$ and $k+m=n$. Say that the ...
- 43
2
votes
1
answer
327
views
Ratio of Standard Deviations from a Normal Distribution to an F Distribution
Apologies if the title is confusing, I couldn't think of a more apt title.
I have that $W_i$s are iid $N(\mu_a,\sigma_a^2)$ and independent of $Z_i$s which are iid $N(\mu_b,\sigma_b^2)$. This means
$...
- 367
2
votes
1
answer
205
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Can the variance of a U-statistic be of the order $O(\frac{1}{n^2})$?
It is not that easy to find estimators $T_n$ such that $\mbox{Var}[T_n] \sim O(n^{-B})$ with $B = 2$. In most cases, $B=1$.Here $n$ is the sample size. It seems, according to this paper on U-...
1
vote
0
answers
256
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Confidence interval for population variance and chi-square distribution [closed]
At present, i am reading the e-book by Robert L. Mcdonald(Professor of Finance,Northwestern University's Kellogg school of Management) named $"Derivatives Markets" 3rd Edition.$ In that book, I didn'...
- 1,216
0
votes
1
answer
56
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Calculating the probability that the standard deviation is above or below a certain value
I'm given $n$ samples from a random number generator that produces normally distributed values. Can I calculate the probability that the standard deviation that the RNG uses is $\sigma > \sigma_{...
1
vote
1
answer
8k
views
How to find confidence interval for variance?
Well, I'm taking a statistics class online, and the problem goes like this:
Drug concentrations (measured as a percentage) for 25 randomly selected tablets are shown in the accompanying table. For ...
- 11
1
vote
0
answers
36
views
What do we use variance of the error term for in regression analysis?
So I get that, for simple linear regression where Y = B_0 + B_1(x) + E, Var(Y|x) = Var(E). Variance of the mean response involves it, as does variance of future responses, but is this ever actually ...
- 11
5
votes
1
answer
1k
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Variance of unbiased estimator for the shape parameter of Pareto distribution
I'm interested in getting the error bounds of the unbiased estimator of the shape parameter ($\alpha$) using maximum likelihood method of Pareto distribution.
The unbiased estimator is known to be
...
1
vote
1
answer
962
views
Confidence interval for $\sigma^2$
I started with any distribution and underwent the CLT on $\sqrt{n}(\widehat{\sigma}^2 - \sigma^2)$ where
$$
\widehat{\sigma}^2 = \frac{1}{n}\sum_{i=1}^n (X_i - \mu)^2
$$
is a sample mean of $\sigma^2$...
0
votes
1
answer
1k
views
Confidence intervals and variance for ordinal scale set [0-5]
We have a known sample of data coming from a multiple choice ordinal scale survey question with scores from the set [0,1,2,3,4,5].
In one sample, the mean of this ...
- 101
0
votes
1
answer
2k
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How to calculate confidence interval for the residual variance in ANCOVA models?
As the question states I need to know how to calculate this.
Given variable $Y$ and $X$ with $\operatorname{cor}(Y,x)=r$, the residual variance is:
$$(1-r^2)\cdot\sigma_Y^2,$$
which represents the ...
- 73
2
votes
2
answers
99
views
How to calculate the confidence interval of a line based on its coefficients?
I fitted a mixed model as following:
$Y = \beta_0 + \beta_1 T + \beta_2 X + \beta_3 X T + \beta_iW_i$
$T$ is time, $X$ is my variable of interest and $W_i$ are various confounding variables. I also ...
- 1,440
1
vote
1
answer
63
views
Confusion about confidence interval
So far I understand, confidence interval (for mean) is defined by treating the sample mean as a proxy for population mean and then finding a interval where the true mean will be in certain percentage ...
- 535
0
votes
0
answers
189
views
95% confidence interval for log odds
I'm looking at data from the O-Ring Challenger disaster and wasn't sure how to get a 95% confidence interval for a particular estimated log odds.
In this case, I'm considering a logistic regression ...
4
votes
0
answers
373
views
Confidence Interval vs Credible Interval for the Variance
I understand the conceptual difference between confidence and credible intervals. But I have difficulties applying these concepts to my application.
I would like to know the concrete difference ...
- 425