What is this mean ( ± 0.06) and How can I calculate it mathematically?
Standard error = s / √n
where:
- s: sample standard deviation
- n: sample size
https://www.statology.org/standard-error-of-mean-google-sheets/
If a mean is +/- 0.06. it's not a mean
, Sample means are unique. best wishes, David Booth
( ± 0.06) could indicate different things. Be sure the author is indicating that this is the standard error of the mean.
Say θ∈RD and ℓ(θ) is the log-likelihood. Then ∇2ℓ(θ) is the Hessian of the log-likelihood (the DxD matrix of the partiel second derivatives for θ). The observed Fisher information is I* = −∇2ℓ(θ∗) with θ∗ being the vector of the maximum likelihood estimates. The standard errors are the square-roots of the diagonal of the inverse Fisher Information:
se = sqrt( diag(I∗−1) )
Example: exponential distribution with parameter θ
L(x) = θ·exp(-θ·x)
ℓ(x) = log(θ) - θ·x
ℓ(x) = n·log(θ) - θ·Σixi (for a sample of n values x = (x1, x2, ..., xn))
∇1ℓ(θ) = n/θ - Σixi
∇2ℓ(θ) = -n/θ²
θ*: ∇1ℓ(θ*) = 0 ↔ n/θ* - Σixi= 0 ↔ n/θ* = Σixi·Σ ↔ n/Σixi·Σ =θ* = 1/x̅
I* = -∇2ℓ(θ*) = n/(θ*)²
se = sqrt( (n/(θ*)²)−1 ) = sqrt(1/n) · θ*
I am grateful for your help, thanks a lot Jochen Wilhelm Sal Mangiafico David Eugene Booth Anton Vrdoljak
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