# Questions tagged [estimation]

For questions about estimation and how and when to estimate correctly

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### All about estimators biased and unbiased

I am unable to understand the difference between an estimator and a distribution, for example what is the difference between variance of a distribution and the variance of an estimator, and what is ...
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276 views

### Drawing marbles from a box

Say we're drawing marbles from a box. The marbles can be labeled X, Y, or Z and can be either black, brown, or white. The probability of drawing a marble with each letter label is unknown but fixed ...
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### Formula to increase concentration in one solution using 2 substances simultaneously

Using the following formula: V2 = ((D-C1)/(C2-D))*V1 It is possible to estimate the amount of higly concentrated V2 with value C2 that has to be added to the base ...
1 vote
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### Showing the big Oh bound for the logarithmic integral $\operatorname{Li}(x)=x/\log x + x/\log^2 (x)+O(x/\log^3 (x))$

Consider the logarithmic integral $\operatorname{Li}(x):=\int_2^x \frac{dt}{\log t}.$ Then I found a result stating that we have $\operatorname{Li}(x)=x/\log x+O(x/\log^2(x))$ and another integration ...
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### Innovation error covariance decreasing but state error covariance inceasing

I am trying to implement Kalman Filter to estimate some random variables. I see that for the system I am using, the innovation error is zero for all times and the innovation error covariance matrix is ...
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### Is there another simple way to find the limit using Stirlings formula?

$n\in\mathbb{N}$, find the limit \begin{equation} \lim_{n\to\infty} e^{\frac{n}{4}}n^{-\frac{n+1}{2}}(1^1\cdot2^2\cdot\cdots\cdot n^n)^{\frac{1}{n}} \end{equation} I calculate the limit in the ...
78 views

1 vote
In the following, I am referring to this paper, p. 14, line (3.14): It is said that from $$\frac{\Vert f^{n+1}\Vert_{2,\gamma}^2-\Vert f^n\Vert_{2,\gamma}^2}{2\Delta t}+\frac{1}{\varepsilon^2}\Vert f^... 0 votes 0 answers 32 views ### Bound for MSE of the Kernel Density Estimator On page 911 of the Paper Adaptivity in convolution models with partially known noise distribution they say: By using classical results on this estimator, we have$$\mathbb{E}_{f, s_k}\left[\left|f_n(x)...
Assume $f(x)$ ($x \in \mathbb{R}$) is a smooth function with a compact support. Assume $0 < \epsilon < 1$ and $i = \sqrt{-1}$ is the imaginary unit. Can we show that there exist a constant $C$ ...