For questions about estimation and how and when to estimate correctly

# Questions tagged [estimation]

1604 questions

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### Multipling / Dividing with Significant Figures

I have:
$$\frac{(10.3) + (0.01345) }{ (10.3) \cdot (0.01345)}$$
The answer need to be given in scientific notation. I know the rules for addition/subtraction and multiplication/division, however, something is messing me up. Do I round before putting…

john

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### Equal expectation and covariance

Let $Y_{i}=\beta_{1}+\beta_{2}X_{i}+u_{i}$ be the underlying linear relationship between observed values $X_{i}$ and $Y_{i}$ with $u_{i}$ being randomness and/or disturbance term.
Let $\hat\beta_{2}$ be an OLS estimator of the underlying parameter…

Omrane

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### Comparing variances for estimators

Let $\tilde \beta$ and $\hat \beta$ be two different estimators of a parameter $\beta$ with $E(\tilde \beta)=\beta$ and $E(\hat \beta)=\beta$.
I want to determine which estimator is superior. Since both are unbiased, I look to their…

Omrane

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### Ordinary Least Squares vs other methods

Suppose we have the relation $Y_{i}=\beta_{1}+\beta_{2}X_{i}+u_{i}$ with $X_{i}$ and $Y_{i}$ observed values, $\beta_{1}$ and $\beta_{2}$ the parameters and $u_{i}$ the disturbance term. We want to construct estimators of $\beta_{2}$.
The method of…

Rankyaku

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### Hadamard product with rank 1 matrix

Let $\odot$ represent Hadamard or pointwise multiplication. If $\pmb{Y}$ is a $\underline{given}$ positive definite square matrix, can i estimate a positive semi-definite $\pmb{X}$ matrix such that
\begin{equation}
\pmb{Y} = \pmb{X} \odot…

Ahmad Bazzi

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### Estimate of $\frac{1}{\pi}\left| \log \left| \frac{1 + \rho e^{i\theta}}{1 - \rho e^{i\theta}}\right|\right|$

Assume $1/4 \leqslant\rho < 1$. Why does
$\displaystyle \frac{1}{\pi}\left| \log \left| \frac{1 + \rho e^{i\theta}}{1 - \rho e^{i\theta}}\right|\right| \leqslant \frac{1}{\pi} \left( \log 4 + \log \frac{1}{\left| \cos(\theta/2)\right|} +…

TheGeekGreek

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### How to price option with limited information?

You have a call option on a security worth 100 now that will either be worth 110 or 95 dollars at a future date. The strike of this option is 105. What is an estimated value of this call option?

Alex F

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### How many terms of $4\sum_{0}^{\infty}\frac{(1/5)^{2n+1}}{2n+1}-\sum_{0}^{\infty}\frac{(1/239)^{2n+1}}{2n+1}=\frac{\pi}{4}$ are needed to estimate

I am working on a $\pi$ estimation formula and I came up with the following series
$$4\sum_{0}^{\infty}\frac{(1/5)^{2n+1}}{2n+1}-\sum_{0}^{\infty}\frac{(1/239)^{2n+1}}{2n+1}=\frac{\pi}{4}$$
How do I find how many terms are needed to give a value of…

ReeSSult

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### Maximum-Likelihood estimator

Imagene we have a sequence of i.i.d random variables $(Y(t))_{1\le t\le s}$. It is possible to derive the density of $Y(t)$ and it is a function of parameters of interest $f(p,\rho, y(t))$. To have a Maximum-Likelihood estimator all i need to do…

holic

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### Asymptotic expansion of $(ix+a)^{q}$ as $x\rightarrow\infty$

let $a>0$ be fixed and $q\in\mathbb{C}$. I would like to know the asymptotic expansion as $x\rightarrow\infty,$ $x\in\mathbb{R}$ of
$$f(x):=(ix+a)^{q}$$
This function looks so natural that I would expect this as known. For example, is there…

Denilson Orr

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### Better estimate for quadratic form over sphere

I have f = $\sum_{ij} a_{ij} x_i x_j$ with reals $a_{ij}$ and $x_i$ from $R^N$ inside sphere $x_1^2+x_2^2+x_3^2+...+x_N^2 < r$.
It is obvious that
$|f|=|\sum...|<=\sum_{ij}|a_{ij} x_i x_j|<=r^2 \sum_{ij}|a_{ij}|$.
But I believe that it is usually…

stiv

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### Find sufficient statistic for a mixed distribution

If I have a random variable $Y$ with a mixed distribution:
$$
F(y)=\begin{cases}
0, & y<1\\
1/\theta^3, &y=1\\
y^3/\theta^3, &1

Zander

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### Show that an estimator is unbiased and it's variance goes towards 0? Poisson distribution

Let X be Poisson Distributed with expectation λt. Show that the estimator is unbiased and has a variance that goes towards 0 when the times goes to infinity.
λ^=X/t
I know that for these questions there is a good thing to have some kind of…

David Lund

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### How to check if an estimator is expectation right?

I am sorry if the terminology is a little bit off, and anyone that knows the correct terminology please correct me.
Let us assume we have 3 independent measures, X1, X2, and X3 from the same population with expectation μ and standard deviation σ.…

David Lund

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### Calculate average life time in system with inputs and observed items inside system in a given time

In a given time (t) i observe the inputs that enter a system and the total items that are the sistem, i.e
time inputs items in system
t1 i1 N1
t2 i2 N2
t3 i3 N3
....
how can i calculate…

Ivan Encinas Trigo

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