# Questions tagged [estimation]

For questions about estimation and how and when to estimate correctly

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### How to estimate a difference?

I have a doubt what is the estimated difference of $91-45$ so I started to think about two methods the first was I will first find the difference of $91-45$ that is 46 than I will just round off 46 ...
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### Prove that when $|x|\geq M_1+M_0t, u(x,t)=0$.

For the following Cauchy problem: \begin{cases} \partial^2_tu-a^2(x,t)\partial^2_xu=f(x,t), x\in\mathbb{R},t>0\\u(x,0)=\varphi(x), \partial_t u(x,0)=\psi(x), x\in\mathbb{R},\end{cases} where \begin{...
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### Characterization of Total Error for Estimation of the Parameters of a System

Suppose that we have a system which can receive different kinds of input (the index $k$ signifies the kind of input $I_k$) and performs a calculation on that input based on the internal parameters of ...
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### "Fusion" of multiple uncertain estimates with covariance matrices

this is my first post here. I tried my best to follow all the guidelines and to state the problem as clear as possible but should something be sloppy or unclear, I will be happy to update the question ...
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### Unscented Kalman Filter Linearly Not Independent Variables

I have an Extended Kalman Filter, where my state vector variables are linearly independent (e.g. conventional position tracking with roll-pitch-yaw angle). Then, when calculating the Jacobians of the ...
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### Computation of whitening matrix for estimation of the covariance matrix for n samples

I am working on data-driven robust optimization, meaning that instead of forming uncertainty sets using conventional approaches such as box-shaped uncertainty sets, I want to determine this set by ...
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### Maximum likelihood estimation intuition for continuous distributions

I was just revisiting the fundamentals and rationale of maximum likelihood estimation when I realised I can't rationalise the continuous case as opposed to the discrete case. For a discrete random ...
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### Why don't we use the mean of the middle pair to estimate the median in a cumulative frequency curve?

I just learned about cumulative frequency curve. The books says I could use this curve to estimate the median of the data. This is the picture that I cut from my book. As you can see, to estimate the ...
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### Estimation of the interval of a proportion (mark, recapture)

I'm a college studen doing statistics homework and Im looking for help. I have tried to solve this exercise, thinking about it in a number of ways, to no avail. This is the problem: To estimate the ...
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### When is the conditional probability formula applicable compared to more rigorous methods?

Imagine that you have a sample of a fruit and some of the fruits of your sample received a certain treatment and others haven't. You want to find out if this treatment has any effect on the acidity of ...
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### Markov inequality to find bound on the probablity over an interval

Is it possible to use Markov inequality, as given in the following, to find bound on the probability over an interval? $$P[X \ge a] \le \frac{E[X]}{a}$$ For example, consider this problem. The number ...
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### Statistical significance in context of financial data?

I understand statistical significance in the general sense: we take a sample from a population and compute some parameter from the sample to infer what is the propulsion parameter to some degree of ...
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### Estimating confidence intervals for the variance of a sampling distribution (from normal), given that the samples are not drawn independently

A random variable $X \sim N(\mu, \sigma^2)$. One day, we draw a sample $X_1, X_2, ..., X_n$ from this population. This gives an estimate of the actual distribution of $X$. What I would like to ...
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### Mle estimation in hardy Weinberg

There is a population of 3 kinds 1 2 3 occurring in hardy Weinberg proportion $\theta^2, 2\theta(1-\theta), 1-\theta$ If we abserve a sample of 3 individuals and obtain $X_1=1, X_2=2, X_3=1$ To find ...
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### $r<s$, a bounded sequence of functions $f_{n} \in H^{s}(\mathbb{R})$ converges and is equicontinuous in $H^{s}(\mathbb{R})$, it converges in $H^{s}$.

For $r<s$, there's a bounded sequence of functions in Sobolev space: $f_{n} \in H^{s}(\mathbb{R}) .$ If $f_{n}$ converges in $H^{r}(\mathbb{R})$ and (uniformly) equicontinuous in $H^{s}(\mathbb{R})$...
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### Monte carlo variation of $E[1_{\{X>0\}}]$
Let's assume that $X \sim N(0, 1)$. I want to calculate variation of crude monte carlo estimator of parameter $\delta = E[1_{\{X>0\}}]$ My work so far Let's generate \$x_1, x_2, x_3,..., x_n \sim N(...