# Questions tagged [estimation-theory]

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### Estimate for the gradient of solutions in an elliptic differential equation in a Sobolev space

Let $\Omega$ be a bounded or unbounded domain in $\mathbf R^{3}$ with a smooth boundary $S$ and a normal vector given by $n$. Now, we consider the following second-order elliptic problem with Neumann ...
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### Parameter estimation of a Taylor expansion

Let $a,b$ two real numbers, $\theta$ a real parameter and suppose that you have an analytic function of the form: $$f_\theta(x)\triangleq \sum_{k\in\mathbb{N}}a_k(\theta)x^k \quad\forall x\in[a,b],$$...
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### Derivative of log-likelihood function for Gaussian distribution with parameterized variance

Suppose we have a parameter $\theta \in R^{n}$ that defines some noisy observation $z=\mu(\theta)+\eta, z\in R^{m}$ where the noise follows a Gaussian distribution whose covariance is a function of ...
203 views

### Singular Fisher information matrix and existence of unbiased estimators

I'm doing some research into the Cramer-Rao bound for time of arrival localization and have come across a rather strange result: the FIM is singular, but there exists an unbiased estimator. My ...
51 views

### Estimation of Nonzero Coefficients of Binary Cylotomic Polynomials

I am reading Fouvry's paper https://msp.org/ant/2013/7-5/ant-v7-n5-p07-p.pdf . I am still confused on section 4.2 why $P\leq x^{\frac{20}{9}\gamma -\frac{2}{3}}\mathcal{L}^{-16}$ leads to estimate in ...
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### A complex problem involving densities (likelihood functions) and optimization

Consider the following autoregressive process with normal errors: \begin{equation}\label{7YlUV4i8nuO}\tag{I} y_t = \phi y_{t-1}+ u_t, \quad u_t \overset{iid}{\sim} N(0,\sigma^2) \end{equation} We ...
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### What journal(s) do you recommend for submitting a paper on a topic that spans information theory and estimation theory?

I've written a paper that a) demonstrates an equivalence between conditional complexity $K$($Y$|$X$) in information theory and the random component of an effect size estimate $r_{xy}$, and then b) ...
1 vote
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### Estimating the average of two gaussians' mean with minimal squared error

This is a follow-up to my previous question. Assume that $X\sim \mathcal N(\mu_1,\sigma_1^2)$ and $Y\sim \mathcal N(\mu_2,\sigma_2^2)$. I want to estimate $\frac{\mu_1+\mu_2}{2}$ after observing $X,Y$....
1 vote
454 views

### Estimating the average of two gaussians' mean

Assume that $X\sim \mathcal N(\sigma_1,\mu_1)$ and $Y\sim \mathcal N(\sigma_2,\mu_2)$. I want to estimate $\frac{\mu_1+\mu_2}{2}$ after observing $X,Y$. In my setting, $\sigma_1,\sigma_2$ are known ...