# Questions tagged [estimation-theory]

Estimation theory is a branch of statistics and signal processing that deals with estimating the values of parameters based on measured/empirical data that has a random component.

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### Difference between MVB and UMVU estimators

I am trying to understand the difference between the UMVUE (uniformly minimum-variance unbiased estimator, also known as minimum-variance unbiased estimator (MVUE)) and the MVBE (minimum variance ...
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### Statistical estimator of expected value of the gradient of an unknown function

Fix a probability space $(\Omega, \mathcal{A}, \Bbb P),$ a continuously differentiable function $f:\Bbb R^n \rightarrow \Bbb R,$ and a random vector $X: \Omega \rightarrow \Bbb R^n.$ Furthermore, we ...
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### New condition of an unbiasedness

The usual unbiasedness condition of an estimand $g(\theta)$ is this $$E_\theta[\delta(X)]=g(\theta).$$ Here $g(\theta)$ is a real valued function over $\Omega$ whose value is to be estimated. This is ...
1 vote
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### Incredibly low standard errors

I am currently estimating the parameters of an interest rate model by means of a maximum likelihood estimation in combination with the iterated extended Kalman filter, and I obtain incredibly low ...
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### Interpolating noisy measurements taking into account derivative bounds

For context, I have a target moving in space which I am able to locate using vision sensors. I end up obtaining $M$ noisy samples of the trajectory $[x(t), y(t)]$ for some time instants $\{t_k\}$. ...
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### Consistently estimate the covariance matrix with weakly correlated observations

Suppose there are T k-dimensional observations following the generating process: $Y_t = \mu + \epsilon_t$, where $\mu$ is the mean and $\epsilon$ is a weak stationary error with zero mean and time-...
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### How to apply MCMC to a exponential complex data-set

I am a beginner in probability, estimation and statistics. I can understand the physics behind the problem really well, but when it comes to estimation using some statistical algorithms I am very ...
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### Correlating two matrices $A, B$ with stochastic dependency structure imposed by cross-validation

Consider a labelled data set $$D = \{(x_1, y_1),...,(x_n, y_n)\}$$ on which we want to evaluate a machine learning algorithm using $k$-fold cross validation with $m$ different random seeds. This ...
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### Covariance of fused poses. Should it be normalised by the number of poses?

I came across this paper from T. Barfoot and P. Furgale: "Associating Uncertainty With Three-Dimensional Poses for Use in Estimation Problems" Link: http://ncfrn.mcgill.ca/members/pubs/...
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### Minimum mean square estimation with 3 random variable

I am trying to find the solution for part "a", I have try finding the expectaion $E[x|y=y] = \int x f(x|y=y) dx = \int x \frac{f(y=y|x=x)f(x))}{f(y=y)}$. With y|x ~ Normal (2x,1). Yet it ...
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### Estimate random variables given estimated function values

Let $X_1$ and $X_2$ be two positive independent random vectors. Let random variable $Y_1$ depend only on $X_1$; and random variable $Y_2$ depend only on $X_2$. If I have the following means square ...
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### Can weak measurement principles of Quantum mechanics be used in similar questions in classical estimation problems?

This is a surface level question and I don't want to go into detail. Imagine an algorithm which when used with a sensor output gives the statistical moments of a variable in nature (for example mean ...
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### Distributing a fixed number of noisy samples of a function to best estimate that function

I want to learn more about how to best spatially distribute noisy samples of a function to reconstruct the function itself. The name of this field of research or some references to papers or books ...
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### Maximum Likelihood Estimator for $r$ with $r^n$ in noise

$x[n]=r^n+w[n]$ for $n=0,1,\ldots,N-1$ where $w[n]$ is WGN with variance $\sigma^2$. I need to estimate $r$. No efficient estimator exists (that I can discover), so I am looking to build a maximum ...
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### What is the difference between MVUE and UMVUE

I was going through the minimum variance unbiased estimators and I am confused about the concept of MVUE and UMVUE. Is the unbiased estimator whose variance attaining CRLB a UMVUE or MVUE? I referred ...
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### Population minimizer for mixture of two regressions

Consider the generative model where, \begin{align*} Z &\sim \mathrm{Bernoulli}\left( \frac{1}{2}\right) \\ Y &= \begin{cases} \pmb{\beta}_{1,*}^T \mathbf{X} + \eta &~~\text{given}~~ Z = 0\\...
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### Use probability theory to estimate the successors of an event out of a countable finite sample space?

Scenario: There exists to two façades in a system: façade zero, and façade one. When façade zero builds a LinearDataStructure, that object contains elements of ...
See the question referenced. How do I find the t-part? If my confidence level is $95\%$ what do I do with that number? I know what to do to find the inverse distribution in other estimations but this ...