# estimation's questions - English 1answer

2.253 estimation questions.

### 3 Optimizing $\chi^2$ using MCMC

I have measurements of an object. Let's say I have its length $L$, mass $M$, and age $t$: $$\mathbf y = (10~\text{m},\ 0.01~\text{g},\ 5~\text{s}).$$ I also have the uncertainties on my measurements ...

### 1 Finding a UMVU estimator for the mean

0 answers, 20 views estimation mean umvue
I am struggling with the following problem. We are given an i.i.d sample of size $n,$ with the form $X_{i}=\mu+n_{i}$, where $\mu$ is a deterministic unknown constant, and $n_{i}$ is a noise with a ...

### 2 Posterior mean estimator with MCMC (Metropolis Hastings Algorithm) - Concrete example

0 answers, 13 views self-study estimation mcmc estimators

### 2 Estimating total events from buckets hit

1 answers, 38 views estimation count-data
I'm working on a project that will run $n=10000$ experiments. In this experiment, $j$ events will occur (an unknown number). Each of the events has a value $E_j$ attached to it. We expect these values ...

### 1 Proof that posterior median is the Bayes estimate of absolute loss?

It is always argued that the posterior median is the Bayes estimate associated to the absolute loss function. The proofs I have come across rely on differentiating the conditional Bayesian risk and ...

### 1 Asymptotic variance of estimated AR(1) coefficient

Consider an $AR(1)$ process \begin{align*} y_{t} + a y_{t-1} &= e_{t} \end{align*} for $t=1,\ldots,N$, where $e_{t}$ is a white Gaussian noise with variance $\sigma^{2}$. How do I express the ...

### How to measure product adoption across different zones

I am very new to this subject, but i've tried searching other questions and haven't found what i need. I'm working on an application that will be promoted in physical meetings. Lets say, for example, ...

### 2 Estimation from two observations

0 answers, 45 views estimation linear-dynamical-system
Suppose there are two vector signals $x$, $z$. The observer 1 receives a linear version of $x$ plus Gaussian noise. Observer 2 receives a linear sum of both $x$ and $z$ plus Gaussian noise as shown ...

### 1 Method of moments for linear regression?

I have been reading about the method of moments, and now I understand how to obtain the method of moments estimator for a random sample $x_1,...,x_n$ from a distribution $f(x;\theta)$, in the ...

### When to use minimum mean square error (MMSE) estimate instead of maximum a posteriori (MAP) estimate [closed]

0 answers, 561 views estimation map-estimation
What are the advantages and disadvantages of MMSE estimates and MAP estimates?

### 6 Minimum no. of observations required for statistical distribution fitting!

1 answers, 18.766 views distributions estimation
I have one conceptual (but sort of vague) question regarding distribution fitting. How many observations one would need to best fit any statistical distribution to given data. Like I am dealing with ...

### Standard Errors for estimates obtained from custom objective function

0 answers, 15 views estimation standard-error

### Estimability in Design model

0 answers, 19 views regression estimation blue