# 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.

430 questions
16 views

### Regressions with two independent variables where one is part of another.

I am doing simple regression analysis where I use one-way fixed effect model to estimate the effects of two variables on dependent variable. The question I am asking is how to interpret these two ...
17 views

### Finding the bias of an estimator

Consider the following model: $$y_i = a + b x_i + c z_i + w_i,$$ where $a,b,c$ are unobserved fixed parameters, $x_i$ and $z_i$ are fixed in repeated samples. Assume also $\mathrm{E}[w_i] = 0$ for ...
37 views

30 views

### ML estimation with given samples

Let $X_i,...,X_n$ be a random independent sample from a distribution with pdf $$f(x;\theta)= (\theta + 1)x^{-(\theta+2)},$$ where $x>0$, and $\theta > 0$. What is the ML estimate for the ...
116 views

### derive sufficient statistic from a random independent sample from a weibull distribution

Suppose $X_i$ is a random independent sample from a Weibull distribution $$f(x) = \frac{\beta}{\theta^\beta}x^{\beta-1}\exp\big(-(\frac{x}{\theta})^\beta\big)$$ Find a sufficient statistic for ...
69 views

62 views

16 views

### Induced bias in r.v. A $= \pi R^2$ where R is unbiased measurement of fixed unknown.

I have particularly poor and incomplete notes that refer to induced bias in the random variable A of the area of a circle that is dependent on random variable R which is the measured radius (true ...
69 views

### Variance of mean estimator with variable sample size

I'm looking at a random variable that takes vectors $\newcommand{\vv}{\mathbf{v}} \vv_1, \dotsc, \vv_n \in \mathbb{R}^d$ and calculates their average, after applying "blankout" noise to them. So we ...
### Estimation $\mu^2$ under certain conditions.
Let $X_1,X_2,....,X_n$ be a random sample of size $n$ from a population with cdf $F()$. Let $E(X)=\mu$ exist. Then estimate $\mu^2$ unbiasedly for the following three cases:- (i) $Var(X)=\sigma^2$ ...