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Questions tagged [parameter-estimation]

Questions about parameter estimation. Estimation theory is a branch of statistics that deals with estimating the values of parameters based on measured/empirical data that has a random component. (Def: http://en.m.wikipedia.org/wiki/Estimation_theory)

Questions about parameter estimation. Estimation theory is a branch of statistics that deals with estimating the values of parameters based on measured/empirical data that has a random component. Reference: Wikipedia.

The parameters describe an underlying physical setting in such a way that their value affects the distribution of the measured data. An estimator attempts to approximate the unknown parameters using the measurements.

1939 questions
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estimate the perimeter of the island

I'm assigned a task involving solving a problem that can be described as follows: Suppose I'm driving a car around a lake. In the lake there is an island of irregular shape. I have a GPS with me in the car so I know how far I've driven and every…
zgsc
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estimation of a parameter

The question is: $x_i = \alpha + \omega_i, $ for $i = 1, \ldots, n.$ where $\alpha$ is a non-zero constant, but unknown, parameter to be estimated, and $\omega_i$ are uncorrelated, zero_mean, Gaussian random variable with known variance…
user2262504
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Finding the MLE of $\theta$ where $\theta \leq x$

consider the following PDF $$ \begin{eqnarray} f(x;\theta) &=& \left\{\begin{array}{ll} 2\frac{\theta^2}{x^3} & \theta \leqslant x\\ 0 & x< \theta; 0 < \theta \end{array}\right.\\ \end{eqnarray} $$ Now the answer stats $X_{1:n}$ so the minimum of…
WiseStrawberry
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Bias, SE and MSE of Uniform Distribution

Let $X_1,\ldots,X_n$ be an i.i.d. sequence of Uniform $(\mu,2\mu)$ and let an estimator be $\hat{\mu} = \frac{1}{2} \max\{X_1,\ldots,X_n\}$. Find the bias, SE, and MSE of this estimator. Hint: Let $U_1,\ldots,U_n$ be i.i.d. Uniform $(0,1)$ and $Y…
Wayne
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Estimation theory: Finding MSE and Variance of an Estimator

Let $\hat{A}$ be an estimator of $A$ where $a
bryan.blackbee
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Estimate parameters in model

Consider the following model: $\hat y = f(x_1, ..., x_n) + \delta$ $\hat x_i = x_i + \varepsilon _i, i=1,..,n$ where $\delta, \varepsilon _1, ..., \varepsilon _n$ are i.i.d. random variables with known $\mathbb E \delta = \mathbb E \varepsilon _i =…
vladkkkkk
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Capture-Recapture method. What happens if the no marked individual was captured?

I am trying to understand parametric estimation theory more in depth. Now, the classic Capture-Recapture method assumes a population of size $N$, of which $R\leq N$ individuals are captured, marked and released. A second catch of, say, $m\leq R$ may…
Peter Strouvelle
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How to find parameters from an equation

the question could be "stupid" but i don't know if it is feasible or not, please don't kill me :) EDIT WITH NEW FORMULAS! I have an equation like this: (unfortunatly in my first Q&A i cannot upload images for "spam" reason, I post latex version of…
Maurizio
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Minimal sufficient statistics for two unknown parameters

I have a problem for finding a sufficient and a minimal sufficient statistics for the next density: let $X_1,...,X_n$ a sample with $$f_X(x;\alpha,\theta)=\frac{\alpha x^{\alpha-1}}{\theta^{\alpha}}I_{(0,\theta)}(x)$$ First of all, I tried to use…
sinbadh
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Bias and asymptotically biased

I have the following problem: Based on a random sample $\{X_1,X_2,...,X_n\}$ of size $n$, two statisticians disagree on which estimator to use to estimate the population mean $\mu$ (where $\mu>0$), of a population distribution with variance…
Slim Shady
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Finding a 2-3 parameter decay function to fit experimental data

I have a series of concentration measurements, that are normalized such that they attain their maximum concentration $y_{max} = 1$ at the location $x_{ \text{max}} = 1$. For $x > 1$ the concentration decays to a known asymptote concentration $y_{…
fmherla
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why estimate a product of domain endpoints for a uniform distribution?

In a book on unbiased estimation I met an example that mentioned an unbiased estimator for the product $\theta_1 \theta_2$ from a sample of a uniform distribution in the interval $(\theta_1, \theta_2)$. The particular reference was: Patel J.K.…
Andrei Zorine
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Sufficient Estimators and Generalized Likelihood Ratios

If you can make the assumption that a sufficient statistic exists for some parameter - let's call it $\theta$. How would you show that the critical region of a likelihood ratio test will depend on the sufficient statistic?
PatternMatching
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Estimation of unbiased estimator for population variance in case of poisson distribution

sample variance is normally biased estimator for population variance. but in case of poisson distribution sample variance is unbiased for population variance. how do you prove this?
user258778
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MLE of two-dimensional distribution

Let $X_1, ..., X_n$ be a random sample from a continuous distribution with pdf $$f_{\theta,\kappa}(x) = \frac{\kappa\theta^\kappa}{x^{\kappa+1}}, x\geq \theta, \theta > 0, \kappa > 0.$$ How to find the MLE of the pair $(\theta,\kappa)$? I tried to…
Jack
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