Mathematics Stack Exchange
Mathematics Stack Exchange

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.

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Why there are two maximum value of $p$ exist in a plot of logarithm likelihood?

The plot of the logarithm of the likelihood shown below indicates that there are two values of $p$ that give the same maximum value for the likelihood. May I know why this happens and find an equation satisfied by these values. Many thanks!
Casilaze
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Estimating Attendence

I am trying to estimate attendance at events. What I have is daily/weekly ticket sales numbers. The goal is to analyze the ticket sales each day and estimate where we might be at by the day of the event. We have hundreds of events so we can…
user112169
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How to prove $W(T)$ is not a MVB estimator

A random sample $X_1, . . . , X_n$ of size n is taken from the Poisson distribution with parameter $\theta$. Let $X = (X_1, . . . , X_n)^T$ and $x = (x_1, . . . , x_n)^T$. It is proposed now to estimate the estimate the function of $\theta$,…
fa fa
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Sensitivity to noise in nonlinear parameter estimation

Consider the model: $$ y(\theta) = \alpha + \beta \cdot \tan(\theta + \gamma) + noise $$ where $\alpha$, $\beta$, and $\gamma$ are parameters I want to estimate and the noise is normally distributed: $N(0,\sigma)$. $\alpha$ and $\beta$ has the unit…
Andy
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Truncated lognormal distribution calibration with MME

To estimate the parameters of a truncated distribution (lognormal for example), we can use the Maximum Likelihood Estimation or Method of Moments. For the Method of Moments Estimation, one needs to write down the mathematical expression of the…
John Smith
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I need a Excel formula to find the coordinates of the point in the new bent cylinder.

In the beginning, I have a straight cylinder where I have the value of the distance of plane 2 from the beginning of the cylinder and an angle value of the point on the surface. Then, I will have a coordinate table of the interceptions of the lines…
Abid Hussain
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How to analyze the sensitivity of the estimator?

I have several equations $y_k = \boldsymbol{a}^T \boldsymbol{Q} \boldsymbol{x}_k, \forall k=1, \ldots, K$, where $\boldsymbol{a} \in \mathbb R^{3 \times 1}$, $\boldsymbol{Q} \in \mathcal{F} \triangleq \{ {\rm det}(\boldsymbol{Q})=1 ,\boldsymbol{Q}…
Kris Prokins
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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 already contained in the word estimand. On the…
user122424
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Calculate $MSE(\hat\mu_2)$

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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unbiased estimate

suppose we have a uniform distribution such that $u\in \left[0,\:\frac{1}{\phi }\right]$ from which a single observation is $x\left(0\right)$. We want to prove that an unbiased estimator $\phi'\:=\:h\left(x\left(0\right)\right)$ would be equal…
JordenSH
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Proving it is a biased estimator

How would I show that if a distribution is equally likely to take values of $1$ or $4$, then the statistic $s_{n-1}$ forms a biased estimator of $\sigma$? My thoughts: Do I find the expression$s_{n-1}$ in terms of the standard deviation…
Aurora Borealis
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Method of Moments for Rayleigh Distribution

Given that $$f(x;\theta) = \frac{\pi x}{2 \theta^2} e^{-\frac{\pi x^2}{4 \theta^2}} \text{ for } x>0$$ I wish to find the method of moments estimators for $\theta$ and $\theta^2$. I have calculated the $k$-th raw moment as…
An Invisible Carrot
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Moment method estimator of binomial population

If question asked... Let X~Bin(n,$\pi$). Find the methods of moments estimator MME of $\pi$. Book answer was $\pi$_hat=X_bar/n Shouldn't it be X_bar/n_hat , or even better 1 -$\sum(X_i-Xbar)^2$/$\sum X_i$? by solving the 2 equations E(x)=$M_1 and…
Rivaldo
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Several Unbiased Estimators

If I have some data set $ D={X_1,...X_N} $ and have an esitmator be "pick the first point" $X_1$, how can I show that this estimator is unbiased? I also have to show why its highly undesirable, and I would assume it uses some variance/convergance…
Diego
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What is an estimator?

If $p_y$ is a probability function for a density, which depends on the value of $y$ (for example, $y$ might be the mean in the poisson distribution). Assuming that $y$ is random -- i.e. unknown -- how would one estimate the probability that $X < x$…
Clearer
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