# Tag Info

• 675
1 vote
Accepted

### Check MLE estimator is asymptotically normal

In this particular case, you should recognize that if $$X \sim \operatorname{Beta}(1/\theta, 1),$$ then $$Y = -\log X \sim \operatorname{Exponential}(\lambda = 1/\theta),$$ hence \hat \theta_n \sim \...
• 140k
1 vote
Accepted

### Min-max optimization and prediction of a parameter in a mathematical model

Let $x$ be a vector in $\mathbb{R}^{11}$ denoting the 11 parameters, i.e., the 10 parameters plus $R$. Let $f$ be some function (which you are trying to find) so that $f(x)$ is a reasonable estimate ...
• 5,243
1 vote

### Efficient and unbiased estimation of the location ($\mu$) of truncated normal distribution with known scale ($\sigma^2$) and truncation points

One observation is not enough to infer $\mu$ with much accuracy at all. I think you are inherently going to be limited by your lack of data. I suspect the best you can do is take a Bayesian approach. ...
• 5,243
Accepted

$\beta$ is the minimum of this Pareto distribution: the question says the density is $0$ below $\beta$ so there is zero probability of observing data below $\beta$. Suppose for example you knew $\... • 159k 4 votes ### Given the maximum likelihood function- estimate the value of the parameter As stated in the solution, the maximum likelihood function, for a fixed$\alpha$, is increasing in$\beta$. Thus, for some fixed sample$(x_1,\ldots,x_n)$we want to make$\beta\$ as big as possible. ...
• 8,729

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