Tagged Questions
0
votes
0answers
31 views
Bias in EM estimation for a mixture of normal distributions
Are the parameter estimates for a mixture of two normal distribution using EM algorithm biased or unbiased?
More specifically, if I use the EM-algorithm to obtain ML estimates of $μ_1$, $μ_2$, ...
3
votes
1answer
48 views
Will two estimators converge to the same answer?
Say I have two estimators for the same quantity and using the same model, $E[f(X)]$. I also know that these two estimators are consistent, meaning, if we have a lot of data, they will be close to the ...
3
votes
1answer
115 views
What is the name of the estimator that takes the mean of likelihood?
Let $X,Y$ be input and output (observed) continuous variables in $\mathbb{R}$. Let $\{y_1,...,y_n\}$ be the set of $n$ observations. Is there a name for the estimator $\hat x = \int_{x \in X} x ...
2
votes
1answer
115 views
Estimate the second moment of a latent variable using a conditionally unbiased proxy
The Setup: Let $X_t$ denote an unobservable stochastic sequence where the first two unconditional moments are finite constants; ie $\mathbb{E} X_t = \mu < \infty$ and $\mathbb{E} X_t^2 = \gamma ...
7
votes
2answers
346 views
Estimating parameters of a normal distribution: median instead of mean?
The common approach for estimating the parameters of a normal distribution is to use the mean and the sample standard deviation / variance.
However, if there are some outliers, the median and the ...
7
votes
1answer
263 views
Bias correction in weighted variance
For unweighted variance
$$\text{Var}(X):=\frac{1}{n}\sum_i(x_i - \mu)^2$$
there exists the bias corrected sample variance, when the mean was estimated from the same data:
...
8
votes
3answers
326 views
Parameter estimation of exponential distribution with biased sampling
I want to calculate the parameter $\lambda$ of the exponential distribution $e^{-\lambda x}$ from a sample population taken out of this distribution under biased conditions. As far as I know, for a ...
2
votes
2answers
462 views
Why doesn't the Cramer-Rao lower bound apply?
Let $X_1, X_2, \dots, X_n$ be a sample of i.i.d. random variables, with density $$f_\theta=\frac{2}{3\theta}\left(1-\frac{x}{3\theta}\right) $$ for $0 < x < 3\theta$. And
$f_\theta=0$ if $ x ...
4
votes
1answer
181 views
Two unbiased estimators for the same quantity
In several situations, I have two unbiased estimators, and I know one of them is better (lower variance) than the other. However, I would like to get as much information as possible, and I would like ...
2
votes
2answers
135 views
Can the ratio importance sampling estimate by made to be unbiased with resampling?
Consider approximating the following integral:
$$
\mathcal{Z} = \int h(x) \pi(x) dx
$$
Where $\pi$ is known only up to a normalizing constant, that is, $\pi(x) = \hat{\pi}(x)/\mathcal{Z}_\pi$. We can ...
5
votes
1answer
283 views
Finding a minimum variance unbiased (linear) estimator
Here is a basic question that perhaps has a simple answer, but one that I was not able to find by quickly scanning the literature.
Suppose that I have a collection of $n$ unopened boxes. Each box ...
5
votes
1answer
419 views
Estimation of probability of a success in binomial distribution
Let's say we have two biased coins. The probability of tossing a head on the first coin is $\alpha$ and the probability of tossing a head on the second coin is $1-\alpha$. We toss both coins $n$ times ...
13
votes
3answers
729 views
Unbiased estimation of covariance matrix for multiply censored data
Chemical analyses of environmental samples are often censored below at reporting limits or various detection/quantitation limits. The latter can vary, usually in proportion to the values of other ...
