All Questions
Tagged with estimators mean
29
questions
1
vote
2
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94
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Covariance of Best Linear Unbiased Estimators and arbitrary LUE
I'm working on a problem involving two linear unbiased estimators $T$ and $T'$ of a parameter $\theta$, defined from a sample $\{X_1, \dots, X_n\}$ with mean $\theta$ and finite variance. I aim to ...
- 13
0
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0
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14
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Optimality criterion for mean estimators
Assume a sample size of $n>5$, a given variance $\sigma^2 > 0$ and a $\delta \in (2e^{-n/4}, 1/2)$.
Proof that there exists a distribution with variance $\sigma^2$ such that for any mean ...
- 1
3
votes
1
answer
149
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Is the sample mean an unbiased estimator of population mean in the presence of autocorrelation?
I've seen previous questions here that the sample mean can be considered an unbiased estimator of the population mean. e.g.1, 2.
While the examples seem to refer to independent sample points, it seems ...
- 539
9
votes
1
answer
979
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When is the median-of-means estimator better than the standard mean?
The median-of-means estimator is often given as an alternative way to, given a sequence of IID random variables $X_1,...,X_N$, estimate the expectation value $\mathbb{E}[X]$ (see e.g. these pdf notes ...
- 383
0
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0
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56
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Estimate $p$ of a Bernoulli after $n$ samples
Suppose I extract $n$ samples $x_i$ from a Bernoulli distribution
$$x_i \sim Bern(p)$$
Based on the samples, I want to estimate the probability that $p$ is below a certain threshold $t$
$$P(p<t \...
- 1,230
1
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0
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58
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What is the joint distribution between the sample mean and sample mediant of rounded normal variables?
I am curious about the relationship between the arithmetic mean and the (generalized) mediant. I took $10^4$ samples (each of size $n=3$) of $\operatorname{Round}(X_i,\text{decimals}=3)$ where $X_i \...
- 9,401
0
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0
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35
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Bias and variance of estimators - Normal Sample
If we consider the two following estimators $$\hat{\mu_1} = \frac{\bar{X_1}+\bar{X_2}}{2}$$ $$\hat{\mu_2} = \frac{n_1\bar{X_1}+n_2\bar{X_2}}{n_1+n_2}$$ where $X_1, X_2$ are samples from a normal ...
- 197
1
vote
1
answer
78
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Can we predict what happens to the sample mean as we increase sample size if the true mean blows up?
The Cauchy distribution is used as an example of a pathological case where the mean blows up. For such a distribution, we can imagine drawing samples and tracking the sample mean as the number of ...
- 2,600
12
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4
answers
1k
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Why isn't this estimator unbiased?
Suppose we have a IID sample $X_1, X_2, \cdots, X_n$ with each $X_i$ distributed as $\mathcal{N}(\mu, \sigma^2)$. Now suppose we construct (a rather peculiar) estimator for the mean $\mu$: we only ...
- 613
8
votes
4
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632
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How to estimate $P(x\le0)$ from $n$ samples of $x$?
Suppose, we have $n$ samples $x_i$ of a random variable:
$$x \sim \mathcal N(\mu,\sigma^2) $$
Based on the samples, we want to estimate the probability that $x$ is negative:
$$P(x\le0)$$
Intuitively, ...
- 1,230
0
votes
1
answer
90
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Estimate a sum using proportional sampling
I have some set of items. Each item has a weight and I can sample the items from the population with probabilities proportional to their weights. I know the size of the population. I want to estimate ...
- 145
3
votes
1
answer
350
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Obtaining an expression for empirical mean from empirical CDF definition
This is my first post so I will try to be as clear and concise as possible. I am doing a course in statistics and we define the true mean of a random gaussian variable to be as follows:
$\mu$ = $\int_{...
- 31
2
votes
2
answers
161
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"... because sample mean gets different values from sample to sample and it is a random variable with mean $\mu$ and variance $\frac{\sigma^2}{n}$."
This answer by user "sevenkul" says the following:
The sample mean $\overline{X}$ also deviates from $\mu$ with variance $\frac{\sigma^2}{n}$ because sample mean gets different values from ...
- 2,096
1
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0
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74
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Is the $\sigma$ estimator more efficient than the $\mu$ estimator?
Are my empirical findings correct? How to get the same result analytically?
I studied the efficiency of the mean and standard dev estimators:
$$\mu_n=\sum \frac {x_i} {n}\space\space\space\space\...
- 1,230
0
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1
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94
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"Ice skater" / "figure skating" / "ISU" method of discarding outliers
So I need a way of ruling out outliers and "the ice skater method" has been suggested. The person who suggested it has a good deal of experience of doing the task I am doing, so I am certainly ...
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