All Questions
Tagged with estimators expected-value
28
questions
3
votes
1
answer
72
views
Tossing Until First Heads Outcome, and Repeating, as a Method for Estimating Probability of Heads
Consider the problem of estimating the heads probability $p$ of a coin
by tossing it until the first heads outcome is observed. Say we get $k_1$
tosses, then $U_1 = \frac{1}{k_1}$ is an estimate for $...
- 33
3
votes
0
answers
34
views
What order of power mean best estimates the median of a gamma distribution?
Suppose we have a gamma-distributed random variable $X$ whose shape/scale parameters are known to be $\alpha$ and $\beta$. What order $p$ for the sample power mean $\hat M_p[X]$ minimizes $$ (\mathcal{...
- 9,401
1
vote
1
answer
463
views
Find the expectation of an exponential distribution estimator
So we've got a sample data coming from exponential distribution with parameter $\lambda$, and we take an estimator $\lambda_n = \frac{n}{X_1+X_2+\cdots+X_n}$.
I need to show that this is a biased and ...
- 13
2
votes
1
answer
88
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Bias of MLE scales with $1/N$?
I was reading this paper (link) and it gave me some confusion.
$P(r|\theta)$ is a distribution that generates sample $r$ based on some Poisson distribution, whose mean and variance are defined as some ...
- 281
12
votes
4
answers
1k
views
Why isn't this estimator unbiased?
Suppose we have a IID sample $X_1, X_2, \cdots, X_n$ with each $X_i$ distributed as $\mathcal{N}(\mu, \sigma^2)$. Now suppose we construct (a rather peculiar) estimator for the mean $\mu$: we only ...
- 613
0
votes
0
answers
67
views
Bias and variance of an estimator of a model mean
I have a binary classification model and I need to use its output to estimate the means of groups of observations. I have two questions:
A. Can I compute the the bias and variance of the estimator of ...
- 111
1
vote
1
answer
24
views
Can't Follow the Algebra in a Estimator MSE Comparison
Little bit of background - working through some maths and stats autodidactically. I simply can not follow the algebra of the following worked example comparing the MSE of two estimators.
I can not ...
0
votes
0
answers
97
views
Taking Expectation Over Inverse Sum of Indicator Functions?
I'm working with a zero inflated Poisson distribution that has the following pmf:
$$f(y|w,\lambda)=wI[y=0]+(1-w)\frac{e^{-\lambda}\lambda^{y}}{y!}$$
I would like to find the expectation of the ...
- 154
2
votes
1
answer
439
views
Are all estimators biased? Is the unbiasedness only a theoretical or approximation case?
The definition of unbiased estimator says that it's expected value has no difference comparing to a true value. So can we say that all estimators are biased (even slightly)? I thought that only in ...
- 491
1
vote
1
answer
569
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Variance and expectation of $\frac{1}{n}\sum^n_{i=1}X^2_i$
Let $X = (X_1, . . . , X_n)$ consist of independent and identically Normal $N(0, θ)$ random
variables, with mean $0$ and variance $θ \gt 0$.
The Moment Estimator for $\theta$ is given by $\hat \theta ...
user255658
4
votes
1
answer
2k
views
MLE as an expectation over the empirical distribution
I am reading Ian Goodfellow "Deep Learning" book. At page 128, it writes the maximum log-likelihood estimator and then says it is equivalent to the expectation over the empirical distribution
To ...
- 2,301
1
vote
0
answers
298
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Expected value of the parameters in linear regression (trying to understand which part is constant and which isn't and why)
I'm studying Linear Regression and trying to proof/demonstrate some properties of the parameters. When I started working with the expected value of the slope, I got confused with something. I actually ...
- 660
1
vote
1
answer
66
views
Expected value without complete sample space
The book way:
Suppose, we have a bag with 8 balls numbered 1-8, we want to estimate the population parameter mean. we note down the entire sample space. (1,1)(1,2).. (8,8) calculate mean of each ...
- 77
0
votes
1
answer
1k
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How do I find bias and variance of estimators of a binomial distribution?
A product-lot arrives in two containers with respectively 300 and 700 units in each container. We examine 30 units in the first container and find that 𝑋1 of them is defective. We check 70 units in ...
- 159
1
vote
2
answers
804
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Expectation on estimator for Poisson distribution
I'm reading through the textbook "All of Statistics" and one of the problems gives the following estimator for the lambda parameter of the Poisson distribution:
$\hat{\lambda} = \frac{\sum_{i=1}^n ...
- 45