All Questions
Tagged with bias estimators
44
questions
1
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0
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49
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Standard practice to show Biased CRBs
I have a problem with four-parameter estimation. I have derived the variances for the estimated parameters using Monte Carlo simulations (numerical ones) and theoretical ones using the inverse of the ...
- 235
1
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1
answer
41
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For a biased estimator, how does one call the point for which the expected value of the estimator is equal to the observed sample estimate? [closed]
Let $\hat{\theta}$ be a biased estimator whose bias depends on the true value $\theta_0$, such that $E[\hat\theta|\theta_0]= f(\theta_0)\neq \theta_0$. Let $t_{sample}$ be a sample realization of $\...
- 3,094
1
vote
1
answer
119
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Difference between consistent and unbiased estimator [duplicate]
I have a problem where I have to think of an example to explain a practical example of consistency and unbiased. The example I thought of is the sample mean.
Consistency is when the estimator (sample ...
3
votes
1
answer
72
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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
2
votes
1
answer
371
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Philosophical insight of Bias Variance Decomposition
As we know that we can perform a Bias Variance decomposition of an Estimator with MSE as loss function and it will look like below:
$$\operatorname{MSE}(\hat{\theta}) = \operatorname{tr}(\operatorname{...
- 31
2
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0
answers
31
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How can we compare biases of two estimators with no parametric form?
I was reading in my textbook that the bias of a statistical estimator $\hat{\theta}_n$ can be quantified as $B(\hat{\theta}_n,\theta)=E[\hat{\theta}_n-\theta]$. This expectation seems to be w.r.t. to ...
- 63
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35
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Bias and variance of estimators - Normal Sample
If we consider the two following estimators $$\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}$$ where $X_1, X_2$ are samples from a normal ...
- 197
1
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1
answer
463
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Find the expectation of an exponential distribution estimator
So we've got a sample data coming from exponential distribution with parameter $\lambda$, and we take an estimator $\lambda_n = \frac{n}{X_1+X_2+\cdots+X_n}$.
I need to show that this is a biased and ...
- 13
2
votes
1
answer
147
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Properties of the sample mode for Bernoulli data
Suppose we have a sample $X_1,...,X_n \sim \text{IID Bern}(p)$ of Bernoulli values with probability parameter $p \neq 0.5$. Denoting the sample proportion $\hat{p}_n$ we define the sample mode as:
$$\...
- 21
1
vote
2
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1k
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Definition of the bias of an estimator
I'm quite confused about the definition of the bias of an estimator.
Suppose we have unknown distribution $P(x, \theta)$, and construct the
estimator $\hat{\theta}$ that maps the observed data sample ...
- 11
0
votes
0
answers
57
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What low bias has to do with "good fit"
Look at the bias-variance decomposition below:
In pratice we often consider low bias as good fit to train data but i dont understand the why this by bias-variance decomposition.Why if i got "...
- 1,220
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
2
votes
0
answers
25
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bias–variance decomposition related to median?
In evaluating or designing an estimator $\hat\theta$ of a population parameter $\theta$, the most common approach is to look at its bias,
$\operatorname{E} \hat\theta - \theta$,
its variance,
$\...
- 3,210
0
votes
0
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67
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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
0
votes
1
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320
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Is Bias Affected By Dataset Size?
I am trying to understand the concept of asymptotic unbiasedness. I understand that an estimator is said to be asymptotically unbiased if, when the size of our data increases to infinity, the bias of ...
