All Questions
Tagged with bias mathematical-statistics
51
questions
2
votes
2
answers
147
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Why is the asymptotic bias of the maximum likelihood estimate $b(\theta) = \frac{b_1(\theta)}{n}+\frac{b_2(\theta)}{n^2}+...$?
Firth (1993) states in his introduction that for a $p$-dimensional parameter $\theta$ the asymptotic bias of the maximum likelihood estimate $\hat{\theta}$ may be written as:
$b(\theta) = \frac{b_1(\...
- 41
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 ...
2
votes
2
answers
172
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Proof of the bias-variance decomposition in Bishop's book
I am trying to rewrite the demonstration given in Bishop's book: Pattern Recognition and
Machine Learning (2009)
I reproduce the figure (page 149) in which I am unclear about the step leading from (3....
- 153
3
votes
2
answers
305
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What would it take for the omitted-variable bias from multiple omitted variables to cancel out?
Let's stick to ordinary least squares linear regression for now, and assume the typical conditions for the Gauss-Markov theorem. If it is helpful to assume Gaussian errors, that's fine.
In such a ...
- 65k
1
vote
1
answer
143
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Can we apply hypothesis testing to not-actively sampled groups?
For argument's sake, in the below please assume that the hypothesis test we'd be considering would be a simple z-test to check whether an observed difference between two groups' means or proportions ...
- 11
0
votes
0
answers
27
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bias is large relative to the variance when we pool information over small samples or when data is highly stratified?
I am reading Yudi Pawitan's In All Likelihood Chapter 5. The book makes the following assertion on MLE bias.
"...bias is large relative to the variance when we pool information over small samples ...
- 1,445
2
votes
0
answers
92
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Expectation of Difference in Means estimator
Given i.i.d. observations $(Y_i, X_i)$ where $Y_i$ is the response and $X_i$ is binary valued, the difference in means estimator is
$$
\hat{\theta} = \frac{1}{n_0} \sum_{i=1, X_i=0} Y_i - \frac{1}{n_1}...
- 1,501
1
vote
0
answers
9
views
Create Score with a skewed data
I'm trying to create a reputation score for sneakers using positive and negative sentiments of twitter on these sneakers (something like score = p+n). The problem is that the mean of positive != mean ...
- 11
1
vote
2
answers
2k
views
How to compute the expected value of the ridge regression estimator?
I am trying to understand this derivation:
I think everything except the last equality is fairly simple, but I do not understand the last equality. Is there an error here?
I appreciate any help.
- 581
3
votes
2
answers
316
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The role of bias terms in binary recommender systems
I realize that a recommender system applied to, for example, the Movielens dataset needs to account for bias. That is, one needs to adjust for the varying popularity of movies, and that users have ...
- 1,152
0
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0
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45
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How to handle retraining after model introduces bias
Here is my problem.
I am retraining a machine learning model to detect fraudulent purchases.
The training data is based on purchases and the target is whether or not they the purchase was considered ...
1
vote
0
answers
26
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Mathematical bias and weight vs machine learning bias and weight
I am a little confused about the term Bias and Weight with respect to machine learning.
Say we want to predict the heights of people whose weights are given. So plot weights to x-axis and height to ...
- 175
2
votes
0
answers
246
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why is the bias of an AR(1) model converging towards 0 for $n \rightarrow \infty$
could someone please explain to me why the statement at the end is true?
The estimator of $\alpha$ in an AR(1) process is biased, meaning:
$E[\hat{\alpha} ]\neq \alpha$ this is because $E[\hat{\alpha}]...
- 21
3
votes
1
answer
111
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How can i find bias of estimator for specific value?
I have $X_1,...,X_n~ Ber(p)$ with MLE estimator $\hat p$ which is equal to sample mean. I need to find bias of estimator $\hat p(1 - \hat p)$ for $p(1-p)$.
I presume $p(1-p)$ is variance of my RVs, so ...
- 33
2
votes
0
answers
43
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Derivation of Neuhaus, Jewell(1993)
I wish to ask a derivation problem in Neuhaus, Jewell(1993) - "A geometric approach to assess bias due to omitted covariates in generalized linear models"
The statistical True model dealt in ...
