All Questions
32
questions
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51
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Why the MSE of the fitted data is not equal to the sum of the bias and the variance in R?
I use simple linear regression and I want to find the decomposition of MSE, that is as a sum of the bias, the variance and the variance of the error terms. I have the following code:
...
1
vote
1
answer
336
views
How error derivative becomes zero in gradient descent
Previous questions this & this does not answer my question
Code
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- 677
1
vote
0
answers
51
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Problem in showing $\rm MSE = Var + Bias^2.$ [duplicate]
I am trying to prove the equality of $$\rm MSE(\langle I\rangle)=Var(\langle I \rangle)+Bias(\langle I \rangle)^2$$ but obviously I got something wrong as they don't equal in my calculation:
So here ...
- 143
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
1
vote
1
answer
582
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MSE : Bias and Variance tradeoff
I have a dilemma with respect to the included (decomposition) between bias and variance in the calculation of the Mean square error (MSE) for the OLS estimator with the equation:
MSE = bias ^ 2 + ...
- 953
1
vote
0
answers
127
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How do you decompose conditional MSE?
I'm trying to decompose the conditional mean squared error but I'm not exactly sure how to expand the terms. Is it the same as just decomposing the general mean squared error?
- 31
6
votes
1
answer
3k
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How to quantify bias and variance in simple linear regression?
In terms of predictive modeling, how can I calculate the bias and variance in a given model (e.g. simple linear regression)? I know that the bias and variance of an estimator (linear regression model) ...
- 91
1
vote
1
answer
3k
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MSE and variance reduction in regression trees
I've seen this statement in the SciKit documentation for Regression Trees: Supported criteria are “mse” for the mean squared error, which is equal to variance reduction as feature selection criterion
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- 213
4
votes
1
answer
4k
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Is the MSE of a vector a scalar or a matrix? [duplicate]
Suppose $Y = X\beta + \epsilon,$ where $Y$ is $n \times 1$, $X$ is $n \times p$, and $\beta$ is $p \times 1$, and $\epsilon$ is $n \times 1$ with mean 0 and variance $\sigma^2$. The OLS estimator of $\...
- 2,909
1
vote
0
answers
52
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Estimating the bias and variance of an estimator [closed]
Suppose I have a vector of values generated by an estimator of $y$. I also have corresponding values of $y$ in another vector. Starting at the first observation, and adding the remaining observations ...
- 475
3
votes
1
answer
2k
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When are biased estimators with lower MSE preferred? [duplicate]
From wikipedia https://en.wikipedia.org/wiki/Bias_of_an_estimator :
because a biased estimator gives a lower value of some loss function (particularly mean squared error) compared with unbiased ...
0
votes
1
answer
48
views
Choosing an estimator function due to variance and bias
I am working on an assignment that requires me to compare two estimators $T1$ & $T2$ for an unknown parameter $\theta$ based on their MSE.
They both have the same MSE of 3, T1 having a variance ...
- 3
0
votes
0
answers
121
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Why i get the same MSE value for two least square models that differ in one explanatory variable?
I have two ols-regression models that just differ in one variable. It means that one model have the same variables like the other plus an explanatory variable more. I estimated both models on a train ...
1
vote
1
answer
1k
views
How to calculate Bias and Variance to get the MSE value step by step?
I want to compute my MSE value for a forecast step by step for test set.
For me the Bias is:
Bias = mean(predicted values - actual values)
Variance = mean((predicted values- actual values)^2)
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4
votes
3
answers
4k
views
Consistent estimator, that is not MSE consistent
I'm trying to understand the concept of consistency in point estimation. Could somebody give me an illustrative example of a (simply) consistent estimator that is not MSE consistent?
Just a recall of ...
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