Linked Questions

3
votes
0answers
165 views

Using Leibniz integral rule when minimizing Expected Absolute Loss [duplicate]

Consider choosing $\theta^*$ that minimizes the expected absolute loss: \begin{align} \tag{1} \int_{\Theta}|\theta-\theta^*|\pi(\theta|\mathbf{x})d\theta= \int_{-\infty}^{\theta^*}(\theta^*-\theta)\...
1
vote
0answers
62 views

Quantile regression, minimizer [duplicate]

Let's consider values $z_1, \dots, z_m$ and the minimizer of the function: $$ \min_q (1-\tau) \sum_{z_i<q} (q-z_i) + \tau \sum_{z_i \geq q}(z_i -q)$$ Why does minimizing this function gives the $\...
28
votes
2answers
3k views

What is the statistical model behind the SVM algorithm?

I have learned that, when dealing with data using model-based approach, the first step is modeling data procedure as a statistical model. Then the next step is developing efficient/fast inference/...
1
vote
3answers
709 views

What does it mean L1 loss is not differentiable?

I was looking through this lecture https://davidrosenberg.github.io/ml2015/docs/3a.loss-functions.pdf Slide 3: Absolute or Laplace or L1 loss not differentiable What does it mean ...
5
votes
1answer
3k views

How do I show that the sample median minimizes the sum of absolute deviations? [duplicate]

I want to show that the sample median $\tilde{x}$ minimizes the sum of absolute deviations, i.e., $\tilde{x} = \underset{a}{argmin}\sum_{i=1}^{n}\begin{vmatrix} x_i-a\end{vmatrix}$ To show this, so ...
3
votes
1answer
177 views

How to find a value that ensures 70% of population is above it

i'm trying to solve this statistics problem. i have a certain number of samples that are randomly chosen to represent a population. (yellow dots in the picture) over those samples are run tests to ...
2
votes
1answer
216 views

Examples of “risk-averse” loss functions

Could you give me some examples and/or references on "risk-averse" loss functions (i.e. penalizing the underestimates more then the overestimates)?
1
vote
2answers
110 views

Appropriate error measure

Statistics is not realy my field of knowlegde but I am trying to find an answer for the following question: Many cities nowadays have a bike share system. Suppose you were asked to predict how many ...
0
votes
1answer
128 views

Formula of quantile regression?

We already know that the estimator of quantile regression defined by LAD (Least Absolut Deviation), minimizes sigma |e_i|. But I also found a formula that minimize with an integral, not a sigma ...
2
votes
0answers
88 views

Different error weighting for positive and negative residuals for OLS?

For OLS-estimators in multivariate regression analysis, it logically doesn't matter whether an error is positive or negative. I was wondering if in some situations it might make sense to weight a ...
1
vote
0answers
29 views

Should we use the absolute value of errors in quantile regression loss function?

I am trying to use quantile regression loss function. Most of the implementations I see here, here, and here are using the error directly: ...
1
vote
0answers
18 views

What does, actually, the quantile regression asseses, assuming single two-level categorical covariate, difference in medians or median of differenes?

I know that, for a single, two-level categorical covariate, like sex={Male, Female}, the linear regression coefficients are about difference in means. It's like the t test. Does the quantile ...