# Tag Info

Accepted

### When is a biased estimator preferable to unbiased one?

Yes. Often it is the case that we are interested in minimizing the mean squared error, which can be decomposed into variance + bias squared. This is an extremely fundamental idea in machine learning, ...
• 20.2k
Accepted

### Maximum Likelihood Estimators - Multivariate Gaussian

Deriving the Maximum Likelihood Estimators Assume that we have $m$ random vectors, each of size $p$: $\mathbf{X^{(1)}, X^{(2)}, \dotsc, X^{(m)}}$ where each random vectors can be interpreted as an ...
Accepted

### Are there parameters where a biased estimator is considered "better" than the unbiased estimator?

One example is estimates from ordinary least squares regression when there is collinearity. They are unbiased but have huge variance. Ridge regression on the same problem yields estimates that are ...
• 120k
Accepted

• 33.3k

### Use of splines in parameter estimation

Edit: In light of Lukas Lohse's answer (which I think should be the accepted one!), my original answer below is misleading. Personally I learned about splines from Tibshirani's books, where he ...
• 3,814
Accepted

### Square of the Sample Mean as estimator of the variance

You have $X_1, X_2, \dots, X_n$ are iid from an unknown distribution with mean (say) $\mu$ and variance (say) $\sigma^2$. $\bar{X}$ is an unbiased estimator of the mean, and thus $E(\bar{X}) = \mu$. ...
• 15.6k
Accepted

### What's the difference between asymptotic unbiasedness and consistency?

In the related post over at math.se, the answerer takes as given that the definition for asymptotic unbiasedness is $\lim_{n\to \infty} E(\hat \theta_n-\theta) = 0$. Intuitively, I disagree: "...
• 59.1k

### Revisiting the Rule of Three

The image below is how I look at confidence intervals. It is an adaptation from an image in the answer to the question 'The basic logic of constructing a confidence interval', which is itself an ...
• 78.8k
I interpret "$B(p)$" to mean a Bernoulli distribution with parameter $p = \Pr(X=1)$ and I suppose $X$ is a single observation from this distribution. Trivial though this situation is, it is ...