All Questions
4
questions
4
votes
1
answer
188
views
Proving that the bias of the derivative of Parzen-Rosenblatt (kernel density) estimator is of order $O(h^2) $ and $O(h)$ when $h$ approaches $0$
I came across this property that I don't get and I couldn't find the proof anywhere:
Suppose we have a density $K$ of the standard normal distribution and $K'$ its derivative. Suppose that the density ...
- 241
3
votes
1
answer
653
views
variance of nonparametric estimator of mean
I'm having some trouble with understanding how to calculate the variance of a non-parametric estimator.
The example comes from Wasserman's "All of statistics book"
Let $X_1, \ldots,X_n \sim ...
- 379
0
votes
0
answers
51
views
Simple method to estimate $\sigma^2$ from i.i.d. samples of $y_i \sim N(\theta_i, \sigma^2)$
This is a normal means model: given $N$ i.i.d $y_i \sim N(\theta_i, \sigma^2)$ or equivalently
$$
y_i = \theta_i + \varepsilon_i\, \text{ where }\varepsilon_i \text{ are i.i.d } \sim N(0, \sigma^2)...
- 702
6
votes
1
answer
301
views
A question on a non-parametric estimating equation
This is a question that arose from studying Hogg and Craig "Introduction to Mathematical Statistics",7th edition, pg 568.
It is assumed that we have taken a random sample of $X_1,\ldots,X_{n1}$ and a ...
- 20.8k