All Questions
9
questions
6
votes
2
answers
296
views
Regression with flexible functional form
I am assuming a model of the form
$$Y_i=\alpha+\beta X_i+g(\mathbf{Z}_i)+\epsilon_i,$$
here $\mathbf{Z}_i$ is an $m$ dimensional vector and $\epsilon_i$ is i.i.d. white noise. I would like to ...
- 340
0
votes
0
answers
53
views
Error $|\hat{f}_n(x)-f(x)|$ with regressogram estimator
I am learning about non parametric estimation, and more specifically about regressogram:
Let $(X_i,Y_i)_{i = 1}^n$ be a sequence of random variables in $[0,1]$ variables and $E[Y_i|X_i] = f(X_i)$. ...
- 11
1
vote
0
answers
23
views
Definition of a 'design adaptive' fit?
When studying non-parametric regression, I've been told that local linear fitting is often better than local constant fitting at the job of estimating regression functions because local linear fitting ...
- 233
0
votes
0
answers
101
views
Nonlinear regression: improving parameter estimates
I'm running a nonlinear regression to estimate $\delta$ and $\alpha$ using the following model, where $X$, $Y$ and $Z$ are the variables:
\begin{equation}
Z = \left(\delta X^\alpha+(1-\delta)Y^\alpha\...
- 161
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
$$
y_i = \theta_i + \varepsilon_i\, \text{ where }\varepsilon_i \text{ are i.i.d } \sim N(0, \sigma^2)...
- 702
5
votes
1
answer
362
views
Nonparametric estimation of regression function: kernel estimation vs series estimation
I am working on a small research project trying to estimate regression function nonparametrically when I have only one regressor. Basically, I am trying to estimate the regression function
$$r(x)=E[Y∣...
- 578
1
vote
0
answers
43
views
Non-parametric estimation of error distribution in regression
Consider the following model: $y = 1$ if $g(X\beta) + u > 0$ and $y=0$ otherwise where $u$ is $iid$ according to some distribution function $F$. I want to recover the distribution $F$ without ...
- 994
77
votes
15
answers
12k
views
Why would parametric statistics ever be preferred over nonparametric?
Can someone explain to me why would anyone choose a parametric over a nonparametric statistical method for hypothesis testing or regression analysis?
In my mind, it's like going for rafting and ...
- 947
8
votes
1
answer
677
views
Computing inverse probability weights -- conditional (multivariate) density estimation?
The general version:
I need to estimate $f(A | X)$ where $A$ and $X$ are continuous and multivariate. I'd rather do it nonparametrically because I don't have a good functional form in mind and $\hat{...
- 12.8k