All Questions
Tagged with nonparametric estimation
59
questions
1
vote
1
answer
70
views
How to estimate how heavy a tail is?
Suppose I have data coming from a single variate distribution. I want to estimate how heavy the tail of the distribution is. For example, if the data comes from the Zipf distribution, I would want the ...
- 145
1
vote
0
answers
32
views
Strong consistency of kernel density estimator
I am studying the book Nonparametric and Semiparametric Models written by Wolfgang Hardle and have difficulty with the following exercise:
$\textbf{Exercise 3.13}$ Show that $\hat{f_h}^{(n)}(x) \...
- 111
4
votes
1
answer
178
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
2
votes
0
answers
60
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How to estimate with confidence the quantiles of an unknown random variable using sample mean and variance?
Let $X$ be a uniform distribution of inputs to be used for sampling. Let $f(x)$ be an expensive function. If we take samples from $X$ and give them as input to $f$ we get outputs $y_1, y_2, \ldots, ...
- 41
2
votes
1
answer
150
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What is an explicit formula for the seventh moment? [duplicate]
I am trying to perform an analysis using the seventh moment but I can't seem to find an explicit formula for anything past the fourth moment.
What is an explicit formula for the 7th moment similar to ...
- 161
2
votes
1
answer
39
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Why might the functional form of a distribution be "inappropriate" for a particular application?
Working through Bishop's Pattern Recognition and Machine Learning(a great read so far!) and on page 67 he says:
"One limitation of the parametric approach is that it assumes a specific ...
- 1,617
6
votes
2
answers
296
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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
333
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Is a non-parametric density estimation required for a bimodal distribution?
How to approach the following two cases is clear, I am mentioning them to set up my question.
(Case 1): For data that appears to be a Gaussian distribution, we can assume the distribution is Gaussian ...
- 893
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
2
votes
1
answer
835
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Convergence of kernel density estimate as the sample size grows
Let $X\sim\text{Normal}(0,1)$ and let $f_X$ be its probability density function. I conducted some numerical experiments in the software Mathematica to estimate $f_X$ via a kernel method. Let $\hat{f}...
- 285
3
votes
1
answer
651
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
1
vote
1
answer
160
views
Credibility evaluation - how to model conditional continuous density from multiple variables of various types?
I recently got dataset for 37000 households with declared income and a few dozens of other variables of various types: continuous, discrete, binary.
The task is to automatically (unsupervised) ...
- 421
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
1
answer
571
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Estimating Expected Order Statistics
I have a fairly basic question that I'm looking for a reference for.
First, a couple definitions. Let's say $X_1,\ldots,X_n$ are IID samples from a distribution $F$ over $[0,1]$. For any $k\in\{1,\...
- 1
4
votes
1
answer
1k
views
UMVUE of distribution function $F$ when $X_i\sim F$ are i.i.d random variables
Let $(X_1,X_2,\cdots,X_n)$ be a random sample drawn from a population with distribution function $F$. Is the empirical distribution function $F_n$ the UMVUE of $F$? ( $F$ itself is the parameter of ...
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