All Questions
Tagged with estimators distributions
35
questions
1
vote
0
answers
39
views
Calculating the mean and error for correlated measurements involving different estimators and quantiles
My goal is to find a way to report a mean $\pm$ error for different estimators and quantiles of the same distribution (same measurement).
I am measuring the width of a distribution (Gaussian core and ...
- 21
2
votes
0
answers
21
views
When are mean and variance estimates uncorrelated or independent
I know that in the case of the normal distribution, the MLE estimates of the mean and the variance are independent. My impression is that this is a rare property for a distribution to have. Are there ...
- 121
1
vote
0
answers
120
views
Distribution of $F_n^{-1}(3/4)-F_n^{-1}(1/4)$ [closed]
Given $X_1,X_2,...X_n\overset{\text{iid}}{\sim}F$, find the distribution of the sample inter quartile range, $F_n^{-1}(3/4)-F_n^{-1}(1/4)$ in terms of $F$ where, $F_n$ is the emperical distribution ...
- 385
4
votes
1
answer
109
views
Probability mass function of sample median (Bootstrap)
Consider a sample $X_1,X_2,...X_n\overset{\text{iid}}{\sim}F$. Let $T_n=F_n^{-1}(1/2)$ be the sample median where, $F^{-1}(x)=\inf\{t:F(t)\ge x\}$ and $F_n(y)=\frac{1}{n}\sum_{i=1}^n\mathbb{I}(X_i\le ...
- 385
2
votes
1
answer
86
views
Maximum Likelihood Estimation for a Unique Probability Density Function
In the context of estimating parameters for a uniquely distributed set of independent and identically distributed random variables, I am examining the following probability density function $ f(x|\...
- 425
0
votes
0
answers
21
views
How to show that the influence function of minimum density power divergence estimator with positive tuning parameter is bounded?
In the linked paper, in the influence function section, the term ${u_{\theta}(y)}{f_{\theta}(y)}^\alpha$ is directly called bounded which i do not get the explanation of? Here $\alpha > 0$ is the ...
1
vote
1
answer
46
views
Way of estimating the parameters of a distribution that encourages samples not to try to game the system?
There is a distribution $D(\theta)$, where $\theta$ represents the parameters of the distribution. To sample from the distribution, a bunch of people are called to give their samples $x_1, \ldots, x_n$...
- 421
1
vote
0
answers
156
views
Influence Function of M-Estimator
I know the following influence function for a M-Estimator:
$IF(x_0,T,F_0)= $ $\frac{\psi(x_0)}{\mathbb{E}_{F_0}[\psi'(X)]}$
where $F_0$ is the centered model ($F_{\theta}(x)=F_0(x-\theta)$)
I am ...
10
votes
5
answers
2k
views
How do we know the true value of a parameter, in order to check estimator properties?
For example, we say that an estimator is unbiased if the expected value of the estimator is the true value of the parameter we're trying to estimate. However, if we already know the true value of the ...
- 103
2
votes
1
answer
49
views
What is this type of data called?
An event occurs once per period, such as once per year. Time is measured in discrete units, such as days of the year. Let $A_y$ be the day in year $y$ on which this event occurs. However, we do not ...
- 1,251
2
votes
1
answer
289
views
Hypothesis testing for detecting signal in Gaussian noise
I have the following two hypotheses:
$\hspace{5cm}\mathcal{H}_0: y=w\\\hspace{5cm}\mathcal{H}_1: y=\sum_{i=1}^{N}h_ix_i+w$
Here $w\sim \mathcal{N}(0,1)$ represents Gaussian noise. $x_i \sim Bern(p), \...
- 214
1
vote
1
answer
2k
views
How to fit Weibull distribution using "MME" method and find the estimates in R [closed]
I am trying to fit a Weibull distribution using Moments Matching Estimation (MME) method. Specifically I am trying to estimate the shape parameter $k$ and the
scale $\lambda$.
I am currently using R ...
- 175
3
votes
0
answers
91
views
What is the estimate of $\mathrm{Var}\left(\frac{nM}{X}\right)$ where $X$ is hypergeometric?
Consider the classical capture-recapture method, where we are to estimate the number of deer (say) in a sanctuary. So a certain number of deer is captured, tagged and released. Then a random sample is ...
- 11.5k
3
votes
0
answers
78
views
Are a distribution's higher-order features harder to estimate?
In what sense, if any, are a distribution's higher-order features (e.g., moments, cumulants) harder to estimate than its lower-order features, for at least some distributional families?
For example, ...
- 416
0
votes
1
answer
67
views
quantifying asymmetry on a sphere
I have a scalar quantity that is distributed on a sphere. I would like to quantify the asymmetry in this scalar field. is there any standard method to do this?
Let's say that the function on the ...
- 119