All Questions
Tagged with estimators estimation
130
questions
0
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0
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41
views
Unbiased Estimator of Nugget Effect
Question: I am trying the measure the nugget effect, which is parameterized by $(1-\lambda)$ in the following variance-covariance used to describe the multivariate normal distribution of my n-...
- 385
4
votes
2
answers
124
views
Must maximum likelihood method be applied on a simple random sample or on a realisation?
I guess my trouble is not a big one but here it is: when one applies maximum likelihood, he considers the realization $(x_1, \dots, x_n)$ of a simple random sample (SRS), leading to ML Estimates. But ...
- 250
1
vote
1
answer
34
views
Why can we get better asymptotic global estimators even for IID random variables?
Let $X_1,...,X_N$ be IID random variables sampled from a parametrised distribution $p_\theta$, and suppose my goal is to retrieve $\theta$ from these samples.
We know that the MLE provides an ...
- 383
4
votes
1
answer
115
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Verifying mean and covariance estimators of a two-dimensional normal distribution
Here I try to verify estimators of the mean and covariance matrix of the two-dimensional normal distribution $N(\mu, A)$ with $\mu=[-2,3]^T$ and $A=\begin{pmatrix}
5 & 11\\
11 & 25
\end{...
- 173
0
votes
1
answer
76
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Unable to estimate AR(p) coefficients and $\sigma^2$
I am currently trying to solve this problem pertaining to the Yule-Walker equations:
Let $\{X_t\}_{t\in Z}$ be a causal autoregressive process given by $$X_t = \varphi X_{t−2} +W_t$$ with $\{W_t\}_{t\...
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
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116
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Cramer-Rao bound (CRB) and Root-Mean-Square-Error / Mean-Square-Error (RMSE / MSE)
My question is regarding the comparison between the CRB of a given vector parameter and RMSE/MSE obtained from Monte-Carlo (MC) simulation. The approach I used is this:
For $\boldsymbol{\theta} \in \...
- 121
2
votes
0
answers
61
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Is there a theory of M-Estimation for non-unique argmins?
Given some i.i.d. random variables $x_1,\ldots,x_n\in\mathbb R^d$, an M-estimator $\hat\theta_n\in\mathbb R^p$ is a parameter which minimizes
$$\hat\theta_n=\arg\min_{\theta\in\Theta} \sum_{i=1}^n\...
1
vote
1
answer
46
views
Way of estimating the parameters of a distribution that encourages samples not to try to game the system?
There is a distribution $D(\theta)$, where $\theta$ represents the parameters of the distribution. To sample from the distribution, a bunch of people are called to give their samples $x_1, \ldots, x_n$...
- 421
2
votes
1
answer
87
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Example when globally unbiased estimator does not exist while locally unbiased estimator exists?
The locally unbiased(l.u.) estimator $\hat{\theta}\left( x \right)$, with $x$ stands for the experiment result, refers to the estimator that satisfies(see Eq(5) of this paper for multiparameter case) $...
- 187
7
votes
1
answer
197
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Let $X_1,\dots, X_n$ be random sample from $Bernoulli(p)$. Which estimator is better?
Let $X_1,\dots, X_n$ be random sample from $Bernoulli(p)$. Compare the risks of the squared loss of two estimators of $p$:
$$
\hat{p}_1=\bar{X}, \, \hat{p}_2=\frac{n\bar{X}+\alpha}{\alpha+\beta+n}
$$...
- 747
0
votes
0
answers
85
views
Estimator for the propensity for consumption c = C/Y
I've an exercise where it asks to propose an estimator for the propensity for consumption: $c = C/Y$ where $C$ is the consume and $Y$ is the income.
Since the consumption function $C = c_0 + c_1 Y$ is ...
- 83
4
votes
3
answers
941
views
Variance estimation for small sample size
The following variance estimator of a set of data points $x = (x_1, ..., x_N)$
$$
\text{Var}\,(x) = \frac{1}{N-1} \sum_{i=1}^N (x_i - \bar{x})^2
$$
has itself a large variance when $N$ is small (in my ...
- 41
5
votes
1
answer
794
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Maximum likelihood vs generalized method of moments
I am trying to understand how maximum likelihood (MLE) and generalized method of moments (GMM) are related to each other. In particular, I often see people saying that MLE can be written in terms of ...
- 133
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20
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What is the expression for covariance in the context of Monte-Carlo estimator? [duplicate]
I am trying to calculate the variance:
$$
\langle(\bar{O}-<O>)^2\rangle
$$
of the Monte-Carlo estimator
$$
\bar{O}=\frac{1}{M}\sum_{m=1}^M{O_m}
$$
For uncorrelated samples.
In order to do so, I ...
- 1