Questions tagged [estimators]
A rule for calculating an estimate of a given quantity based on observed data [Wikipedia].
870
questions
0
votes
1
answer
76
views
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\...
0
votes
0
answers
27
views
One off the advantages of the bootstrap is that i don't have to worry about having a good estimator?
I'm learning about the theory of estimators and saw that sometimes the analytical formula of the estimator has to be diferent off the formula for the parameter, for example the standart deviation, and ...
1
vote
0
answers
33
views
Large samples property of bayes procedures
I was reading through Wasserman's All of Statistics and I came across this property in the Bayesian statistics chapter:
I think I don't really get what is supposed to be the intuition behind it, and ...
- 41
3
votes
1
answer
149
views
Is the sample mean an unbiased estimator of population mean in the presence of autocorrelation?
I've seen previous questions here that the sample mean can be considered an unbiased estimator of the population mean. e.g.1, 2.
While the examples seem to refer to independent sample points, it seems ...
- 539
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
1
answer
119
views
Difference between consistent and unbiased estimator [duplicate]
I have a problem where I have to think of an example to explain a practical example of consistency and unbiased. The example I thought of is the sample mean.
Consistency is when the estimator (sample ...
0
votes
0
answers
29
views
How to derive the (partial) maximum likelihood estimator for a simple autoregressive model
I am trying to derive two maximum likelihood estimators which I have seen in a statistics book, but I am unable to derive them and would really like some help.
It goes like this:
Consider the simple ...
- 65
1
vote
1
answer
218
views
Is convergence in probability implied by consistency of an estimator?
Every definition of consistency I see mentions something convergence in probability-like in its explanation.
From Wikipedia's definition of consistent estimators:
having the property that as the ...
0
votes
0
answers
10
views
Variations of Correlation Coefficient of Simple Linear Regression with Estimators [duplicate]
Suppose we are using an Ordinary Least Squares (OLS) estimator of $\alpha_{0}$ and $\alpha_{1}$ for the simple linear regression below:
$$
H_{i} = \alpha_{0} + \alpha_{1}X_{i} + \epsilon_{i}
$$
How ...
4
votes
1
answer
186
views
Is it more correct to say "bias of the standard error of the estimator" or "bias of the standard error of the estimate"
I understand an estimator is a "rule" (e.g., a function, say $g$) that produces an estimate ($\hat\theta$) of an estimand (say, a population parameter, $\theta$).
My question: is it ...
1
vote
1
answer
69
views
Does increasing number of observations lead to the decreasing of Mean Square Error of consistent estimators?
I know that not all weakly consistent estimators exhibit MSE-consistency : https://stats.stackexchange.com/a/610835/397467.
Anyway, does increasing the sample size leads to a reduction in their mean ...
- 11
0
votes
0
answers
44
views
How to compute the FGLS estimator for simulated data in Matlab (or any other language really)?
first time posting here so please let me know if I can improve my question.
As an exercise, I have to simulate 1000 iterations of a sample of 500 observations from a linear model:
$$ y_i = \beta_0 + \...
- 1
3
votes
1
answer
52
views
Properties of statistical estimators when data is a collection of estimates
Assume I have a statistical estimator $\theta$ that has nice properties (say, unbiased and consistent) when the data $Y=\{y_1,y_2,\dots,y_n\}$ is i.i.d. (possibly with additional assumptions). But now,...
- 213
3
votes
1
answer
166
views
How does Huber compute the $\operatorname{var}(s_n)/E[s_n]^2$ and $\operatorname{var}(d_n)/E[d_n]^2$?
(N.B. I am cross posting this question from math stackexchange since after
x days I have still not received any responses.)
How does Huber in book 'Robust statistical procedures' in chapter 1 compute ...
- 31
0
votes
0
answers
27
views
How to know errorbars on accuracy to nonlinear fit: $A(1-\cos(x+\phi))$ with poisson noise?
I am trying to write some code that accurately estimates the parameters for the following function:
$$ Y = A(1-V \cos(X+\phi)) $$,
where this output data is poisson distributed.
To do this, I first ...
- 486