Questions tagged [estimators]
A rule for calculating an estimate of a given quantity based on observed data [Wikipedia].
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Model has higher (and closer to 1) $\beta$, but similar $R^2$ and correlation
I have model one which produces prediction $\hat{y_1}$, later I came up with a new model which produces prediction $\hat{y_2}$. I have ground truth $y$. The models are not regression based but they ...
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variance of the estimator of unconditional mean of AR(1) process
AR(1) process is defined as: $y_t=c+\phi y_{t-1}+\varepsilon_t$ where $\varepsilon_t$ is IID with mean zero and variance $\sigma^2<\infty$. For a stationary process, i.e. $\phi\ne 0$, the ...
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Combining information from different quantiles
I have a number of "mostly" Gaussian distributions (in truth a Gauss core and longer tails). I am interested in the width of this distributions.
Given that I do not know the amount of tails ...
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Sum of asymptotically independent random variables - Convergence
Let $\theta_N=\frac{1}{N}\sum_{i=1}^N \pi_i\cdot g_i$ where $0<\pi_i<1$ and $0<g_i<1/\pi_i$ such that $\theta_N\overset{N\rightarrow \infty}{\rightarrow}\theta$.
If $X_i\sim Ber(\pi_i)$, I ...
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How to get an unbiased estimator
Defining the sample mean as $\bar{x} = \frac{1}{N}\sum_{n=0}^{N-1}x_n$, and having $N$ realizations of a random variable $x$ with mean $\mu$ and variance $\sigma^2$
Defining $\bar{x}^2=\hat{\mu^2}$, ...
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Confidence interval on ratio of estimates for exponential random variables
Given exponential random variable X, the MLE for the scale parameter is $\hat{\beta_x} = \bar{x}$, and the confidence interval for that estimate is:
$$\frac{2n\bar{x}}{\chi^2_{\frac{\alpha}{2},2n}} &...
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Are all random variables estimators? [duplicate]
My hand-wavey understanding is a random variable is a function from a domain of possible outcomes in a sample space to a measurable space valued in real numbers.
We might denote a random variable from ...
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confidence intervals for proportions containing a theoretically impossible value (zero)
This is really a hypothetical question not related to an actual issue I have, so this question is just out of curiosity. I'm aware of this other related question What should I do when a confidence ...
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No Existence of Efficient estimator
I need to prove that given $(X_1,...,X_n)$ from the density $$\frac{1}{\theta}x^{\frac{1}{\theta}-1}1_{(0,1)}$$ no efficient estimator exists for $g(\theta)$=$\frac{1}{{\theta}+1}$.
I have shown that ...
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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-...
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How to accurately estimate the probability of a rare event in a large dataset?
I have a dataset of 30,155 names and out of curiosity I verified that the longest name has 68 characters, which is quite big considering the mean and SD were 24.78 and 5.64, respectively. Based on ...
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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 ...
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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 ...
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Unbiased and consistent estimator with positive sampling variance as n approaches infinity? (Aronow & Miller) [duplicate]
In Aronow & Miller, "Foundations of Agnostic Statistics", the authors write on p105:
[A]lthough unbiased estimators are not necessarily consistent, any unbiased estimator $\widehat{\...
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Why don't asymptotically consistent estimators have zero variance at infinity?
I know that the statement in question is wrong because estimators cannot have asymptotic variances that are lower than the Cramer-Rao bound.
However, if being asymptotic consistent means that an ...
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