Questions tagged [estimators]
A rule for calculating an estimate of a given quantity based on observed data [Wikipedia].
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Difference in differences to estimate differential impact of treatment?
I'm having some trouble thinking through the implementation of difference-in-differences / if DD is the best approach to use when I am comparing two groups who are both treated, but which I ...
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Estimators vs. Sequence of Estimators: Clarifying Definitions
Many times I've read that the following expresion $(x_1+x_2+...+x_n)/n$ is an estimator of the population mean. I also read, for example here: that the previous expresion defines a sequence of ...
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What is the minimum number of data points/observations required to use Theil-Sen?
I am working on an algorithm which requires estimating trend magnitudes of data points. I have been told to use Theil-Sen as it is more robust to outliers and it is non-parametric. As users will be ...
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Estimating ratio of regression coefficients
What is the best method of estimating a ratio of regression coefficients $\beta_1/\beta_2$ under the usual assumptions / in practice? I have two relatively well approximated signals $X_1, X_2$ and ...
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Validating Parameterized Std Deviation Estimator
I'm looking to estimate the size of the intersection between two sets, $A$ & $B$
I have a function to estimate this ($\verb|est_set_intersect_size|(A, B)$) that purports to have a standard ...
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Tossing Until First Heads Outcome, and Repeating, as a Method for Estimating Probability of Heads
Consider the problem of estimating the heads probability $p$ of a coin
by tossing it until the first heads outcome is observed. Say we get $k_1$
tosses, then $U_1 = \frac{1}{k_1}$ is an estimate for $...
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Finding the Variance of the MLE Variance of a Joint Normal Distribution
I have a random sampling of $Z_1,...Z_n$ from a normal distribution $N(\mu,\sigma^{2})$. I am considering them within a joint likelihood function.
I know that the MLE ($\hat\sigma^{2}$) of $\sigma^{2}$...
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How to illustrate the validity of bootstrap with monte carlo simulation?
Suppose I have a random sample $S_n=\{W_i\}_{i=1}^n$ where $W_i\sim F $, and I have an estimator $\widehat{\beta}$ computed using this sample. I want to illustrate that the bootstrap approximation ...
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Combining two success runs in parallel
The goal is to calculate the reliability of a process. Here reliability is defined as follows:
Definitions and tests I used
Let $X$ be a random variable that is equal to $1$ when no defect is present ...
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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 \...
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Best estimate of conditional probability P(C|A and B) from P(C|A) and P(C|B)?
Assume I have three events A, B, and C, and I know the following probabilities:
Scenario 1:
$P(A)$ and $P(B)$
$P(C|A)$ and $P(C|B)$
Scenario 2:
I additionally know $P(C)$.
I am looking for $P(C|A\...
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Curve fitting: Scaling the sigmas so that the reduced chi-squared statistic = 1. Is this a good heuristic?
In the official documentation for the python function scipy.optimize.curve_fit, the following description is given for a boolean-typed parameter absolute_sigma.
If False (default), only the relative ...
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Cramer-Rao lower bound for the variance of unbiased estimators of $\theta = \frac{\mu}{\sigma}$
Let $X_1, \cdots, X_n$ be a sample from the $N(\mu, \sigma^2)$ density, where $\mu, \sigma^2$ are unknown.
I want to find a lower bound $L_n$ which is valid for all sample-sizes $n$ for the variance ...
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Hierarchical models: Estimating variance and combining two estimators
Assume that $y_i \sim N(50,10)$.
I observe a signal with additive Gaussian noise $s_i \sim N(y_i, \sigma_d^2)$
I observe $n$ such signals, each corresponding to a different $y_i$.
I want to estimate $\...
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Bayesian Learning: Finding the variance of noise
Suppose $x_i \sim N(10,4)$ - ie, the distribution is known.
There is a noisy signal $s_i \sim N(x_i, \sigma_e^2)$ and I want to estimate $\sigma_e$.
I see some pairs ($s_i, x_i$) but they are not '...
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