Questions tagged [estimators]
A rule for calculating an estimate of a given quantity based on observed data [Wikipedia].
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Intuition behind between-group covariance matrix from MANOVA?
Suppose that we have samples from $m$ different $p$-dimensional normal multivariate distributions, where they share a common covariance matrix $\Sigma$ but the mean vectors may be different for each ...
- 69
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Why does not this underlying hypergeometric distribution lead to unbiased estimators?
This example is take from Lippman's "Elements of probability and statistics".
Let N be the number of fish in a lake the warden wants to estimate. He catches 100 fish, tags them and releases ...
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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
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Adjusted R2 and bias
Consider the population $R^2$:
\begin{equation}
\rho^2 = 1- \frac{\sigma^{2}_u}{\sigma^{2}_y}
\end{equation}
This equation describes the proportion of the variation in $y$ in the population explained ...
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What's the difference and relationship between theta, theta star and theta hat?
I understand that $\theta$ is the true distribution parameter (great explanation here). I also know that $\hat\theta$ is an estimator of the true $\theta$ (so for example, MLE is an example of $\hat\...
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Is an estimator that always have a value of zero is a linear estimator?
Consider a simple linear regression model:
$$Y=\beta_0+\beta_1 X +u$$
Here, we can consider an estimator that does not use any data:
$$\hat{\beta}_1=0$$
That is, regardless of the observed data, the ...
- 401
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57
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What is a measure of hardness-of-approximation by samples?
Suppose there is a large vector $\mathbf{x}$ of real numbers, and I want to estimate a certain aggregate function $f(\mathbf{x})$ by taking a small sample of the population $\mathbf{x}$. I would like ...
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Optimality criterion for mean estimators
Assume a sample size of $n>5$, a given variance $\sigma^2 > 0$ and a $\delta \in (2e^{-n/4}, 1/2)$.
Proof that there exists a distribution with variance $\sigma^2$ such that for any mean ...
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For a biased estimator, how does one call the point for which the expected value of the estimator is equal to the observed sample estimate? [closed]
Let $\hat{\theta}$ be a biased estimator whose bias depends on the true value $\theta_0$, such that $E[\hat\theta|\theta_0]= f(\theta_0)\neq \theta_0$. Let $t_{sample}$ be a sample realization of $\...
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Showing that the estimator of the log posterior used in stochastic gradient MCMC is unbiased
In the SGLD paper as well as in this paper it is claimed (paraphrasing) that
the following estimator:
$$\widetilde{U}(\theta) = -\dfrac{|\mathcal{S}|}{|\widetilde{\mathcal{S}}|} \sum_{{x}\in \...
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Confidence interval on ratio of estimates for exponential random variables
Given exponential random variable X, the MLE for the scale parameter is $\hat{\beta_x} = \bar{x}$, and the confidence interval for that estimate is:
$$\frac{2n\bar{x}}{\chi^2_{\frac{\alpha}{2},2n}} &...
- 1,162
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What is the variance decomposition method?
For $i = 1, \ldots, m$ and $j = 1, \ldots , n$ we have observations $x_{ij}$. We can assume that
$$
x_{ij} = y_{i} + z_{ij}, \qquad y_{i} \sim \mathcal{N}(\mu_{y},\sigma_{y}^{2}), \quad z_{ij} \sim \...
- 101
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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|\...
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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 ...
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Mathematical Step for consistency
Let me state my problem from the beginning:
Let $i$ be an index representing countries ($i = {1,2,\ldots,N }$), and $t$ represent time, denoted as available data for country $i$ ($t = {1,2,\ldots,T_i }...
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