# Questions tagged [estimation]

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### Where does the linear regression assumption that the errors are uncorrelated enter into the proof of Gauss Markov and that Least Squares is BLUE?

I often see that the "Spherical Error" assumption is invoked for Gauss Markov. One of the parts of the assumption is that the variance is constant given $X$. The other is usually that the ...
17 views

### Expected magnitude of cosine similarity among $B$ Gaussian vectors?

Take an IID sample of $B$ vectors $x$ drawn from a Gaussian with mean $\mu$ and covariance $\Sigma$. Define the following: $$S=\frac{1}{B^2}\left\|\sum_i^B x_i x_i^T\right\|^2_F$$ $S$ gives the ...
1 vote
17 views

### Why has the admissibility of the Graybill–Deal estimator eluded a proof for so long?

The Graybill–Deal estimator is used to estimate the shared mean of two normals with unknown variances. I understand the literature has proven it is unbiased, but a proof of admissibility has not yet ...
23 views

### 95% Confidence Interval should mean 95% probability that the interval contains the true parameter [closed]

What the image below represents is true. Black intervals belong to samples which properties allow produce CI that contain the true parameter, and purple intervals belong to samples which properties ...
83 views
+50

### Unbiasing estimator of $\|\Sigma\|_F^2$

I have access to samples of some distribution with second-moment matrix $\Sigma=E[xx^T]$ and need an estimate of $\|\Sigma\|_F^2$ (which can be used to set optimal size for LMS) We can use Frobenius ...
34 views

### Can there be any situations where MLE performs better than MPS in terms of MSE or Bias?

Cheng and Amin (1983) proposed the maximum product of spacing estimation method as an alternative to maximum likelihood estimation. They stated that MPS behaves better in small sample cases than MLE ...
1 vote
36 views

### Ratio of first two moments of sample covariance eigenvalues

Suppose we form $X$ by stacking $b$ examples drawn from some distribution in $n$ dimensions as rows and look at $\{\lambda_i\}$, the eigenvalues of $\Sigma=X^TX$. Consider the following random ...
256 views

### How can I fit distribution for data which "almost fits"?

I have a sample for events occurring at certain continuous distances (kilometers), let's suppose emergency calls to hospitals. I have 200k observations, coming from 500 hospitals for an entire month. ...
31 views

### Fixed effects or independent models?

Suppose we are running a model, let's say a linear regression model or a logistic regression. Suppose also that we have gathered data for three cities: City A (4000 surveys), City B (5000 surveys) and ...
25 views

### Can Calder 2022 find boundaries of multiple connected components?

Calder et al. 2022 (version 2) shows an interesting method for estimating the boundary from a point cloud. One of the impressive aspects of this is the algorithm should be able to find non-convex ...
1 vote