Questions tagged [james-stein-estimator]
The james-stein-estimator tag has no summary.
14 questions
1 vote
2 answers
72 views
Are there superefficient statistics that shrink toward the true parameter value, in probability?
Stein (1964) defined a superefficient estimator for the univariate normal variance with population mean unknown. (It's unrelated to James-Stein; see here for a summary.) He gave an indicator variable ...
- 862
1 vote
1 answer
111 views
James-Stein estimators for position in 3D
Say I measure a position in 3D: $(x,y,z)$ and I assume that $X,$ $Y,$ and $Z$ are normally distributed with the same variance (measurement error): $$ X \sim N(\mu_X,\sigma) $$ $$ Y \sim N(\mu_Y,\sigma)...
3 votes
1 answer
307 views
Sample mean or James-Stein estimator?
I have a simple practical question, which I posted in Quant Finance SE (posting here as well, as I am not getting an answer(s) for it). Suppose we have $n\geq3$ financial time series (correlated or ...
- 559
13 votes
2 answers
1k views
If OLS estimator minimizes MSE, how does James-Stein Estimator achieve a lower MSE?
OLS estimator solves the following minimization problem: $$\min ||y-X\beta||^2.$$ By taking the FOC, we obtain $\hat{\beta}$, which minimizes the objective function. But the James-Stein estimator ...
- 183
5 votes
1 answer
256 views
What is the expected value of $X_i/\|X\|^2$ when $X \sim \mathcal{N}(\mu, \sigma^2I)$
Let $X$ be an N-dimensional normal random vector with non-zero mean $\mu$ and diagonal covariance matrix $\sigma^2I$. I would like to understand if it is possible to derive the expected value of the ...
- 334
1 vote
0 answers
136 views
Distribution of James-Stein estimator
For reference, I'm working with something like $${\mathbf Y} \sim N_d({\boldsymbol \mu}, \sigma^2 I)$$ We can estimate $\boldsymbol\mu$ using the JSE $$ \widehat{\boldsymbol \theta}_{JS} = \left( 1 - ...
- 148
1 vote
0 answers
130 views
Can we choose any arbitrary vector to “shrink” towards for the James-Stein Estimator?
My understanding of the James-Stein estimator is that the choice of the origin as the point to shrink towards is more for neatness than anything else, and that the estimator still dominates MLE for ...
- 31