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Tagged with least-squares pr.probability
4 questions
3
votes
1
answer
379
views
Concentration inequality for norm of solution to nonlinear least-squares problem
Define the piecewise-linear function $\psi(t):=\max(t,0)$ for all $t \in \mathbb R$.
Let $d,n,k \to \infty$ at the same rate (i.e $n \asymp k \asymp d$).
Let $y_1,\ldots,y_n \in \{-1,1\}$ uniformly ...
2
votes
2
answers
106
views
Non-parametric regression and curvature
Given a finite set of points $(x_1, y_1), (x_2, y_2), \ldots, (x_n, y_n)$ in the plane, Linear Regression tells us how to find the straight line "$y=a+bx$" best approximating the given points, in the ...
1
vote
1
answer
170
views
Minimization Proof of Conditioning on Gaussian is Gaussian
It is well known that $E[X|X+Y]$ is Gaussian if both $X$ and $Y$ are, and the result can be derived using standard density arguments. However, how can one prove it by only resulting to optimization ...
1
vote
1
answer
138
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MSE of measurable function is still conditional expectation
Motivation
Then the usual stochastic filtering problem says that:
$$
\operatorname{argmin}_{Z \in L^2(\mathscr{G}_t)}\,\mathbb{E}[(Y_t-Z_t)^2],
$$
where $\mathscr{G}_t$ is the $\sigma$-algebra ...