# Tagged Questions

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### Non-linear least squares with two dependent variables

I have data in the form $(t_i,x_i,y_i)$, i.e. position in 2D as a function of time. I have non-linear equations which I want to fit to the data. They give me a position $(X,Y)$ as a function of time ...
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### Strong duality in trace maximization

I'm working on understanding the derivation of the solution for principal components analysis. Let $\mathbf{S} \in \mathbb{R}^{p \times p}$ be a positive semi-definite matrix with rank $d < p$. ...
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I am trying to understand an example in my stats course notes, the example relates to calculating the best value for the next experiment. The function of the line is very simple: $$ln(Y_i) = ... 0answers 109 views ### Solving for Analytical Maximum Likelihood Estimate Parameters I have a statistical model whose parameters I would like to find a closed form maximum likelihood estimate for if possible. There are two parameters and I can solve for one, but the second is a bit ... 1answer 277 views ### Generating a random monotonically increasing polynomial? Given a polynomial y : \mathbb{R} \mapsto \mathbb{R} of degree p:$$ y(x) = \sum_{k=0}^p c_k\, x^k, can a random set of coefficients $\{c_0, \cdots ,c_p\}$ be generated such that $y$ is ...
Here is a convex programming problem I encountered while working on an estimation problem for a mixture of multinomial distributions. We have a matrix $A_{m \times n}$ containing non-negative real ...
$X=\{x_{i}\}$ and $Y=\{y_{i}\}$ are numeric samples: $y_i \ge 0, x_i \ge 0, i \in [0..N]$. I need to find the mapping $F(X)=\{F(x_i)\}$ with fairly simple formula such that: Euclidean distance ...