Tagged Questions

This tag is for questions about mean-square-error. In statistics, the mean squared error (MSE) of an estimator measures the average of the squares of the errors or deviations, that is, the difference between the estimator and what is estimated.

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How to perform OLS on multivariate cointegration model?

So, I'm not too much of an expert in time series but here it goes ... Suppose there are time series X, Y, Z and the linear combination for some yet-unknown constants a,b,c of aX + bY + cZ forms a ...
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Find the variance and mean squared error of $T=\max(X_1, X_2, …, X_n)$

Let $X_1, X_2, ..., X_n$ be i.i.d. uniformly distributed on [$0, \theta$]. Consider the estimator $T=\max(X_1, X_2, ..., X_n)$ of $\theta$. Determine the variance and mean square error of $T$. My ...
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minimization problem: finding smallest deltas that satisfy equation.

After long derivations to find a better backpropagation algorithm for neural networks, I got this elegant optimization problem. Index $i=1..n$ given constants $c_i \in R, w_i \in R$ variables to ...
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Analysing error in Multiple Regression Analysis. [closed]

Hello everybody, I have the following multiple linear regression model LN(Number_of_person_in_househol)=1.514-0.13(Age_of_respondent)+0.486 (Married_PEOPLE)+0.25(Higestyearofschoolcompleted)+.097(...
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Error in average of $x^2$ from error in average of $x$?

Is there an easy way to obtain the error in $\langle{x^2}\rangle$ from $\langle{x}\rangle$ or are they independent? The values of x are from a molecular simulation application, I obtained a set of ...
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Number of measurements for least squares and relation to maximum likelihood

I have a simple overdetermined system of equations: $$y = Xc + e$$ $y, e \in \mathbb{R}^n$, $c \in \mathbb{R}^m$, $X \in \mathbb{R}^{n \times m}$, $e \sim \mathcal{N}(o,\sigma^2)$, $n>>m$ ...
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Root Mean Square Error - How did he get this number?

So I am studying for a college final exam, and following a past exam paper at the moment. The lecturer has provided us with solutions to the previous years exam paper, not very clear in some cases ...
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PCA: MSE of projecting a set of points to a subspace

Let $\{x_1,\dots,x_n\}$ be a dataset of n vectors in $\mathbb{R}^d$ s.t. $\sum_{i=1}^n x_i = 0$. Let $p_1, \dots, p_k$ be a set of k orthonormal unit vectors and V the subspace that they span. Given ...
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Is $Φ^T$ a linear operator which transforms simultaneous equations such that we obtain LMS solution?

The below explanation is long winded, if you already know about using pseudo inverse to find the best fit solution to a set of simultaneous equations please go down to the tl;dr The Problem Given a ...
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Absolute and relative errors

I am trying to compare two regression models, say $A$ and $B$ and calculate the absolute error measure (MAE, RMSE) and relative ones. But it turns out that both the absolute measures for $A$ are ...
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error calculation when the error is not constant

I have to calculate the error on the following quantity: $$f(\epsilon^M,\epsilon^S)= \sqrt{ \frac{1}{N}\sum_{i=1}^N (\log{\epsilon_i^M} - \log{\epsilon_i^S})^2 }$$ Usually I would use this standard ...
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How to find the bias, variance and MSE of $\hat p$?

If $X_1,\dots,X_n$ are iid $\mathrm{Binomial}(3,p)$, then the maximum likelihood estimator of $p$ is $$\hat p = \frac{1}{n}\sum_i X_i$$ Find the bias, variance and MSE of $\hat p$? We are asked to ...
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Standard error of RMSE?

If I want to calculate the RMSE between an estimated value $\hat{x}$ and its reference value $x_{\textrm{ref}}$, let $$y_i = \hat{x}_i-x_{i,\textrm{ref}}$$ Since \begin{...
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Finding a relative error measure on a data set proportional to another

I have a set of exact data points $\mathcal{X}=\{X_i\}$ and another approximate one $\mathcal{Y}=\{Y_i\}$ where there is a correspondence between $X_i$ and $Y_i$ for all $i$. If $\mathcal{Y}$ was ...
How do I find the best linear predictor of $X_{n+1}$ in terms of $X_{n-1}, X_n$, if $X_t$ is the MA(1) model $X_t = Z_t + \theta Z_{t−1}$.