# Questions tagged [mean-square-error]

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.

152 questions
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### Finding estimator that minimizes the weighted mean-square error

I have continuous multivariate random variable $x$ in $R^n$ with known prior $p(x)$ over the latent random variable. I observe $z$ and want to come up with a estimator for $x$ that minimizes the ...
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### What's the intuitive purpose of RMSE (root mean square error) compared to MAE (mean average error)?

When I want to find out what the average difference / error there is between two datasets, such as a predicted output vs. observed output of any system (i.e.: I predict output to be 100V, how does the ...
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### Given the Laplace transform of a function $f(t)$, can I find the “total squared error” $\int_0^\infty f(t)^2\ dt$?

I'm modeling the behavior of an aircraft using ordinary differential equations. I've written an equation for the angle of attack $\alpha(t)$, and then taken the Laplace transform of this equation to ...
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### Normalise the root mean square error

I have $10$ people in a group and they undergone a surgery. I have the root mean square of each subject before and after the surgery. ...
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### MSE Minimized by Mean

In the Gaussian case, it is well-known that the MSE, is minimizer by the mean value. However, in general, if $X \in L^2(\mathcal{F};\mathbb{P})$, is a random-variable in $\mathbb{R}$, then is the ...
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### Determine the value of $α$ for which the $MSE(T)$ is minimal.

Let $X_1$ be an estimator for the probability $θ$ of unauthorized access. Let $X_2$ be another estimator for $θ$. Assume that $X_1$ and $X_2$ are independent, unbiased estimators for $θ$. ...
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### How to quantify the confidence on a Bayesian posterior probability?

Consider a physical system that depends on a parameter $0\leq \phi <\infty$. I want to (i) find the probability that this parameter is smaller than a critical value: $\phi\leq \phi_c$, and (ii) ...
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### Check if the estimator is unbiased

For $X_i\sim U[0,a]$ where $i=1,2,\dots,n$ so, $E(X_i)=\dfrac a2$. Is $a'=\max\{X_1,X_2,\dots,X_n\}$ an unbiased estimator of $a$? This is what I thought. Since $a'=\max\{X_1,X_2,\dots,X_n\}=X_k$ ...
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### Relationship between covariance eigenvalues and MSE

I have a matrix $A$, and $\tilde{A}$ is the approximation matrix calculated as the projection of $A$. Now I calculated the MSE between $A$ and $\tilde{A}$, and the $C$ as the covariance matrix of $A$. ...
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### What does this notation in minimal square error mean?

My book defines minimal square error as: $$MSE(\theta, T) = E_\theta\Vert T - \theta \Vert^2$$ What does the $E_\theta$ mean? Is it an expectation? If yes, what does the theta supscript do there?
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### What is best way to represent this false +ve error to reflect original scenario?

My aim is to represent false +ve error in a better way. I have 500 samples. Each samples contains some distinct values (there exists total 16 distinct values). Ideally, a sample should contain any 4 ...
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### Finding the sample size given bound of error and standard deviation.

The personnel manager wants to determine if there is a difference in the average time lost due to absenteeism between two plants. From historical data, the estimated standard deviations of lost time ...
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### Introduction Mathematical Statistics, finding the Mean Square Error of estimators

I'm working on a problem from my introduction to mathematical statistics course. So far, I've done the following work: Let $X_{1},...,X_{m}$ and $Y_{1},...,Y_{n}$ be independent samples form the ...
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### MSE of the MME of $\theta$

A random sample of size $n$ is taken from a gamma distribution with parameters $α = 8$and $λ = 1/θ$. The sample mean is $\bar{x}$ and $θ$ is to be estimated. Determine the mean square error of the ...
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### Incremental (“online”) computation of the root-mean-squared-error (RMSE) for a linear regression

I've been able to calculate a least squares linear regression's slope incrementally. (https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Covariance shows one-pass "online" methods for ...
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### Minimum mean squared error of uniform distribution

Let $X_1,X_2,\ldots,X_n$ be i.i.d $\operatorname{Uniform}(-\theta,0)$. Now consider all of the estimates of the form $S_\rho=\rho \hat{\theta}_\text{MLE}$. I have to find which of these estimates has ...
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How do we use Jensen's inequality to prove that $\operatorname E(T_2-\theta)^2 < \operatorname E(T_1-\theta)^2$, where $\theta$ is an unknown constant, $T_1$ is an estimator for $\theta$, and $T_2 =... 0answers 78 views ### Time Series Mean Square Convergence with given acvf Let$(X_t)_{t\in \mathbb{Z}}$be a stationary time series with$E[X_t]=0$and acvf$\gamma(h)={1}_{0}(h)+\rho1_{h \ne0}(h)$with$\rho \in (0,1)$. Show that$\frac{1}{n}\sum_{j=1}^nX_{-j}$... 1answer 155 views ### Derivation of complex number for Linear MSE estimator Given a system $$y = h x + n$$ where$x$is unknown to estimate,$y$is observed data,$h$is known,$n \sim \mathcal{N}(0,\sigma^2)$. They are complex numbers. I am trying to prove the linear ... 0answers 61 views ### For$X_i\sim N(\mu,\sigma^2)$, how to find the MSE of estimator:$\hat \sigma^2 = \frac 1{n+2}\sum_{i=1}^nX_i^2$. This is part of a larger problem. I have already found the MSE of two other estimators:$\hat\sigma_1^2 = \frac1{n-1}\sum_i^n (X_i-\bar X)^2$and$\hat\sigma_2^2 = \frac1{n+1}\sum_i^n (X_i-\bar X)^2\$. ...
I am trying to run a simple regression $$Y = a+bX +e$$ however I want to optimize it on Mean Square Percentage Error and not Mean Square Error as in OLS. Like this: $$argmin: e/Y = (Y-a-bX)/Y$$ ...