A measure of performance of an estimate or prediction, equal to the mean squared difference between the true value and the estimated value.
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72 views
Want to evaluate how uniform my data is?
I have a feature vector of size nx3 where n = no. of data points and no. of features = 3.
So the mean is a 3x1 vector.
The data actually is a set of pixels of an image segment(not a whole image). and ...
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1answer
45 views
Mean squared error definition
I'm currently working through (part of) a textbook on non-parametric regression techniques. Regarding the choice of smoothing parameter the book starts out explaining the MSE which is defined as:
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1answer
79 views
How to show that $E[(\hat\theta -\theta)^2]<Var(\bar X)=\dfrac{1}{n}$?
Suppose $X_1, X_2, \dots, X_n$ are i.i.d $N(\theta, 1),\theta_0 \le \theta \le \theta_1$, where $\theta_0 \lt \theta_1$ are two specified numbers. Find the MLE of $\theta$ and show that it is ...
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25 views
What if the MVUE depends on the parameter?
The minimum variance, unbiased estimator $\hat \theta$ of $\theta$ is defined by
$$\hat \theta = \text{argmin}_{\hat \theta} \; \mathbb{E} \left( (\hat \theta - \theta)^2 \, | \, \theta\right), \quad ...
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76 views
Gauss-Markov theorem: BLUE and OLS
I'm reading up on the Guass-Markov theorem on wikipedia, and I was hoping somebody could help me figure out the main point of the theorem.
We assume a linear model, in matrix form, is given by:
$$ y ...
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44 views
Unbiased estimator of weighted sum of two poisson variables
Suppose that $X_1$ and $X_2$ are two random variables sampled from a Poisson distribution with parameter $\mu$. Let $T_1=\bar{X}$ be the sample mean and let $T_2=(1/3)X_1 +(2/3)X_2$.
Are T1 and T2 ...
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275 views
How to get Standard Deviation from Mean Squared Error
So I've been working on the same question in my homework for days. I've done it over and over and I know I'm doing something wrong. I can't get a straight answer from anybody about it. I just want to ...
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77 views
Automatically choose a bandwidth in R
I have a function that I have added noise to. I want to test a few smoothers, but for each smoother I want to minimise MSE. I know the underlying function, so how can I make R automatically choose the ...
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0answers
71 views
Mean Square Error definition for symmetric models
I want to estimate the parameters of the sum of two complex sinusoids embedded in Gaussian noise:
$y[n]=a_1 {\rm e}^{\,j n \theta_1} + a_2 {\rm e}^{\,j n \theta_2} + w[n]$
where $w[n]\sim {\cal ...
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99 views
MSE of filtered noisy signal - Derivation
I'm working on understanding the derivation of the optimal time constant for filters based on minimizing mean squared error. Unfortunately the text made a big jump between steps and lost me.
Here's ...
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2answers
3k views
What is the “root mse” in stata?
I have a question that has been confusing me ever since I took econometrics last year. What does the "root MSE" mean in stata output when you regress a OLS model?
I know that it translates into "root ...
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2answers
310 views
Confusion regarding correlation and mse
I have a dataset containing three variables. I have this confusion, low mse means higher correlation isn't it? Now when I calculate the mse for variable two and three where the third variable is my ...
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3answers
152 views
Mean square error or mean squared error
As a non-native english speaker I was wondering which of the square or squared expression I should use. For instance in mean square error or mean squared error.
According to the Internet, it seems ...
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4answers
378 views
Is the mean squared error used to assess relative superiority of one estimator over another?
Suppose we have two estimators $\alpha_1$ and $\alpha_2$ for some parameter $x$. To determine which estimator is "better" do we look at the MSE (mean squared error)? In other words we look at $$MSE = ...
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1answer
1k views
The difference between MSE and MAPE
i was wondering what is the differences between Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE) in determining the accuracy of a forecast? Which one is better? Thanks
