# Tagged Questions

A measure of performance of an estimate or prediction, equal to the mean squared difference between the true value and the estimated value.

31 views

### How to present the results of numerical comparisons

I ran a comparison where I estimated the parameters of a model using $S$ different methods several times. More specifically I simulated $M$ datasets $\boldsymbol{y}_1, \dots, \boldsymbol{y}_m$ from a ...
67 views

### Unsure how to calculate mean square error of a variable with a joint distribution

I'm working through a homework assignment and I'm having an inordinately difficult time trying to calculate the MSE of two different estimators. The homework is described as this: Let $X$ and $Y$ be ...
86 views

### Mean Squared Error and Residual Sum of Squares

Looking at the Wikipedia definitions of: Mean Squared Error (MSE) Residual Sum of Squares (RSS) It looks to me that $MSE = \frac{1}{N} RSS = \frac{1}{N} \sum (f_i -y_i)^2$ where $N$ is he ...
73 views

### Bayesian MMSE estimators from a transformation of the observations

Consider a random variable X whose value we want to estimate using a Bayesian MMSE estimator. Let $O_1(X)$ be a set of observations which depend on $X$ in some complex way (captured by $P(O_1|X)$) ...
51 views

### MADE and MSE pros and cons

When assessing the performance of an estimator, in which scenarios should one prefer the use of the Mean Absolute Deviation Error (MADE) over the Mean Squared Error (MSE) and vice versa? Edit / ...
333 views

### Replicate simulation study from a paper and calculate the MSE in R

I have implemented a Gibbs Sampler for the Bayesian Elastic Net (BEN) according to this paper on Penalized Regression by Kyung et al. In this paper, they execute a simulation study that has been used ...
460 views

### Interpretation of MSE (mean square error) and ME (mean error)

I'd like to produce forecasts by considering different scenarios. I'm using Mean Error (ME), where the error $=$ forecast $-$ demand, and Mean Square Error (MSE) to evaluate the results. For the ...
78 views

### Existence theorem for LASSO

In case of ridge regression we have the theorem that always exists such a shrinking parameter that Mean Squared Error (MSE) of ridge is less than that of least squares. But do we have a similar ...
104 views

### Questions on Definitions and Notation (MSE, SSE, Sxx)

It is said that $S_{xx} = \sum_{i=1}^n(x_i−\overline x)^2 = \sum_{i=1}^n x_i^2 −n\overline x^2$. I suspect this is simple algebra but I am missing something still. How does this work? Further, ...
111 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 ...
158 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: ...
138 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 ...
44 views

58 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 ...
520 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 ...
90 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 ...