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4
votes
1answer
785 views

Linear MMSE estimate of MMSE estimator

This question is prompted by a recent discussion about the relationship between conditional expectation and covariance. Suppose that $X$ and $Y$ are zero-mean unit-variance random variables with ...
3
votes
1answer
142 views

Straight line through data by eye - least squares? [closed]

I heard an interesting fact a while ago about how people draw a line through a cloud of points on a scatter plot. Usually, when calculating lines of best fit, we use the minimal the sum of squares of ...
2
votes
3answers
64 views

Why root mean “square” error?

Root-mean-square error is frequently used in for calculating the error between a predicted value and actual value. The formula for RMSE is given below: $\mathrm{RMSE} = ...
2
votes
1answer
172 views

Minimizing Mean Squared Error for Exponential Function

I have a function that I'm trying to model using an exponential function and I'm trying to determine the constants for the exponential. I know I could optimize it using trial-and-error in R or another ...
2
votes
0answers
142 views

root mean square distance between two simplices

As the title says, I want to compute the root mean square distance between two n-dimensional simplices. Say I have two surfaces $S$ and $S'$, the mean error is $$ d_m(S,S') = \frac{1}{|S|} ...
2
votes
0answers
68 views

Measuring Model Bias

If given the choice between two statistical models (for argument's sake, let's say Model 1 is $y = \beta_0 + \beta_1 x_1 + \epsilon$ and Model 2 is $y = \beta_0 + \beta_1 x^2_1 + \epsilon$), is there ...
1
vote
2answers
99 views

Value minimizing mean absolute percentage error

What value for $c$ would minimize the formula: $$\frac{1}{n}\;\sum^{n}_{i=1}\left | \frac{y_i-c}{y_i}\right|$$ given the values $y_1, ..., y_n$. For example in the mean squared error we have the ...
1
vote
2answers
132 views

Given a function, calculate MMSE and LMMSE

Let $X = \frac{1}{1+U}$ where $U$ is uniformly distributed over $[0,1]$. I need to evaluate $E[X\mid U]$ and $\hat{E}[X\mid U]$ and the calculate the MSE, $E[(X-E[X\mid U])^2]$ and ...
1
vote
2answers
186 views

Least squares fit with a trick

Fitting a circle with least squares is easy once you get the trick for $c = r^2 - a^2 -b^2$ and you got a linear set of equations. my problem is as follows: $$z = \alpha x + \beta y + \alpha \beta$$ ...
1
vote
1answer
259 views

Minimize combined variance of multiple measurements with known (but varying) variance

I have multiple measurements for the same property but with different but known uncertainty (variance). And I would like to combine that measurements in a way that I get as close to the real value as ...
1
vote
2answers
97 views

Linear Regression to quadratic function

What is the optimal linear regression (w and w/o y-intercept) for a quadratic curve w.r.t. mean square error. Mathematically speaking: Given, $$y = x^2$$ for $$x = [-a,a]$$. What is the best ...
1
vote
1answer
290 views

Minimizing mean squared error

I want to find a $d$ that minimizes the value of the expression below. I think the first step is to find the derivative w.r.t. $d$ (is that correct? If not, what is the first step?). If so, I'm having ...
1
vote
1answer
24 views

Calculate the Mean earnings of a person

There are $12$ employees who earn $\$750$ collectively. I need to calculate the mean salary earned by a single employee. My workings so far: I tried to divide $750 / 12$, but I am not sure if this ...
1
vote
0answers
17 views

Can convergence in distribution say anything about mean-square convergence rate?

Suppose I have a sequence $\{x_n\}$ that I already know converges in the mean-square-sense ($\lim_n E |x_n|^2\to 0$). Suppose further I know that the sequence $\{x_n\}$ converges in distribution to ...
1
vote
0answers
26 views

Geometric accuracy analysis of 2d rectangular models

I have reconstructed set of rectangular objects lie on a 2D plane (for ex. ABCD). All these objects are in a one coordinate system. On the other hand, I have reference models for all of them ...
1
vote
0answers
44 views

MSE For a Single Calculation (intel processor errors)

This is the question, from a practice final for a stat course: The Intel Pentium Processor chip has been discovered to make small errors occasionally; that is, errors of +1 or –1 (in $10^{-4}$ ...
1
vote
0answers
121 views

Unbiased estimators of theta

Suppose $\hat\theta_1$ and theta $\hat\theta_2$ are both uncorrelated and unbiased estimators of $\theta$, and that $\text{var}\hat\theta_1=2\cdot \text{var}(\hat\theta_2)$. a) Show that for any ...
1
vote
0answers
230 views

What is the difference between RMS and RMSE?

I did not unserstand what is the difference between root mean square (RMS) and root mean square error (RMSE). In some sources RMS term is used for error analysis, in others RMSE. Can you explain ...
1
vote
0answers
324 views

Hypergeometric Distribution Probability (mean, variance, Std Deviation)

The distribution of the number of children per household for households receiving aid to dependent children (ADC) in a large eastern city is as follows: 5% of ADC households have one child, 35% of ADC ...
1
vote
0answers
52 views

How to estimate error pattern of a set of line segments with respect to given reference segments (2D case)

I am having set of pair of line segments (2D). Though each pair should be coincided on top of each other they are not so. I have been the reference data and then I extracted other line segments ...
1
vote
0answers
87 views

Getting the correct error for a mean calculation

A constant k needs to be calculated including its gaussian error. $k = f_{(u,t)}$ $k_i$ can be calculated with the values and errors of $u_i$ and $t_i$ and their respective errors. Main issue is ...
0
votes
2answers
267 views

Step by step correlation calculation

I must understand how I can calculate the correlation for the following probability variables. ...
0
votes
1answer
17 views

Error of function with errors on arguments and size of arguments

EDIT: my question is not how to derive the formula below (I think the derivation is more or less what I guessed, like the answer below supports), but whether it can be made valid for the case where ...
0
votes
1answer
81 views

MMSE (Minimum min square estimate) problem

I have a problem as follows. As of now, I cannot provide the definition of X and Y but can anyone provide a rough overview of what needs to be done ? An experiment consist of rolling a single ...
0
votes
2answers
362 views

What is the purpose of subtracting the mean from data when standardizing?

What is the purpose of subtracting the mean from data when standardizing? and What is the purpose of dividing by the standard deviation?
0
votes
0answers
5 views

Performance of an optimum estimator for Gaussian random variables used against Non-Gaussian random variables

Consider an optimum estimator for some parameter where the underlying distribution is following a Gaussian distribution with mean 'mu' and standard deviation 'sigma' (denoted by N(mu, sigma)). Let ...
0
votes
0answers
15 views

Asymptotic Mean Square Error for kernel regression estimator

I want to derive the optimal rate of convergence for the kernel-based estimator for $E [Y|X = x]$ based on observations $(X_{1},Y_{1})$,...,$(X_{n},Y_{n})$ (where the $X_{i}$'s are $\mathbb{R}^{d}$ ...
0
votes
1answer
25 views

Mean Square Estimate problem

I have to find $\textbf{s}_{MS}$ given $\textbf{r} = h\textbf{s}+\textbf{n}$ where $h$ is a Bernoulli random variable with $Pr(h=1)=Pr(h=0) = 1/2$ and $\textbf{s}$ and $\textbf{n}$ are independent ...
0
votes
1answer
24 views

Test for, and compare means of folded normal distribution

I have two datasets of absolute distances to a single point in a 2D space. I have reasons to expect that if I had the sign and magnitude of these distances, my datasets would be normally distributed ...
0
votes
0answers
51 views

Calculating the “likelihood of progressive fit”

I am faced with the following least squares model fitting problem: I have a process that generates time series data. This time-series data have a specific structure (i.e. i can fit a model with ...
0
votes
0answers
50 views

Multinomial/Binomial MSE

Let $T_{1}=\sqrt{\frac{N_{1}}{n}}$ and $T_{2}=1-\sqrt{\frac{N_{3}}{n}}$, where $N_{1}\sim\operatorname{Binomial}(n,\theta^{2})$ and $N_{3}\sim\operatorname{Binomial}(n, (1-\theta)^{2})$. Compute the ...
0
votes
2answers
68 views

least square adjustment of resection

By setting up at an unknown point, and measuring the horizontal angles between three points with known coordinates, it is possible to calculate the coordinates of the unknown point. This process is ...
0
votes
0answers
28 views

Norms for minimizing arbitrary error distribution

Assume we are doing regression on the function $f(x)$ with error term $e(x)$ with distribution $g(e; \theta)$: $ y = f(x) + e(x), \; e(x) \sim g(e; \theta) $ Let's say we know the analytic form of ...
-1
votes
0answers
23 views

Trying to find the bias and MSE of the $S^2(n+1)$ estimator [closed]

Trying to answer this question but can only find notes for $\frac{1}{n}$ and $\frac{1}{n-1}$. Nothing for $\frac{1}{n+1}$
-3
votes
2answers
265 views

Finding the angle $\theta$ of the line through the origin that matches the given points the best

How to find angle $\theta$, that the line passing through the origin that is the best fit for the points given below in the mean square sense makes with the horizontal axis. $$x_1=[1\;\; 2]^T$$ ...