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2answers
149 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 ...
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1answer
25 views

linear regression, expectation and mean squared error

Let us assume that data is generated according to a true model $$y_i = \beta_{true}x_i + \epsilon_i$$ for $i = 1, ..., n$ Assume that $x_i$ are fixed, and $\epsilon_i$~ N(0, $\sigma^2$) ...
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1answer
39 views

Finding the best linear predictor

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 $X_t = Z_t + \theta Z_{t−1}$.
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1answer
17 views

Getting the average of values with errors.

I have five data values each with an associated error. I want to find the mean of these values but also take the errors into account. How do I do this? Lets say the data values and errors are: ...
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1answer
50 views

differentiating MSE

I have a error signal which I want to minimize using MSE. This error signal at time $k$ is a vector of length $3$: $e_k = C^{T} R_k - B^{T} A_k = [c_0, \ldots, c_{N_c-1}] \begin{bmatrix} r_{2k}\\ ...
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1answer
27 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 ...
2
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0answers
173 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
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0answers
76 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
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0answers
60 views

Calculating MSE for two different size matrixes

I have two $2$-column matrixes, one of the has $467$ rows while the other one has $61468$ rows. Both them are trajectory paths of same robot, the big matrix is kind of raw data and the smaller one is ...
1
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0answers
26 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
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0answers
32 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
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0answers
50 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
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0answers
148 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
429 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
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0answers
506 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
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0answers
55 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
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0answers
125 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 ...
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0answers
32 views

closed-form solution for this constrained optimization

I want to find a closed-form solution for the vector $w=\left[\begin{array}{c} c\\-b \end{array}\right]$where $c$ and $b$ are column vectors, such that the following MSE is minimized: $\begin{align} ...
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0answers
9 views

how can I find the resulting MS error with linear estimation?

The problem says: If $\eta_x=\eta_y=0, \sigma_x=\sigma_y=4$ and $\hat{y}=0.2x$ (linear estimate), find $E\{(y-\hat{y})^2\}$. I am doing this, based on Papulis formulas for homogeneous linear estimate: ...
0
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0answers
11 views

MSE in case of log-transformed dependent variable

Let's consider the following log-linear model: $log(Y_i) = \alpha + X_i\beta + \epsilon_i$ for i = 1, ..., N The fitted value is: $\widehat{log(Y)} = \hat{\alpha} + X\hat{\beta}$ Assuming ...
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0answers
12 views

How Can I show that a=A in this linear MS estimation problem?

How can I show that if the constants A,B and a are such that $E\{[y-(Ax+B)]^2\}$ and $E {\{[(y-\eta_y)-a(x-\eta_x)]^2 \}}$ are minimum, then $a=A$. I am trying to use this: $e=e_m$ is minimum if ...
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0answers
12 views

Multivariate mean square error

Consider a one-dimensional vector: $X = (X_1, X_2, ..., X_n), \ \ \ \ X_i \in \mathbb{R} $ The mean squared error compared to a certain value is: $MSE = \frac{1}{n}\sum_{i=1}^n (X_i - \mu)^2$ But ...
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0answers
21 views

Mean Squared Error

According to existing literature, what greek symbols - not roman - are commonly used to represent MSE (Mean Squared Error) and RMSE (Root-Mean-Square Error)? Thanks,
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0answers
23 views

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 ...
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0answers
36 views

How to solve this linear MMSE equation?

I have a linear equation: $\hat{\tau}_{k+1} = \hat{\tau}_{k}+\alpha(\tau_k - \hat{\tau}_{k} + n_k)$, where ${n_k}$ are i.i.d zero-mean Gaussian random variables with variance $\sigma^2$, $\alpha$ is a ...
0
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0answers
23 views

what are some good ways to define the errors between two functions?

I have two functions. One is the original function (that contains 4 variables), and the second one is the approximation to the first one (also contains 4 variables). The question is, if I want to ...
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0answers
6 views

To find error in time histogram

I have a data which is recorded from a detector. Whenever the detector produce signal it records the time. I have recorded the data for several cycles, one cycle is 0 to 1 second. Finally I made the ...
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0answers
14 views

Mean square relative error. Some considerations

I'm facing with the following mean square relative error $$\frac{1}{T}\sum_{t=1}^T s_t^2 = \frac{1}{T}\sum_{t=1}^T \left(\frac{a_t - b_t}{b_t}\right)^2$$ There are two circumstances I don't know how ...
0
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0answers
22 views

Monte carlo error: Combining “experimental” and statistical errors

I'm doing a slightly involved Monte Carlo approximation of a quantity $E$ where I end up with the following formula: $E=\frac{\sum_{i=1}^np_ie_iG_i}{\sum_{i=1}^np_iG_i}\ .\ \ \ \ \ \ \ \ \ $ (1) ...
0
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0answers
11 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
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0answers
27 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 $\mathbb{R}^{d}$ ...