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-1
votes
0answers
10 views

How can I minimise the MSE in binomial distribution

$X_1$-Bin(n,p) and $X_2$-Bin(n-$x_1$,p). n is the unknown total population. I am given that $T_b$ is the estimator of n where $T_b$=a$X_1$+b$X_2$. Also, the ...
0
votes
1answer
15 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, $\sigma^2$) ...
0
votes
0answers
17 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 ...
0
votes
1answer
29 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 $X_t = Z_t + \theta Z_{t−1}$.
0
votes
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: ...
0
votes
0answers
29 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
votes
0answers
19 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 ...
0
votes
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 ...
0
votes
0answers
13 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
votes
1answer
44 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}\\ ...
1
vote
0answers
44 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 ...
0
votes
0answers
20 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) ...
1
vote
1answer
99 views

Improving the mean squared error of the ordinary least squares solution

I have the following relationship that holds: $y = a x_1 + b x_2$ Now I would like to determine constants $a$ and $b$ by performing tests. Each test results in 10 values for $y$, $x_1$ and $x_2$. ...
0
votes
0answers
8 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
25 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
22 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
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 ...
1
vote
0answers
23 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 ...
2
votes
3answers
111 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} = ...
0
votes
1answer
36 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 ...
1
vote
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
vote
2answers
173 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 ...
0
votes
0answers
56 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 ...
1
vote
0answers
48 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 $10^{-4}$ ...
0
votes
1answer
109 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
0answers
67 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 ...
1
vote
0answers
140 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 ...
0
votes
2answers
132 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 ...
1
vote
2answers
183 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
210 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
0answers
372 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
450 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 ...
2
votes
1answer
238 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 ...
1
vote
1answer
467 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
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
vote
2answers
110 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 ...
0
votes
2answers
748 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?
1
vote
1answer
320 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 ...
-2
votes
2answers
407 views

How do I find 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. $$x_1=[1\;\; 2]^T$$ ...
2
votes
0answers
169 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|} ...
1
vote
1answer
26 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 ...
0
votes
2answers
424 views

Step by step correlation calculation

I must understand how I can calculate the correlation for the following probability variables. ...
4
votes
1answer
159 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
0answers
74 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
0answers
122 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 ...
4
votes
1answer
881 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 ...