The expected squared deviation of a random variable from its mean; or, the average squared deviation of data about their mean.

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21 views

averaging after n trials of monte carlo simulation or not? which is better statistically?

related to my job I want to code a realistic monte carlo simulation for availability, reliability and related sensitivity analysis. Scenario will be complex and there will be many parameters. What I ...
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0answers
8 views

How can I calculate what proportion of variance is shared by two correlated variables based on the correlation coefficient?

Say, for instance, you have the following correlation coefficients: r = 0.25 r = 0.33 r = 0.90 r = 0.14 How can I calculate what proportion of variance is shared ...
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0answers
20 views

How to constrain the variance of a linear model

Let's say I have a model y=a+bx, and I have the distributions of b (B), x0 (X0), and y0 (Y0), and I would like to compute the distribution of a, A. One way to do this is to independently sample data ...
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0answers
16 views

Monthly realized variance, different number of observations per month

The monthly realized variance is usually computed as: $\sum_{i=1}^n (r_i-\bar{r})^2$, where $\bar{r}$ denotes the average return of the month, or as $\sum_{i=1}^n r_i^2$ (I am not sure which ...
3
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1answer
64 views

How to detect noisy datasets (bias and variance trade-off)

Studying the bias-variance trade-off: expected loss = bias + variance + noise I understand that we minimize this quantity by finding the "best" balance between ...
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1answer
41 views

What is Bootstrapping in statistics? How can I use it to determine error in the mean, variance, kurtosis and skewness of a data set?

From what I understood from searching randomly is that it has something to do with resampling. What does this resampling mean? Is it selecting random data from a distribution or is it getting data ...
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24 views

How do you test if there is a statistically significant change in variance using dependent variarables?

Given a group of subjects and a value measured across a baseline period and a measure period, how do I test if the spread of the data is statistically significantly different?
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28 views

Samples needed for variance accuracy [on hold]

How many samples should one take to guarantee $n$ digits of accuracy ($n$ digits total digits both before and after decimal Eg: truncating $412.243$ to $2$ digits is $410.000$ while truncating to $5$ ...
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1answer
22 views

How to compare different variances of the same population? [on hold]

Lets say I have a set of numbers distributed as {5, 5, 5, 5} which has a mean value 5 and variance of 0. Now I can redistribute the data in different ways like for instance {4, 3, 5, 8}; mean = 5, ...
2
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0answers
35 views

Help explain the “redundancy” of canonical correlation

I am reading a material about canonical correlation and it introduces a concept named "redundancy". I have been puzzled for one day but still could not get a understanding. The following is a screen ...
4
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3answers
74 views

Interpreting random effect variance in glmer

I'm revising a paper on pollination, where the data are binomially distributed (fruit matures or does not). So I used glmer with one random effect (individual ...
2
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1answer
40 views

What is the long run variance?

How is long run variance in the realm of time series analysis defined? I understand it is utilized in the case there is a correlation structure in the data. So our stochastic process would not be a ...
1
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0answers
19 views

variance and sample confused

When solving (b), is the variance $$ V\bigg(\frac 1 2 (x_1+x_2)\bigg) = \frac 1 4 V(x_1+x_2) = \frac 1 4 \big(v(x_1)+v(x_2)\big)= \frac 1 2 \sigma^2 $$ or should I divide the variance by the sample ...
3
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0answers
28 views

Variance of binomial vs. multinomial distribution in cross-validation

Suppose we have a dataset with $N=100$ observations. We do $K$-fold cross-validation with $K=10$ and $K=100$. In the first case, the classification decisions are sampled (can I say it like this?) ...
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0answers
35 views

Combining the Standard Deviation for Multiple Populations; Small Data Sets

I have been presented with a very small dataset which describes a material property for a particular cast of stainless steel, in this case fracture toughness. The data is: ...
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0answers
36 views

Two-way ANOVA: error variance in numerator of F statistic for main effect

Let us consider a balanced two-way ANOVA without replications, having $m$ columns and $n$ rows. If we want to test the column effect, we use the statistic $F(c)=MS(c)/MS(e)$, where $MS(c)$ is the mean ...
4
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1answer
218 views

Is the following dataset possible?

"Is it possible to create a data set where $\bar{x}=30.0$, range $R=10$ (meaning the max-min=10), and variance $s^2=40.0$?" I feel sort of dumb asking this question, but I'm not quite sure I'm on the ...
4
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1answer
49 views

Question about bias-variance tradeoff

I'm trying to understand the bias-variance tradeoff, the relationship between the bias of the estimator and the bias of the model, and the relationship between the variance of the estimator and the ...
3
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1answer
49 views

Variance stabilisation

$Y$ has mean $\mu$ and variance function $V(\mu)$. If $V(\mu) = \alpha.\mu^v$ then $h(y) = y^{(2-v)/2}$ is variance stabilising which means that $Var(h(Y))$ is approximately constant. I tried to ...
0
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1answer
36 views

Estimate variance of a function given variances of variables

I'm given the mean and the standard deviation of N random variables $A$, $B$, $C$, $D$... I compute the function $f:=f(A, B, C, D...) = \frac { AB... }{ CD... } $. How can I estimate the variance of ...
0
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1answer
45 views

Sample variance from second moment

if I have a sample composed by values lesser than 1 and i want to compute the sample variance with $ \frac{n}{n-1}(\langle x_i^2 \rangle - \langle x_i \rangle^2)$ how can i do? Because the mean of the ...
4
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1answer
44 views

Looking for a distribution where: Mean=0, variance is variable, Skew=0 and kurtosis is variable

I am aiming to run simulations in order to estimate the influence of the distribution of $Y$ (independent variable) on a certain binary outcome $X$ (dependent variable). $Y$ must always has a mean of ...
0
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0answers
22 views

How would I calculate the t-statistic for this data and then determine if it's significant?

Say we want to test the hypothesis that a control group of cancer patients would report higher mean pain ratings than an experimental group receiving special massage treatments. Group 1: Mean = 78.1 ...
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0answers
9 views

binomial error calculated with formula

i have uploaded a 2D histogram ,, actually it is filled by dividing two 2Dhistograms with same bins.i want to calculate manually each error which is shown with each value i.e binContent.Please ...
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0answers
19 views

Expected Value and Variance of a summation of correlated sample means

Let $\gamma_i$ be constants and $f(\gamma_i)$ be normally distributed random variables. More specifically, $f(\gamma_i)$ is the sample mean of the population $\gamma_i$. Now I have a sum of the ...
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0answers
31 views

Cointegration and variance of time series

If we know that $X_t , Y_t$ are two cointegrated discrete random processes, what can we say about the relationship between variance of the two increments $var(X_{t+h}-X_t)$ , $var(Y_{t+h}-Y_t)$ for a ...
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1answer
86 views

When is Variance Statistically Significant?

This may seem like a rudimentary question relative to other posts, but how do I determine whether the variance is statistically significant? For example, let's say I have a population of 10000. I ...
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0answers
12 views

Overlap between 1) regression results and 2) correlation between residualized versions of variables

Scenario: 1) Regress a standardized variable A ("stand. A") on a standardized Variable B "(stand. B"). Since both Variable A and Variable B have a number of potentially confounding influences on ...
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0answers
19 views

How to compare variability between two variables when using the coefficient of variation is inadvisable?

I have two variables with different means. They both include negative and positive values. How can I compare their variability, given that the coefficient of variation should not be used when I have ...
0
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0answers
30 views

Superposition of two renewal processes

Usually, superposition of two independent renewal processes may not lead to a renewal process. However, in my problem, the interval time between two events of the renewal process is more specific ...
1
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0answers
25 views

Error of the variance

I have a collection of $(x,y,z)$ data points. I want to compute the mean, $\mu$, and variance, $\sigma^2$, along each axis, as well as the errors on each. I know that the standard error of the mean ...
0
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1answer
57 views

Residual variance formulas difference

There is a bi-dimensional table of frequencies: Doing the regression analysis with the fit formula being $\hat y=a+bx^2$, where $\hat y$ is the same as $y^{est}$, the filled table looks like this: ...
3
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1answer
71 views

What is the covariance called when it is not divided by N?

I noticed that in signal processing they have this term called cross-covariance. The cross covariance function produces covariances of two functions with different lags. At the center of the vector ...
1
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1answer
40 views

How do I show that $-\frac{1}{2}\sum_{i=1}^n(X_i - \bar{X})^{T} \sum^{-1}(X_i - \bar{X})=-\frac{n}{2}trace(\sum^{-1}S)$?

In multivariate statistics the variance $S=\frac{1}{n}\sum_{i=1}^n(X_i - \bar{X})(X_i - \bar{X})^T.$ My lecturer showed me that $-\frac{1}{2}\sum_{i=1}^n(X_i - \bar{X})^{T} \Sigma^{-1}(X_i - ...
2
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1answer
174 views

What is Bartlett's theory?

This neuroimaging paper has been cited thousands of times. In it, a method is proposed for computing the correlations among several seed regions and all other brain voxels. Part of this method ...
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0answers
30 views

Assigning variance in regression

Say we have a linear regression model $$y_t = \mathbf{x}_t'\boldsymbol{\beta} + \epsilon_t, \qquad \epsilon_t \sim \mathcal{N}(0, \sigma^2)$$ Assuming $y_t$, $\boldsymbol{\beta}$, and $\sigma^2$ are ...
2
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2answers
108 views

Double integral, monte carlo estimation

Suppose I have pairs of random variables where $X_i$~$U[0,1]$ and $Y_i$~$U[0,1]$ and I want to estimate it $$\theta=\int_{0.5}^{1}\int_0^{0.5}e^{xy}xydxdy$$ but $\theta$ needs to have variance less ...
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0answers
16 views

Concerns regarding correlation structures and random variance using lme

I’m modeling some variables repeatedly measured over a three months period for a total of 300 individuals. These variables (e.g. activity) were measured at three different time scales: daily (90 ...
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0answers
19 views

Logistic Regression with negative signal

I'm trying to build Logistic regression to identify bots. But I found in my dataset that presence of one feature indicate that this is NOT a bot. Unfortunately this feature is not appearing often ...
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26 views

Estimate the population variance from a set of weighted means

Proviso: I do not have a lot of experience with statistical theory, so please forgive my occasionally poor choice of notation.$$\\$$ My problem is as follows: I have a set of measurements $X_i, ...
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28 views

Median Absolute Deviation vs Standard Deviation

To measure spread we use Variance or Standard Deviation. Variance and hence Standard deviation uses mean to find out the spread. Recently came across the MAD (median absolute deviation). ...
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1answer
21 views

Unbiased estimator and variance

A random sample of n people are asked whether they are against smoking or not. Suppose x are against smoking. What is the distribution of the random variable X (number of those against smoking). State ...
1
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1answer
28 views

What is the meaning of averaging combinations of independent random variables?

I'm getting into the management of multiple independent random variables in determining expectation and variance, but cannot see where averaging of a linear combination of independent random variables ...
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20 views
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42 views

Using variance in place of standard deviation for z-normalization

I'm implementing a 1-nearest neighbor (with dynamic time warping as the distance measure) classification algorithm on a severely constrained embedded platform with no FPU, so we're doing fixed point ...
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0answers
33 views

How to explain to laypeople that in a VAR model some variable explaines its own variance?

Background: I observed that people not familiar with vector autoregressive (VAR) models often struggle with the interpretation of a forecast error variance decomposition. I am frequently asked, why a ...
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2answers
46 views

Variance of the linear transformation of a random variable

I have a problem where the variance I'm calculating does not seem right. I have the following data: ...
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0answers
19 views

Variance partitioning into trait and method variance using CFA

I am concerned that my data is biased because of common method variance; i.e., the variance shared between the latent factors in my model is only due to the employed survey method (self-reporting ...
1
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0answers
12 views

Binary variance? Comparing two sacks of uneven coins or two heterogenous groups of people

I have two sacks of coins. In one sack, the coins are all uniform, each giving a fairly constant 0.5 chance of heads (based on tossing a few of them and also visual inspection). I then estimate the ...
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0answers
8 views

Do odds ratios have an effect on the variance components (level-2 variance) in multilevel models

I am estimating logistic multilevel models and have a question regarding the variance components (i.e. level-2 variance). I want to report my results as odds ratios and I am wondering if the ...