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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-3
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1answer
18 views

Standard deviation of sample mean - unknown equation answered

Does anyone recognize mathematically or statistically what this formula's purpose is. If it is not statistically useful what does dividing a value by a constant and taking a square root mean? For ...
1
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3answers
32 views

Variance of a distribution of multi-level categorical data

I am currently analyzing large data sets with various characteristics (such as city). I wanted to find a measure which would essentially say how much or how little of a variance there was across the ...
0
votes
0answers
5 views

Unbiased weighted variance with reliability/importance weights

I need to provide a reference for the use of a modified version of the formula in wikipedia for the unbiased weighted variance with reliability (aka. importance or non-random) weights: https://en....
2
votes
1answer
49 views

Intuition (geometric or other) for $Var(X+Y) = Var(X)+Var(Y) + 2 \ Cov(X, Y)$

Is there any way to make sense out of this formula intuitively? I rederived it algebraically (took me a while...), which made me happy because I used to be incapable of doing that kind of stuff, but ...
1
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0answers
18 views

Variance of an unbiased estimator is 0 when the sample size goes to infinity

So I would like a proof for the following but I can't seem to do it myself. I have a random variable $X$ and I draw $n$ samples($\{X_1, \ldots, X_n\}$) from it and I have $$ Z_n = \frac{\sum_{i = ...
3
votes
1answer
43 views

Variance of the modulus of a random variable

Let $X$ be a random variable with mean $\mu$ and variance $\sigma^2$. What is the upper-bound on the variance of $Y=\left|X\right|$? My gut feeling says that $\operatorname{Var}(Y) \leq \operatorname{...
2
votes
0answers
15 views

What do we know about the rate of convergence of the mean of RVs with infinite variance?

What, if anything, do we know about the rate of convergence of of the mean of identically distributed, independent or stationary random variables drawn from a distribution with a finite mean and ...
0
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0answers
13 views

Why var.test and levineTest produce very different p-values? [duplicate]

I run var.test in R using two samples sample1<-c(1,2,3) and sample2<-c(1, 10, 1000). I got a p value of 0.000006. When using Levene's test, I got a p value of 0.3689. SO is the variances equal ...
0
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0answers
9 views

Pairwise comparison among variance

I would greatly appreciate any help on this! I'm doing a research where I need to compare variances (or standard deviation) of several samples (9 samples). I did some research and found the "Bartlett ...
0
votes
0answers
18 views

Robust one sample tests of variance or scale

A common one sample test for variance is the chi-square test, e.g., http://www.itl.nist.gov/div898/handbook/eda/section3/eda358.htm. What are some robust testing alternatives for variance when the ...
0
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0answers
4 views

Add Structure on Experimental semivariogram and validation of semivariogram [on hold]

im fairly new to this so please be patient with me. I am using surpac 6.3.2 and i want to know when to add a "structure" to the experimental semivar, also, once i have completed a semivar, how to i ...
0
votes
0answers
17 views

RSS of correlated variables

Suppose that I have the variance-covariance matrix for a 3D point $$ c = \begin{bmatrix} S_{X} & S_{XY} & S_{XZ} \\ S_{XY} & S_{Y} & S_{YZ} \\ S_{XZ} & S_{YZ} & S_{Z} \end{...
2
votes
1answer
25 views

estimating variance using only data at the tails without resorting to Gibbs sampling

Suppose we know that the population size is $n=1,000$ but for whatever reason, we only have the bottom $n_1=100$ observations and the top $n_2 = 200$ observations. Furthermore, suppose we know the ...
1
vote
0answers
11 views

Expected value of a semi-partial correlation

Say I have 4 random variables. $X^{(1)}$ and $X^{(2)}$ are jointly multivariate normal with mean 0 and covariance $\Sigma_X$, and $Y^{(1)}$ and $Y^{(2)}$ are jointly multivariate normal with mean 0 ...
1
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0answers
19 views

Why do loadings of princomp in R report identical proportion of variance for all principal components? [duplicate]

I'm trying to run a few tests using princomp in R. In princomp there is a value called <...
0
votes
0answers
17 views

Variance of error $Y* = y_i/c_i$

If I have this model: $Y_i = B_1 + B_2logx_i + 2e_i$ $e_i$ ~ $N(0, σ^2)$ how to solve this $Y* = y_i/c_i$ --------> if : $V(Y*) = σ^2$ ? the constant is $c_i = 1/2$?
1
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0answers
29 views

Is there easiest way to derive variance of continuation-ratio logit estimator?

I wanted to calculate the variance of continuation-ratio logit estimator that defined as $\hat{\theta}^+_j=\ln\frac{\pi_j}{\sum_{k=1}^{j-1}\pi_k}$, for $j=2,...,C$, where $C$ is number of categories. ...
0
votes
0answers
26 views

Variance of stationary VAR process

Suppose we are given stationary VAR(p) process. How to estimate variance of its components: $y_{1t}, y_{2t}...y_{mt}$? Will be very grateful for help!
-3
votes
0answers
31 views

How do i use PCA? [duplicate]

I am not sure i understood the concept of PCA that well. I know it is used to reduce the dimensionality by the help of the eigenvector and eigenvalues of the covariance matrix, and thereby compute ...
1
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0answers
53 views

Variance of Maximum Entropy solution [closed]

Background: Assume we are interested in solving the Maximum Entropy solution for a six sided dice with expected value of 4. $$H= - \sum_{i=1}^6 p_i \log(p_i) $$ $$\sum_{i=1}^6 p_i = 1$$ $$\sum_{i=...
3
votes
0answers
32 views

Sufficient conditions for variance convergence in CLT

More generally, if $\{X_n\}_{n\in\mathbb{N}}, X$ are real random variables with finite variance such that $X_n\xrightarrow{d}X$, what are some sufficient conditions to assure that $\operatorname{Var}(...
0
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0answers
13 views

Simple English translations regarding thematic textual analysis

I have run a thematic textual analysis of economic select committee meetings in the UK using t-lab. I ran a thematic analysis of the E.C.U.s, and categorised the E.C.U.s into (for example) 5 thematic ...
1
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0answers
16 views

How to calculate VPC in glmer?

For a specific analysis I want to calculate the variance partition coefficient (VPC). I am using the following formula: ...
1
vote
0answers
10 views

Choosing a cluster with low variance and many data points

I have data points that have been grouped using k-means clustering. Some of these clusters may only have one data point, which would give them a variance of zero. But I am more interested in the ...
1
vote
0answers
15 views

Variance of Estimator (uniform distribution)

In my script for statistical signals, I have some troubles to get the same result for the variance of an estimator $T$. Here is the example: Given the observations $X_1, \dots , X_N$ of a uniquely ...
4
votes
2answers
33 views

Minimising MSE of $\sigma^2$ estimator of specific form

I have found a past exam question for a statistics course and can't seem to find the required result. Part A is fine but my working for part B must be incorrect [see below]. Can anyone figure out ...
0
votes
0answers
11 views

Variation between and within

I work in an industry that uses a variable raw material. Assume we are allocated 80,000 units of this material and we have a measurement for each unit. Our technique for managing this variation is to ...
0
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0answers
19 views

What is the null distribution of the between-group variance?

Scenario From a population, we randomly sample $n$ individuals, measure the normally distributed random variable $X$ and compute the total variance $V_T$ of $X$ in this sample. Then, we randomly ...
0
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0answers
12 views

From successive samples of increasing size how do I measure “variability is within the error band” for a particular confidence level?

In the section 5.6 of book Data Preparation for Data Mining, by Dorian Pyle it states This is a complex subject, and it is easy to confuse what actually has been captured here. In the example ...
0
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0answers
7 views

Heteroskedastic errors may still explain more deviance?

Among a population, N = 1,100, you employ 10-iteration, 10-fold cross-validation on 1,000 observations using OLS model #1: $Y_i = \beta X + \epsilon$ This has an Adjusted $R^2$ of Q1 with a standard ...
1
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0answers
10 views

Variance from bootstrap sample

For a given set of parameters I get a prediction from a model. Can I bootstrap my data for the given parameters and take the variance of my estimates for the given parameter values to approximate the ...
1
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0answers
22 views

Same mean, different variance - test?

I have conducted an experiment where I am interested in how well different models for directional hearing works. For each model a sound is presented to a test subject, and the test subject expresses ...
18
votes
4answers
1k views

Is variance a more fundamental concept than standard deviation?

On this psychometrics website I read that [A]t a deep level variance is a more fundamental concept than the standard deviation. The site doesn't really explain further why variance is meant ...
1
vote
0answers
12 views

Estimating covariance matrix from multiple distance measurements

I have a setup that can measure the distance between two beacons. The first beacon is aware of its 2D location and is moving around while measuring the distance to the second beacon. I've setup a ...
3
votes
1answer
61 views

Why Is Total Sum of Squares Result from K-Means Analysis Different from Variance?

I'm working on a project that requires some clustering analysis. In performing the analysis, I noticed something that seemed odd to me. I understand that in k-means the total sum of squares (total ...
0
votes
0answers
23 views

how to average standard deviations of independent groups

I have means and standard deviations on a given variable, $X$, for six independent samples of unequal sample sizes: Group 1: $SD = 0.96 , n = 290$ Group 2: $SD = 1.082, n = 250$ Group 3: $SD = 0.70, ...
0
votes
0answers
40 views

Why does RMSE underestimate model variance?

I have read that RMSE of calibration/validation/cross validation is frequently used for model selection (e.g., for ANN), but can lead to over-fitting because the prediction error represents the ...
1
vote
0answers
23 views

Variance explained - equivalent statistics for categorical data?

I have a multinomial response variable and a multinomial "independent" variable. Is there an equivalent statistics or method for calculating the variance explained by the independent variable?
2
votes
1answer
72 views

Difference in expressions of variance and bias between MSE and MSPE

The difference between Mean Square Error (MSE) and Mean Square Predicted Error (MSPE) is not the mathematical expression, as @David Robinson writes here. MSE measures the quality of an estimator, ...
3
votes
0answers
32 views

Unbiased estimator variance of sample variance

I was reading the section on k-statistics on wolfram alpha. It was known to me that for the sample variance $k_2 = \frac{1}{n-1}\sum_{i=1}^n (x_i - \overline{x})^2$ it holds that its variance ...
0
votes
1answer
23 views

How to test for enough variance in Logistic regression?

I would like to find out if there's enough variance in my dependent variable which is binary. Which techniques would be best for this?
0
votes
0answers
5 views

A specific way to minimise the variance when importance sampling

Consider the following problem. We are interested in approximating from samples the expectation of $h$: $$ \int_t p(t) h(t) d(t) $$ We seek to obtain a lower-variance estimate by using importance ...
1
vote
1answer
5 views

How can I quantify the multivariate variances of several characters in different groups?

I have a multivariate dataset of linear measurements. Where I measured several characters (e.g. skull length, skull width, skull height, ...) for several different species. My questions is, if the ...
1
vote
1answer
41 views

Help Beginner Q: Explanation on pooled variance and when it is used

If I am conducting a difference in means hypothesis test, when do we use the pooled variance and why? Lets say the population variance was unknown for two samples, the sample sizes for the two means ...
0
votes
2answers
37 views

Is this controversial that in PCA, we want the variance as large as possible, while in bayesian, a large variance means a low precision?

I am wondering about the variance. We say the variance is inverse proportional to precision, then we also say the variance is proportional to the information, which means that a large variance means ...
4
votes
1answer
107 views

Why is my kalman filter trusting so much my observations?

This question follows the one asked there. I am trying to filter an equity index (Stoxx 600) time series using kalman filter. I'm using the R package dlm and my code is inspired from the dlm ...
2
votes
0answers
15 views

Higher variance in sample mean or sample median? [duplicate]

The variance of the sample median depends on the distribution you are sampling from. This is also true for the variance of the mean. But can one say that the variance of the sample mean is always ...
0
votes
0answers
7 views

Compare GLM with different dependent variables (that have not the same variance)

I would like to know if it is possible to compare the effects of one predictor on different response variables that follow e.g. a Poisson distribution. I have already read this topic with excellent ...
6
votes
5answers
749 views

How can we ever know the population variance?

In hypothesis testing, a common question is what is the population variance? My question is how can we ever know the population variance? If we knew the entire distribution, we might as well know the ...