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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2
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0answers
15 views

Determine how much and why a sample differs from its population

I'd like to be able to determine a) how much and b) why a non-random sample “differs” from the population (there's probably a better word than “differs”; I was tempted to use “does not represent” but ...
0
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0answers
17 views

Covariance Matrix using Delta Method

I am trying to get the variance-covariance matrix of a transformation using the Delta Method. Originally, I have coefficients (let's call them X1, X2, etc...) and their variance-covariance matrix. ...
0
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1answer
20 views

Inverse-variance weighting

I'm writing a Bachelor Thesis in engineering an a small part of it has two deal with assigning weights to independent measurements. This is from the thesis: I am pretty sure that what equations ...
0
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0answers
10 views

Summary statistics & CIs for sample variances from multiple populations

Suppose $X_i$ are $n$ random variables that are all distributed normally, but with differing means and standard deviations: $X_i \sim N(\mu_i, \sigma_i)$. Now suppose $y_{ij}$ is the $j$-th random ...
1
vote
0answers
28 views

Distribution of sample variance for non-normal random variable [duplicate]

For a sample of size $n$ of non-normal random variables $x_1,...,x_n$. Is it possible to know which distribution the sample variance estimator follows? Details: The distribution of $x_i$'s is not ...
2
votes
1answer
59 views

How to calculate variance of Gaussian given mean and average deviation

I want to calculate the variance sigma of a Gaussian (normal) distribution given its mean mu and average deviation d (i.e. average of absolute value of difference from the mean). How can I do this? ...
2
votes
1answer
51 views

What is the name of the distribution of unbiased sample variance for a sample from Gaussian distribution?

Suppose $X_i$'s are iid Gaussian random variables with mean $\mu$ and variance $\sigma^2$. The distribution of $\sum_i (X_i - \bar{X}_i)^2 / (n-1)$ isn't Chi square. What is its distribution called? ...
7
votes
2answers
258 views

In simple linear regression, where does the formula for the variance of the residuals come from?

According to a text that I'm using, the formula for the variance of the $i^{th}$ residual is given by: $\sigma^2\left ( 1-\frac{1}{n}-\frac{(x_{i}-\overline{x})^2}{S_{xx}} \right )$ I find this hard ...
0
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0answers
9 views

Adequacy of forecasted volatility vs realized volatility. GARCH model

Below I have performed forecasting of volatility, in my simple case of 6 days: ...
0
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0answers
20 views

How to study the property of a score e.g. its variance in R

I'm trying to develop a score for biomarker discovery in two-class high throughput biological data. At this stage the significance of the score (p-value) is estimated by permutation of the class ...
0
votes
3answers
74 views

Calculating the Variance (Standard Error Estimation)

I am studying the book "An Introduction to Statistical Learning: with Applications in R", on page 66 While the book explains how to calculate $\beta_0$ and $\beta_1$, it skips how the actual ...
2
votes
1answer
54 views

First order statistics (min) of n non-identical but independent normal variates [duplicate]

While I have seen papers and posts about mean and variance of n i.i.d normal random variables, I am looking for the first order statistics of $n$ (specifically $11$) normal, non-identical (different ...
0
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0answers
34 views

When are correlation coefficients and variances not enough?

I am reading a paper and found the following, Statistical uncertainties and dependencies are often measured by variances and correlation coefficients, but both uncertainty and dependence can be ...
0
votes
0answers
23 views

How do I relate the variance of a Normally distributed variable to the variance of the exponentiated transform

If I have a Normally distributed variable with a Mean of zero and a given variance, how will this variance relate to the variance of the exponentiated form?
1
vote
1answer
26 views

How to work with conditional expectations and variances?

I have seen this statement in a lecture note : $$E[(Y-f(X))^2\,|\,X]=Var[Y|X]+E^2[(Y-f(X)\,|\,X]]$$ If $Z,X$ are random variables, then shouldn't be $Var[Z|X]=E[Z^2|X]-E^2[Z|X]$?In which case ...
0
votes
0answers
9 views

unconditional volatility from an Arma-Garch process

I know that one can easily get variance (unconditional) of a Garch (r,s) process : $\sigma^2= \frac { \alpha_0 } { (1- \Sigma_{i=1}^r \alpha_i - \Sigma_{j=1}^s \beta_j ) }$ However I am struggling ...
1
vote
1answer
58 views

Is there a kind of random walk process for wich the reciprocal of the variance is a sum of reciprocals of variances of compound processes?

Context: The variance of a sum of independent random walks is a sum of their variances: $\sigma^2 = \sigma_1^2 + \sigma_2^2$. In case of a dependent random walks with bivariate normal distribution it ...
5
votes
2answers
96 views

Detecting whether website visits are automated

I am trying to detect automated visits to a website. A typical data set for an automated client is of the form: ...
0
votes
1answer
26 views

Random variable variance

I have the model $y_i=\beta_1+\beta_2 X_i+ u_i$ where $u_i\sim\text{iid } N(0,\sigma^2)$. I estimate $\beta_1$ and $\beta_2$ by drawing a straight line between the first $(x_1,y_1)$ and last dot ...
3
votes
1answer
50 views

Variance of random variable for normal distribution

How do I find the variance for $z_n=\prod_{i=1}^n(1-k_i e^{a_i x})$ where $x$ is the random variable with a normal distribution and is the same for all $i$ (which is a subscript for time dependency ...
1
vote
0answers
18 views

Calculate the variance explained in matrix Y by matrix X

I have two matrices corresponding to the same set of $n$ samples, with $j$ and $k$ variables, respectively ($j > 10000$, $k > 10000$). $X$ is an $n \times j$ matrix and $Y$ is an $n \times k$ ...
1
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0answers
13 views

Homogeneity of variance for time variable

I have four groups of plant treated with different temperatures and I conducted repeated measurement on their growth rate. I use ANOVA with Mixed Model to analyze the data by specifying both ...
2
votes
1answer
39 views

In OLS is it methodologically correct to use the variance of a variable as an explanatory variable?

Are some OLS assumptions not satisfied if I use the variance of a variable as a proxy of uncertainty in a regression? For instance, would it be methodologically correct if I use moving averages of ...
0
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0answers
56 views

Are time series variances additive?

I am trying to measure and quantify risk, variance, and standard deviation over a time period $T$. It is broken into two sub-periods $t_1$ and $t_2$. $X_1$ is the time series for $t_1$, and $X_2$ is ...
1
vote
1answer
64 views

Proof of asymptotic variance

How do you prove that $X_n - E[X_n] = O_p(\sqrt{Var(X_n)})$ It's used in my textbook and I don't know where they get it from.
0
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0answers
25 views

P-value multiplied by 2 for two tail hypotheses F-test

There is a following answer to an exercise in a text book: The hypotheses are \begin{align*} H_0 &: Var_1 = Var_2\\ H_1 &: Var_1 \neq Var_2 \end{align*} Computation: $f = 78.800/913.333 = ...
3
votes
0answers
26 views

Is there a test/technique/method for comparing principal components decompositions between samples?

Is there any methodical way to compare the directions, magnitudes, etc of PCA results for different samples? I'm leaving the nature of the test deliberately vague because I'd like to hear all the ...
6
votes
0answers
117 views

Applying a variance-stabilizing transform to a fitted function (rather than data)

Outline I'm working with data corrupted by a mixed Poisson-Gaussian noise model (for example with images gathered in astronomy or electron microscopy), and have been using the generalized Anscombe ...
4
votes
3answers
54 views

Analytic or sample standard deviation with binomial data

I've been looking for recommendations on whether it's better to use the sample standard deviation (SD) for a binomial distribution or use the analytic SD (or variance). It's for experiments with ...
0
votes
0answers
18 views

Can you combined two sources with difference variance to reduce error? [duplicate]

I have two samples of data each estimates of a position x, y with Gaussian noise. One source has a larger variance than the other. Is this source in any way useful ...
5
votes
1answer
69 views

Why are Winsorized random variables independent?

While studying trimmed mean I understood that if I have some random variables $X_1, X_2, .., X_n$ by ordering them and trimming, the variables are no longer independent. However it is said that "by ...
0
votes
0answers
32 views

Finding the variance when you know the population mean

So my basic understanding is that I may end up in one of the following situations. I have a sample mean and therefore calculate a sample variance I have a population mean sand calculate a population ...
0
votes
0answers
31 views

model noise with Gaussian(0, Gamma)

Can anyone help me in understanding what kind of noise is it? Noise = Normal(0, v) v = GammaFromShapeAndRate(alpha, beta) I mean what is the advantage of making a normal noise with a Gamma ...
1
vote
1answer
21 views

Is there a value to show how fragmented is a group?

I would like to know if there is a way to calculate a number that can show how fragmented is a group? It should be something like "variance of categorical data"? For example I want to see how ...
3
votes
1answer
81 views

Should you report variance of asymmetrical data, such as ratios?

I have measured the time taken to solve a problem by algorithm $X$ and by algorithm $Y$. It takes a quite long time, so I have only 10 data for each algorithm: $$ X : ( x_1, x_2, \dots , x_{10}) \\ Y ...
0
votes
0answers
26 views

Answering Research Questions with Multi-level Structural Equation Modeling (ML-SEM)

This time, I have a more theoretical than computational predicament. I have a path model that I am interested in testing on a data set with two groups. It is a very simple two predictor model outlined ...
0
votes
2answers
30 views

Model regression of means different size and variance

I want to explain the relation between getting a reply and posting in a e-commerce. I want to know how much a reply increases postings. I know I could do a regression of postings=f(replies) but the ...
1
vote
1answer
27 views

Variance of a variable constructed from parameter estimates and predicted values of a linear regression

My data set is an annual panel data set on individual income, the year of unemployment and a number of demographic variables. I run an OLS regression of the form $y_{it} = \sum _{j=1} ^n D_{j,it} ...
0
votes
0answers
32 views

Mean and variance of a general multivariate skew normal distribution

I have a problem about a general multivariate skew normal distribution. There is a $p\times 1$ vector, $\mathbf{y}=(\mathbf{y}_1',\mathbf{y}_2',\ldots,\mathbf{y}_n')',p>n$, which has the density as ...
3
votes
4answers
41 views

Conditional variance - $Var(X + U | X) = Var(U)$?

I am wondering if the following equality holds - $Var(X + U | X) = Var(U)$? where $X$ and $U$ are two independent random variables? It seems can we say $Var(X + U | X) = Var(X|X) + Var(U|X) = ...
2
votes
2answers
29 views

Multiple comparisons with t-test: one group with different variance

If I have 3 groups that I want to compare with a t-test (correcting for multiple comparisons afterwards) but one of the groups has different variance than the other two, should I use a Welch ...
1
vote
0answers
25 views

Mean accuracy for sum of squares/variance

Formality says that when computing the sample variance or sum of squares one computes a sample mean with the sample data given. If for some reason I had access to a better estimate of the mean (from ...
0
votes
0answers
28 views

Web Videos that can provide me with a better understanding of statistical concepts

I have an exam coming up and I would like to know are there youtube videos/playlist or any videos online that can explain the following concepts below in a simple manner. The concepts are: ...
0
votes
0answers
26 views

Beta-t-EGARCH model, what is the unconditional variance

I am trying to implement Beta-t-EGARCH model in R, however, I fail to understand what is the unconditional variance of this model. I know for simple GARCH model, unconditional variance is ...
3
votes
3answers
67 views

What do I need in order to draw conclusions from this data?

I have three techniques, called A, B and C. Each can be used independently when trying to perform four related tasks (Tasks 1, 2, 3 and 4). I have run lots of tests, trying all combinations of each ...
0
votes
0answers
151 views

Calculating average variance extracted (AVE) in AMOS discriminant validity

I was asked to calculate average variance extracted (AVE) to establish discriminant validity; I've ran CFA but ask how to calculate AVE following Fornell & Larcker’s (1981) test when having two ...
1
vote
1answer
60 views

How to calculate the variance for mean of means?

I have been reading up on how to calculate variance for different situations and the following has me confused….. If I take a number of samples (e.g. choose 5 kids in a class and ask them how many ...
0
votes
0answers
43 views

How to convert daily variances to a monthly volatility and then annualize it?

I work out the conditional variance using a GARCH model based on daily returns as follows: ...
2
votes
0answers
24 views

Correlation fitted-residuals in mixed models

IN OLS linear models, fitted (predicted) and residuals scores are uncorrelated. I was under the impression that the same held true in mixed models. However, I have here an example model where fitted ...
0
votes
0answers
10 views

Adding the variances of spatially correlated data

I have a geographical grid, for every cell in that grid I know that the variable I am looking at is normally distributed and I have its mean and variance. Now, imagine I am looking at an individual ...