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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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12 views

Understanding an undocumented weighted variance bias correction

Can anyone explain, intuitively or otherwise, the following bias correction for a weighted sample variance? (The wikipedia page 1 does not have the answer.) $$s^2 = \sigma^2 \frac {W^2} {W^2 - N}$$ ...
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7 views

which control chart can use for error variance/

I have a series of error variances from the model With what type of univariate shewhart control chartI can control monitor error $variance(\sigma^2)$?
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1answer
14 views

Relation between number of features, higher order polynomial features and overfitting

Recently I came across an information stating that, if we have too many features, the model is most likely to overfit. I not sure why exactly this is happening. I mean, if I don’t use any higher order ...
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0answers
33 views

Confidence intervals and variance for ordinal scale set [0-5]

We have a known sample of data coming from a multiple choice ordinal scale survey question with scores from the set [0,1,2,3,4,5]. The mean of this sample is 3.941 ...
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0answers
15 views

How to estimate sample mean/variance from another, smaller sample?

Let's say I record some variable from Sample 1 of size = 10 and find that mean = 10 and ...
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0answers
18 views

Explain why $df(S_{xx}) = 2$ [duplicate]

Consider $X = \{x_1, x_2, x_3\}$. Then $\bar{x} = \frac{1}{3} (x_1 + x_2 + x_3)$ with degrees of freedom, $df(\bar{x}) = n = 3$. Now consider the total variation in $x$: $$S_{xx} = (x_1 - \bar{x})^2 ...
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1answer
26 views

Asymptotic distribution of sample variance via multivariate delta method

I was trying to get the asymptotic distribution of sample variance using multivariate delta method and without normality assumption. So I defined the random vector $ z = \left( \begin{matrix} X \\...
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0answers
20 views

Cross validation and the Bias Variance trade-off

So I know that there have been a lot of questions about this topic but I try to understand it from a bit more theoretical/mathematical point of view. I have some basic questions of how cross-...
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8 views

Measure of goodness of 2D data points for classification

Is there a good measure of how good my dataset is for the task of classification. The ideal scenario for classification is that points for each class should be clustered closer and each cluster of ...
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1answer
27 views

Graphical proof of variance decomposition for linear regression

Suppose we aim to predict $Y$ from $X$ using the linear regression model $Y = mX + b$. There is a standard variance decomposition: $$\operatorname{Var}[Y] = \operatorname{Var}[\widehat{Y}] + \...
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0answers
19 views

Variance estimator for sum of random variables [duplicate]

I want to compute the variance of $X$, which is the sum of 4 random variables $A, B, C, D$, i.e. $X=A+B+C+D$ For performance reasons (the overall context is that I use convolutional layers in PyTorch)...
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0answers
20 views

Choice of residual function for least squares error minimization

Good morning, I have the a set of data $(\sigma,D,\alpha_0)_i$, $i=1...n$ data. I want to determine two parameters $K_{IC}$, $C_f$ in the basic equation given as $K_{IC} = \sigma \sqrt{D} k_0(\...
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17 views

Defining “variance” of a partially defined random variable

Elsewhere within CrossValidated the following survey sampling problem was mention. To each member $i$ of a population $\{1,\ldots,N\}$ there is assigned some value $c_i$ whose average $\mu=(c_1+\cdots+...
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1answer
26 views

Finding the variance, summing up the difference between the mean and each value of X is not outputting zero as it should

I am new to stats, I am trying to find the variance of a very simple set of numbers, Z = { -2, 4, 7 }, I calculated the mean and I Got 9, the sum of each Z(i) the Iteration and the mean not 0, but 4 ...
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1answer
13 views

Question on Scale-Location Graph

Hi guys, so I am working on an R assignment and I need to find whether or not one variable depends on the other. First, I want to check for assumptions before doing anything so I produced this graph ...
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1answer
23 views

How to calcualte confidence interval for the residual variance in ANCOVA models

As the question states I need to know how to calculate this. Given variable $Y$ and $X$ with $\operatorname{cor}(Y,x)=r$, the residual variance is: $$(1-r^2)\cdot\sigma_Y^2,$$ which represents the ...
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1answer
23 views

How to perform a simulation of stock investment, capturing the variance?

I am simulating an individual, who invests throughout his lifetime in stocks and bonds. Bonds have fixed returns $r_f = 11\%$. Stocks are highly volatile and have returns $\mu = 22 \%$ and standard ...
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0answers
10 views

Statistical difference between time values.

I am comparing the activity onset times of a bat species across different sites. I have the onset time values for 5 different sites for a period of one month. I want to check if the activity onset is ...
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1answer
37 views

How to prove two models beta variances' relationship

I have two models: 1. $y=bx$ ($a=0$) 2. $y=\alpha+\beta x$. I have to calculate the variance of $b$ and then show that $\operatorname{var}(b)\leqslant \operatorname{var}(\beta)$. The estimate of b is ...
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1answer
18 views

Determine sample size and mean variance

Currently my data looks like this; there're 50 videos, and each video has been viewed and rated by 30 people, and I want to find out if I could have a smaller sample size (n<30) that gives similar ...
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1answer
17 views

Find the mean, variance and others of a “RV = Gaussian RV + Discrete RV + ”?

Since I am solving a preparatory examen to study, it is not clear to me how to approach the question because I don't know what is the specific topic to study rigorously in order to know how to do it. ...
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1answer
32 views

GARCH specification - why are $\sigma_t^2$ and $\epsilon_t^2$ not the same?

Often times people specify the GARCH model as follows: $$ \sigma _{t}^{2}=\omega +\alpha _{1}\epsilon _{t-1}^{2}+\cdots +\alpha _{q}\epsilon _{t-q}^{2}+\beta _{1}\sigma _{t-1}^{2}+\cdots +\beta _{p}\...
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0answers
18 views

within vs between subject variability:LME?

I have multiple time points of data for my subjects and would like to look at a individual variability measure and see if that has a different associations with my predictor than the between-subject ...
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0answers
40 views

Proving that $V(\hat{y}_{x_0}) = \sigma^2\bigg[\frac{1}{n}+\frac{(x_0-\bar{x})^2}{S_{xx}}\bigg]$ [duplicate]

Exercise : Prove that the variance of $\hat{y}_{x_0} = \hat{b_0} + \hat{b_1}x_0$ is : $$\text{Var}(\hat{y}_{x_0}) = \frac{\sigma^2\sum x_i^2}{n\sum(x_i-\bar{x})^2}+\frac{\sigma^2x_0^2}{\sum(x_i-\...
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2answers
49 views

What is the probability that sample variance decreases by adding random Gaussian noise to the variable?

If we assume WLOG that our variable X has mean zero (mean-centered), then this can be stated $Pr \bigg(\sum x^2 > \sum (x-n)^2 \bigg)$ for some random variable $n$ distributed under $N \sim N(0, \...
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0answers
8 views

Estimate variance of next element in heteroskedastic time series

I have a time series $X$ of which I can reasonably assume the mean is constant at zero. However, I know it to be heteroscedastic. Given $X_1$ through $X_N$, I'd like to estimate the variance $\sigma_{...
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1answer
36 views

random effects with very large variance

I'm getting really very large variance for my random effects ...
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1answer
13 views

matrix inequality related to finance

I'm trying to show that, for certain investment strategies, it pays to have more precise estimates of the covariance matrix of your returns. I have always took this for granted, but I've been having ...
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1answer
46 views

What to conclude for the data-set when the variance for principal components is too low or too high?

I am working on analysing and visualizing a dataset having 12 features and came across PCA. I reduced the dataset to 2 principal components which together explain a variance of 18%. I was able to plot ...
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0answers
25 views

Calculating variance and standard deviation of continuous time series

I am trying to calculate the variance and standard deviation of an unevenly spaced continuous time series. Example data: ...
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1answer
26 views

Why are variances of observed variables estimated in Factor Analysis / SEM?

Let's say we have one latent factor L and three observed variables X1, X2 and X3. From the variance/covariance matrix of X1, X2, X3, we create this latent factor that explains the most out of the ...
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40 views

Replacing summation by integral in classical variance of sum formula, is it possible?

It is well known that the variance of the sum of $x_1,...,x_N$ random variables is the sum of their variances plus twice their covariances: $\text{Var} \displaystyle\sum_{i=1}^{N}x_i =\displaystyle\...
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0answers
13 views

How to model a variance in relation to a covariate.

I would need to learn how to model a variance in a parametric way with respect to a covariate, in independent data, from a Bayesian point of view. Can someone give me some basic references to start?
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0answers
15 views

Measures of Variability and/or Polarity Changes for Time Series

I am trying to measure the variability or "choppiness" of a time series but I am aware that standard measures of standard deviation do not apply due to auto-correlations between the observations. I ...
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0answers
22 views

How to optimize ratiometric loss function with variance term in it?

I'm training a neural network (or any ML model with non-convex gradient-based optimization) to predict a continuous outcome variable. Currently, I use the mean squared error loss function, i.e., if $y$...
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0answers
24 views

Why is the sum of two variances is larger than two times the covariances?

I saw the following inequality: $$ \sigma_{X_1}^2 + \sigma_{X_2}^2 \geq 2\sigma_{X_1X_2} $$ and the brief explanation said that it is based on Cauchy-Schwarz inequality. But I couldn't make the ...
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0answers
17 views

Variance of distribution for maximum likelihood estimator

We're looking at maximum likelihood estimators in my stats course at the moment. As I understand it, the idea is that we have some data. We come up with a model. The model has some parameter $\theta$. ...
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0answers
13 views

Ignoring correlation in longitudinal data (Diggle)

I am going through "Analysis of Longitudinal Data" by Diggle, but I am having trouble understanding his succinct explanation of the consequences of ignoring correlation in longitudinal data. Here is a ...
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0answers
6 views

How to analyze the within-person and between-person consistency in a dataset and compare them?

how would I go about analyzing the within-person and between-person consistency in a dataset and comparing them? I have a dataset with driving data of people who use carsharing vehicles. For each row,...
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0answers
40 views

Calculating the Shared Variance from a Correlation Coefficient?

We often square coefficients like the R coefficient in simple/multiple linear regression or standardized factor loadings to get a percentage of variance accounted for by predictor variables. Can the ...
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0answers
27 views

What is the name of this type of plot and what does the shape of the bell and the red line indicate?

I get the basic idea but I don't know what some of the extra stuff is for. Does this type of plot have a name?
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3answers
182 views

Variance of Coin Flips Until H

If we flip a fair coin until we get heads, what is the variance of the number of flips to do this? My attempt is: $$E(flips):=Y=1\times P(H)+(1+Y)\times P(T)$$ $$\Rightarrow Y=\frac{1}{2}+\frac{1+Y}{...
2
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2answers
66 views

Variance being negative

Let $X$ and $Y$ have joint pdf such that $$f(x,y) = 3e^{-3x-y}, 0 < x< \infty, 0< y< \infty.$$ (a) Show that $X$ and $Y$ are independent. (b) Calculuate $Var(X)$. In ...
3
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1answer
113 views

When is the variance of the sum of random variables greater than the sum of the variances?

My professor asked my class to 'qualitatively' analyze the two scenarios with the assumption that there is no previous knowledge held in the concept of covariance (as we have not covered that chapter ...
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0answers
36 views

Robust (Newey West) beta, covariance and variance

Let's start with a simple linear model $$Y_t = β_0 + β_1*X_t + ϵ_t$$ If $ϵ_t$ is serially correlated and heteroskedastic, I can calculate N-W standard error of $β_1$. I have also read in the ...
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0answers
24 views

Simple but tricky problem regarding variance and standard deviation

I am having some trouble figuring out something regarding variance and standard deviation. The problem is the following. Suppose i have a variance of 4 days, if I wanna turn days into weeks I could ...
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1answer
65 views

Simple Random sampling with replacement - Variance

If just a single unit is drawn at random from the whole population and y1 is the value of y for this sampled unit, how can I prove that the VAR(y1)=by (1 − 1/N)σ^2 (where N is the population size and ...
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0answers
19 views

calculating mean and variance of non-stationary time dependent samples

I know normal procedure for calculating mean and variance which assumes that samples are iid.. I first want to know, how to calculate these two parameters if samples are time dependent but time ...
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1answer
45 views

How to measure how “good” or accurate a probability distribution is? Entropy, variance or what?

How can one measure the accuracy of the probability distribution of, say, a physical magnitude? I know one good candidate is the entropy, which measures the amount of information one has about the ...
3
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1answer
51 views

MVUE is unique - wrong proof?

Here is the proof of "MVUE is unique" that my lecturer gave: Now I understand the following: The first expansion is done using the formula for the sum of correlated random variables (https://en....