The expected squared deviation of a random variable from its mean; or, the average squared deviation of data about their mean.
0
votes
0answers
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.)
$$s^2 = \sigma^2 \frac {W^2} {W^2 - N}$$ ...
0
votes
0answers
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 $variance(\sigma^2)$?
1
vote
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 ...
0
votes
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 ...
0
votes
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 ...
1
vote
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 $x$:
$$S_{xx} = (x_1 - \bar{x})^2 ...
0
votes
1answer
26 views
Asymptotic distribution of sample variance via multivariate delta method
I was trying to get the asymptotic distribution of sample variance using multivariate delta method and without normality assumption.
So I defined the random vector $ z = \left( \begin{matrix}
X \\...
1
vote
0answers
20 views
Cross validation and the Bias Variance trade-off
So I know that there have been a lot of questions about this topic but I try to understand it from a bit more theoretical/mathematical point of view.
I have some basic questions of how cross-...
0
votes
0answers
8 views
Measure of goodness of 2D data points for classification
Is there a good measure of how good my dataset is for the task of classification. The ideal scenario for classification is that points for each class should be clustered closer and each cluster of ...
1
vote
1answer
27 views
Graphical proof of variance decomposition for linear regression
Suppose we aim to predict $Y$ from $X$ using the linear regression model $Y = mX + b$. There is a standard variance decomposition:
$$\operatorname{Var}[Y] = \operatorname{Var}[\widehat{Y}] + \...
0
votes
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)...
0
votes
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(\...
0
votes
0answers
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+...
0
votes
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 ...
0
votes
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 ...
0
votes
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 ...
0
votes
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 ...
0
votes
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 ...
2
votes
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 ...
0
votes
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 ...
0
votes
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.
...
1
vote
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:
$$ \sigma _{t}^{2}=\omega +\alpha _{1}\epsilon _{t-1}^{2}+\cdots +\alpha _{q}\epsilon _{t-q}^{2}+\beta _{1}\sigma _{t-1}^{2}+\cdots +\beta _{p}\...
0
votes
0answers
18 views
within vs between subject variability:LME?
I have multiple time points of data for my subjects and would like to look at a individual variability measure and see if that has a different associations with my predictor than the between-subject ...
0
votes
0answers
40 views
Proving that $V(\hat{y}_{x_0}) = \sigma^2\bigg[\frac{1}{n}+\frac{(x_0-\bar{x})^2}{S_{xx}}\bigg]$ [duplicate]
Exercise :
Prove that the variance of $\hat{y}_{x_0} = \hat{b_0} + \hat{b_1}x_0$ is :
$$\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-\...
2
votes
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, \...
0
votes
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_{...
0
votes
1answer
36 views
random effects with very large variance
I'm getting really very large variance for my random effects
...
0
votes
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 ...
0
votes
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 ...
1
vote
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:
...
0
votes
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 ...
1
vote
0answers
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\...
-1
votes
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?
0
votes
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 ...
1
vote
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 $y$...
2
votes
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 ...
0
votes
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 $\theta$. ...
0
votes
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 ...
0
votes
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,...
0
votes
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 ...
0
votes
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?
1
vote
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:
$$E(flips):=Y=1\times P(H)+(1+Y)\times P(T)$$
$$\Rightarrow Y=\frac{1}{2}+\frac{1+Y}{...
2
votes
2answers
66 views
Variance being negative
Let $X$ and $Y$ have joint pdf such that
$$f(x,y) = 3e^{-3x-y}, 0 < x< \infty, 0< y< \infty.$$
(a) Show that $X$ and $Y$ are independent.
(b) Calculuate $Var(X)$.
In ...
3
votes
1answer
113 views
When is the variance of the sum of random variables greater than the sum of the variances?
My professor asked my class to 'qualitatively' analyze the two scenarios with the assumption that there is no previous knowledge held in the concept of covariance (as we have not covered that chapter ...
0
votes
0answers
36 views
Robust (Newey West) beta, covariance and variance
Let's start with a simple linear model
$$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 ...
-1
votes
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 ...
0
votes
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 ...
1
vote
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 ...
0
votes
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
votes
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....
