Questions tagged [variance]
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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The Variance Covariance Matrix of an Estimator Stacking Two OLS Estimators
I am looking for how to derive the variance covariance matrix (henceforth, VCOV) of an estimator stacking two OLS estimators.
Suppose that we have two OLS estimators:
$$\hat{\alpha}\sim N(\alpha,\;\...
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Calculate variance on not normal distributed groups
Is there a way to calculate if the variances of two groups are equal when one of the groups is not normal distributed?
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Calculating sampling variance in multilevel meta-analysis
I'd like to conduct a three-level meta-analysis using R. I see that several papers recommend calculating the level 1 sampling variance using Cheung's 2014 formula 14. However, I'm wondering if it is ...
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Can the F test be generalized for a null hyp where variances are unequal?
Sorry for the question, maybe this appears in a book a little more advanced than the ones I have seen.
Suppose we have two samples from normal distributions with sample variances $S_{n,1}^2$ and $S_{m,...
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How to obtain the variance from an ANOVA table
I was under the expression that the mean square error (MS) of a 1-way anova table is the estimated variance, and that the between and within group variance add to the total variance. However, using an ...
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Variance explained at each level of a categorical variable
I have a deep learning regression that predicts the value of a continuous variable Y. There is a categorical variable Z that has ...
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How to incorporate uncertainty when inferring from a sample?
My question relates to the use of a representative sample to make inference regarding the number of individuals with a certain characteristic in a population. I am analysing a study that attempts to ...
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Relationship between $Var(X)$, $Var(Y)$ and $Cov(X,Y)$ for random variables with zero mean
I have two correlated random variables $X$ and $Y$, both with zero mean.
Are there any relationship/constraints between $Var(X)$, $Var(Y)$ and $Cov(X,Y)$, apart from the obvious $Var(X) > 0$ and $...
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Trying to understand the math behind Avi Wigderson's simple example
In his celebrated talk on randomness and pseudorandomness
https://youtu.be/Jz1UoAWD80Q?t=366
legendary mathematician Avi Wigderson makes the powerful statement that sampling is perhaps the most ...
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How can I estimate the variance of the error terms in a conditional/multinomial logit model?
Conditional/multinomial logit models(CML) can be esimated by the Maximum Likelihood Estimation(MLE). The likelihood would consists of choice probabilities:
\begin{equation}
P_{ij}=\frac{e^{V_{ij}}}...
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Validity of assumptions to compare groups with different distributions
My experiments result in four different groups of data. Here is one example:
I wanted to compare the means and variances of these groups. I learnt that a test such as Welch's ANOVA with a Games-...
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Bounds on the conditional variance of a truncated binomial
I have a binomial variable $R$ drawn from $binom(N, p)$, and I'm interested in the variance of $R$, given $R \ge Q$. The pmf of this variable $R^*$ is
$$
\phi_{R^*}(l) = \frac{\phi(l, N, p)}{P}
$$
...
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Measuring variability of log in hours
I'm working on measuring the usage patterns of an app for a population of users. I want to find out if they usually log in at the same hours or if their usage times vary a lot. The variance of the ...
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Use of PCA to model variance for dependent variables
I am working on a math problem with some friend and there is some disagreement on the meaning of what we are doing. We have 3 independent variables measured tens of thousands times and we have a model ...
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Is "Information" somehow Related to "Variance"?
Recently, I have learned about the principle of Maximum Entropy with regards to Probability Distribution (https://www.youtube.com/watch?v=2gTrsLVnp9c) - in particular, when certain "information&...
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Are there possibilities to determine 95% confidence interval for right skewed data?
The dataset that I'm using for my thesis is right skewed. It is about lead times (days) I tried log10 transforming it in SPSS but it still does not meet the requirement p>0,05 (Shapiro-wilk). So ...
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How to approximate MAE of monthly values from MAE of daily values?
Suppose I have the Mean Absolute Error (MAE) of daily values for a period of, say, 1 year. Assume the errors are normally distributed.
The value for a month is equal to the sum of the values for each ...
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Quantile Variance and Mean
As I read articles related to quantile measurements of moments, I only found quantile skewness and kurtosis definitions. However, I couldn't find any quantile estimation of variance or mean. Is it ...
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Can adding a Level 2 predictor impact the Level 1 variance?
Heck et al (2013) p.137 write:
[O]ne approach often used is to examine the change in residual
variance that occurs by adding predictors within a sequence of models.
The analyst begins with the ...
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Find the principal component and the proportion of the total population variance explained by each when the variance covariance matrix is given
I can understand the part where we have to find the principal component from the variane covariance matrix- find eigen values, make eigen vector and normalise. The principal component would be ...
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Intuition relating OLS Variance-Covariance matrix and the OLS sampling variance equation
I'm looking at the variances of OLS slope estimators and I found the following equation that holds under the Gauss-Markov assumptions. Suppose that we have a multiple regression model of the following ...
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Parameter estimator and its variance estimator covary
In classic linear regression, estimators of the coefficients of the mean model and the estimator for the residual variance are uncorrelated. However, what to do when this is not the case, for instance ...
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The variance of the weighted median and optimal weights
The median $\tilde{\mu}$ of a sample in many ways is analogous to the sample mean $\mu$.
Both are an estimate for the population median or mean respectively, and both approach a Gaussian distribution ...
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Intuition for why mean of lognormal distribution depends on variance of normally distributed rv
Let $X\sim\mathcal{N}(\mu,\sigma^2)$, which is a normal distribution. Then, $\text{exp}(X)\sim\text{Lognormal}(\mu,\sigma^2)$, and its mean is
$$
\mathbb{E}[\text{exp}(X)]=\text{exp}\left(\mu+\dfrac{\...
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Variance of random walks in time series analysis [duplicate]
“For a random walk stochastic process, the variance is infinite.” Do you agree? Why?
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EFA: Eigenvalues or Loadings after extraction (SPSS)
I've been doing a EFA with ML extraction and Promax rotation, whereby three factors were extracted. For reporting the results, I was wondering whether to use the 'Initial Eigenvalues' or the '...
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variance of Y based on a simple linear regression of X in which the slope and intercept are not constants
Consider a linear regression $y = aX + b$, where mean(a) = 5, SE(a) = 0.5; and mean(b) = 3, SE(b) = 0.1. When a and b are constants, $Var(Y) = a^2 Var(X)$. Do the SE's make a and b non-constants? If ...
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How is the difference between 2 normal distributions a normal distribution? [duplicate]
I've learned that if we sum or subtract 2 normal distributions, the result would be another normal distribution with $\mu=\mu_{1}\pm\mu_{2}$ and $\sigma=\sqrt{\sigma_{1}^2+\sigma_{2}^2}$
https://www....
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Variance functions for Poisson, negative binomial
I'm having some trouble understanding how the variance functions of the Poisson or negative binomial tie in to the standard errors on the coefficients. I'm mentioning 2 models because I'm not sure if ...
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How do I prove the general formulation of LRV to verify that LRV for AR(1) is in fact (σ²)/(1-α)²
I understand the equations separately but don’t know how they are connected! Please give me an explanation / hint
Given the AR(1) structure, the long run variance (LRV) of Xt is known to be (σ²)/(1-α)...
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Examining stationarity, mean and variance of time series
Hi guys, I encounter this question for a Business Forecasting module and I am very confused by it. Firstly, this looks like an autoregressive model of order 1. From the looks of it, the φ coefficient ...
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How is the standard deviation of random effects estimated?
For example, the sd of the random intercept reported by lme4 when I use lmer or glmer is much higher than if I just calculated the sd on the list of intercepts generated from ...
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How to correctly analyse a reduction in variance, and a trend towards a desired value over time?
I have a dataset consisting of some integer values collected over a series of five games, and was hoping someone might be able to recommend an appropriate test to determine whether:
the interquartile ...
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Finding Variance of Proportional Hazards Regression Coefficient Estimates in Weibull Regression
So I am doing Weibull regression in R with the exponential relative risk function. The proportional hazards model formulation assumes that the hazard rate is given by $$\alpha(t;a,\sigma, \boldsymbol ...
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Mean term in simple linear regression
I am trying to derive the expression for the $E(y_i \epsilon_i)$ in simple linear regression. I substitute using $Cov(X,Y) = E(XY) - E(X)E(Y)$, so $E(y_i \epsilon_i) = Cov(y_i , \epsilon_i)- (E(y_i)...
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Expectation of indicator variable squared to compute variance of a binomial
$$ X \tilde{} Bin(n,p)$$
I know that X can be written as the sum of indicator variables like this:
$$Then ~ X = I_{1} + ...+ I_{n}, where,~ I_{i} = 1 ~ if~success,~0~ otherwise.$$
This is quite ...
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How do I derive the variance of OLS estimators when I have dummy explanatory variables?
I know this isn't the smartest question, however I need to derive the variance of the OLS estimators in a Simple Linear Regression Model when the explanatory variable is a dummy one and all the ...
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Variance of the sum of multiple random number generators
Let's assume I have "n" random number generators, each one has a different variance value, but has the same mean value, zero.
If I generate "n" random numbers with these generators,...
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Is this a sufficient statistic for variance?
I have $X_1,\dots,X_n,X_{n+1}\overset{iid}{\sim}F_X(x)$, where $F_X$ has a finite mean $\mu$ and variance $\sigma^2$.
If I calculate $\bar X_n = \dfrac{1}{n}\sum_{i=1}^n$ and $S^2_n = \dfrac{1}{n-1}\...
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Variance for exponential smoothing
I want to obtain the analytical expression of variance for simple exponential smoothing . Please help verify and see if the expression could be further simplified , thanks .
Assume the discrete time ...
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Compare within subject variation between groups
I have run two experiments (exp). In each experiment, we have measured the same property in a number of subjects twice (V1 and V2). The number of subjects are different in the two experiments. and the ...
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Variance estimate in a gillespie simulation
Lets say I simulate a immigration-death process:
$P(X(t + \delta t) = x+ 1 | X(t) = x) = \lambda \delta t$
$P(X(t + \delta t) = x-1 | X(t) =x) = v x \delta t$
using a Gillespie simulation - I pick a ...
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Which raw data to include for heterogenous autoregressive (HAR) model
I constructed the realized variance of bitcoin returns per day from 8-10-2015 to today. The realized variance is calculated by taking the cumulative squared intra-day returns. 5-minute high frequency ...
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Is the variance of the distribution of $A/B$ directly related to the correlation of $A$ and $B$
I have a large data set in which I am trying to produce an effective plot to show the correlation between fields $A$ and $B$ for multiple different groupings, where $A, B \gt 0$. A correlation matrix/...
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Variance of OLS estimator with binary treatment
I know that in general, given a (stacked) regression of the form
$ y = X \beta + \epsilon$, where $\mathbb{V}(\epsilon_i) = \sigma^2 \forall i$, then letting $\hat{\beta}$ denote the OLS estimate of $\...
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How to optimize transform function to make the variance and mode of the variance roughly stable?
$ curl -s https://i.stack.imgur.com/rl1eT.gif | tail -c +43 | zcat
x y
x2 2030667
x2 2343967
...
I have data like the above. If you compute the mean and ...
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Why does "Hoeffding's bound greatly overestimates the probability of large deviations for distributions of small variance"?
I've read in a paper using Hoeffding's inequality to derive a bound on the probability of the difference of means of two samples being larger than a threshold that "Hoeffding's bound greatly ...
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Can I use a least squares polynomial fit on residuals to estimate variance?
Given some residuals, is there any problems with using a least squares polynomial fit to estimate the variance?
The resulting fit looks like this using ...
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Variance estimate for Student's t-distribution with heavy tails
The variance of a Student's t random variable when the degrees of freedom $\nu$ is greater than $2$ is $\nu/(\nu-2)$. In R, when I try to estimate the variance using the usual estimator $$1/(n-1)\sum_{...
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How do I calculate the variance of a Hermitian form?
Suppose $\mathbf{x}\sim\mathcal{CN}\left(\mathbf{0},\mathbf{I}_n\right)$ is a circular complex Gaussian random vector, and $\mathbf{Q}$ is a Hermitian matrix. How do I calculate the variance of the ...
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