Questions tagged [variance]
The expected squared deviation of a random variable from its mean; or, the average squared deviation of data about their mean.
176 questions from the last 365 days
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How to estimate population variance from a mixed model with a categorical variable?
I supposed it is a basic question, but I'm stuckle on it and I can't find the solution.
I have a date base with the slurry dry matter content from different pig production stages (CATEGORY), also, ...
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Does it mean that we don't need a normal assumption for using sandwich estimator in normal linear regression?
According to this post,
the blogger uses the theory of estimating equations to construct the robust sandwich variance estimator.
In this post, it said that:
Now we ...
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Derive gamma-parameters from preset R^2 in mixed models
For a simulation study in R, I want to select the effect sizes according to a preset $R^2$.
Consider this two level random intercept mixed model, with one L1 predictor $X_{ij}$ and one L2 predictor $...
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Compare variance explained between 4 x 300 multiple linear regressions
I calculated four different multiple linear regressions (model 1-4), each with a different set of independent variables. Model 2 contains all the independent variables of model 1, plus some extra. ...
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Finding the variance of a stochastic process
This is part 2 of this question Calculate the mean and variance of a stochastic process?
For the Polya Urn problem, I am trying to understand why the ratio of the variance is:
$$\operatorname{Var}(X_n)...
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Variance estimation from dependent data
I would like to estimate the variance of a zero-mean normal distribution, $x_n \sim \mathcal{N}(0, \sigma^2)$, from data of the form $y_n = u_n x_n$ where the input $u_n \in [u_{\min}, u_{\max}]$ can ...
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If $n\operatorname{var}( \sum_{ij}M_{ij}v_{i}v_{j}) = (\sum_{i}v_{i}^{2})^{2} - \sum_{i}v_{i}^{4}$ for any $v_i$, what can we say about $M_{ij}$?
Let $M_{ij}$ be a real random matrix, constrained to be symmetric $M_{ij}=M_{ji}$, and with zero diagonal, $M_{ii}=0$.
Suppose we know that, for any real vector $v_i$, the following holds:
$$\...
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If $\operatorname{var}\left(\sum_{ij}A_{ij}v_{i}v_{j}\right)=0$ for any $v_i$, then $\operatorname{var}(A_{ij})=0$?
Let $A_{ij}$ be a random matrix, satisfying $A_{ii}=0$ and $A_{ij}=A_{ji}$. Suppose we know that $\operatorname{var}\left(\sum_{ij}A_{ij}v_{i}v_{j}\right)=0$ for any vector $v_i$. What can we say ...
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Compare two variances
I am reading this paper
I have difficulty understanding Section 6: A Linear Time Statistic and Test.
At the beginning, they claim that $\text{MMD}^2_l$ has higher variance than $\text{MMD}^2_u$ (we ...
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Predicting the probability distribution of a deterministic dataset
In classical machine learning regression, we often assume the target variable $y$, given an input $x$, follows a probability distribution, allowing us to model and predict not just the expected value ...
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R issue with the same random effect variance value (sigma^2) in sjPlot::tab_model() for two separate glmmTMB models
I have two glmmTMB models fit with binomial distributions that I am attempting to display their model summary output using sjPlot::tab_model()
Databases, Models, and tab_model() code
...
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exploratory factor analysis, oblique rotation, variance explained
The question how to compute the variance explained by a factor model obtained through exploratory factors analysis pops up from time to time. A summary with many possibilities is here: Calculating ...
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Variance of product of multiple i.i.d. random variables? [duplicate]
Definition: Random variables X1, X2, ..., Xn are said to be independent and identically distributed (i.i.d.) if they are independent, and they have the same marginal distributions:
FX1(x)=FX2(x)=...=...
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Learning to do the parametric bootstrap
I learned about the parametric bootstrap (Can we bootstrap regression coefficients instead of data?) and I am interested in applying this method to determine the confidence interval on the ratio of ...
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Maximum Variance of 3 Numbers in a Range
If I have a set of 3 numbers $(x, y, z)$, all between $A$ and $B$ inclusive (e.g. $A = 0 $ and $B = 1$), what would the maximum variance be? Intuition says it would be (e.g.) $0.1666...$, given by $x =...
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Can we bootstrap regression coefficients instead of data?
I have a question about using the bootstrap in situations (e.g. Confidence intervals for the ratio of marginal effects? (GAM Regression)) where the traditional bootstrap method might be complicated (e....
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Comparing two samples with same number of observations and having same mean but different variances
Given two different set data samples have same mean and same number of observations; if their variances are same, what can be concluded? Also if both variances are different what can be concluded?
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Connecting two different meanings of "degree of freedom"
I have heard at least 2 meanings of "degree of freedom".
The parameter in a t-distribution.
The the number of values in the final calculation of a statistic that are free to vary (like ...
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How to test for equal variances of correlated observations?
Let $r$ be a vector valued random variable with mean zero and variance $\Omega$.
Let $r_t$ denote a specific observation of $r$ at time $t$.
$\Omega$ is unknown but I have 2 estimates of it: $\Omega_a$...
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Variance of weighted average of 𝑛 correlated random variables
This answer explains how to calculate the variance of an average of n correlated random variables. How can I do it for a weighted average of n correlated random variables? My random variables are ...
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How to separate 2 variances from observed variance?
I have that I broke down to the following:
var(predicted_conc) = actual_conc*var1 + var2
Note that the random variable generators are independent, hence variance is added not standard deviation.
I run ...
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Unbiased Variance MLE Distribution
If you take $10000$ samples from a normal distribution, the unbiased variance MLE (with Bessel's correction) is
$$\hat{\sigma}^2 = \frac{1}{9999}\sum_i (x_i - \hat{\mu})$$
Apparently the distribution ...
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Why is the second assumption (i.e., known population variance) unrealistic when calculating Z-interval for a mean?
I'm learning the calculation of confidence interval about the mean by Z-interval. The lecture said that:
... the second assumption about the population variance being known is
unrealistic. After all, ...
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Clarifying the default "standard error" for error bars in Microsoft Excel/Powerpoint plots (calculated without N or SD) [closed]
I have noticed that Excel allows you to toggle "error bars" for any given plot and one of the options is to have the error bars denote standard errors. This is peculiar since if you do a ...
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Is it possible for the residual variance in a model to be greater than the total variance of the variable being modeled?
I've fitted a linear regression in R with svyglm from the survey package. The data is weighted, and the model uses a ...
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Cross-fitting seems to always reduce asymptotic variance for estimators converging slower than $\sqrt{n}$ - how can this be true?
Setup: Imagine the situation where you for a fixed value of your covariates have a regression estimator $\tilde{f}$ based on $n$ i.i.d. observations which is asymptotically normal with convergence ...
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Variance of MLE's in mixture distribution
I am studying mixture models, and I am interested in calculating the variance of the estimators using maximum likelihood. How is the variance calculated in this case? I already implemented the EM ...
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How do I estimate the mean and variance from data?
I have made a periodogram (plot given below) from some 1D data, and would like to estimate the bias and variance of it. because by minimizing both I could select the ideal window size for calculating ...
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how do I compute radial variance given sigma_x, sigma_y given that x and y are uncorrelated?
sigma_x, sigma_y are given and sigma_xy = 0.
How can I convert coordinate system for covariance matrix from cartesian to polar and by that compute sigma_rho?
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When can bagging actually lead to higher variance?
Under the Gauss-Markov assumptions for linear regression, the ordinary least squares estimate (OLS) famously has the minimum variance amongst all unbiased linear estimators.
"Bagging" in ...
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Intraclass correlation -- which one?
I have data collected from an employee survey, in which employees are asked to rate various aspects of their work experience (like engagement, collaboration, and teamwork). Each row is a record of an ...
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Calculating mean variance between double determined measurement of random variable
I have two sets of data, measuring a varible that changes at random (concentration of a gas). The measurement are double determined, providing two data points for each measurement.
I would like to ...
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Detecting Volatility Clusters in Time Series, Stock Returns (%) in particular
My primary objective is to detect the presence of volatility clusters in financial time series, stock returns (%) in particular. So, it can be translated into the detection of "conditional ...
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How do we stop bayesian estimates from being overconfident?
I posted this question today about strategies for regression with small sample sizes. I thought Bayesian regression might be a good choice here: Bayesian regression for correcting small sample sizes
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How do I compute the Standard Error for summed percentages?
I feel profoundly stupid for having to ask this question--it feels like the answer should be obvious, or at the very least that it should be easy to find on the internet, but so far I have been unable ...
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Error in derivation of variance of $\beta_1$ in SLR [duplicate]
I'm trying to derive the variance of the slope parameter for a simple linear regression in the following way, however I'm running into an issue I don't know how to resolve. Define $y_i=\beta_0+\beta_1\...
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variance of known finite population from all possible bootstrap sample means
A question I know has little practical interest but I was asked this and have been stuck for a day thinking about it.
If we take the set of all possible bootstrap samples size n from a small/finite ...
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Bounding the variance of random variables which solve a linear equation
Consider a matrix $\boldsymbol{M} : \mathbb{R}^{N\times N}$ where every element $M_{ij}$ is a continuous i.i.d. random variable of unspecified distribution, but with known mean and variance. Consider ...
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Welch-Satterthwaite degrees of freedom (combining rule for indirect comparison)
In Network Analysis, an indirect comparison of the mean difference between treatment "A" and "B" from different studies over a common reference treatment "C" is made by:
$...
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Second order statistics of sample statistics for random vectors
Good morning.
I have a set of iid random vectors $\{\boldsymbol{X}^i\}_{i=1}^N$, whose expected value is $\mathbb{E}[\boldsymbol{X}^i] = \boldsymbol{\mu}$ and whose variance - covariance matrix is $\...
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Coefficient of Variation between two ratio metrics
I want to compare which metric is more stable (cost per impressions vs. cost per video view).
I have used CV (coefficient of variation) and looked for which metric CV is lower for the same campaign ...
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Beta hat conditional variance - Hansen Econometrics
I'm working through Econometrics by Bruce Hansen, and I'm not sure how to get to his conditional variance proof on page 90.
Hansen says:
For any $n \times r$ matrix $\mathbf{A} = \mathbf{A}(\mathbf{X})...
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Monte Carlo simulation with Importance Sampling - variance of estimator vs weighted variance
I am using Monte Carlo simulations associated with Importance Sampling and I have some difficulties interpretating the variance estimator:
Using a dummy example extracted from here, I use Monte Carlo ...
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If the errors are homogenous but non-normal, can the linear estimator be BLUE?
Under the Gauss-Markov assumptions, the requirements for OLS to be BLUE are:
Linearity: The estimator must be a linear function of the data
Unbiasedness: The expected value of the estimator should ...
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Modeling time-varying variance of a signal
I have a signal whose variance varies in time
It turns out, by observation, that these fluctuations of the variance arise when some other variables (let's call them input features) transition sharply ...
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Are intraclass correlation (ICC) and the correlation within groups related concepts? How so?
I'm attempting to re-learn linear mixed-effects models with lmer via some tutorials online, but I'm struggling with the concept of intraclass correlation (ICC). I'm ...
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Bishop Gaussian Basis
In Pattern Recognition and Machine Learning by Christopher Bishop he says in Section 3.3.2 titled Predictive distribution
If we used localised basis functions such as Gaussians, then in regions away
...
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Can standard deviations from multiple studies be averaged to use for a sample size calculation?
Imagine you are planning a clinical trial to evaluate the effectiveness of a new treatment for improving VO2peak in patients with chronic stroke. Based on an initial study by Jin et al., you estimate ...
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Deriving MSE($\hat{\beta}$) under Linear regression
I was able to derive the MSE, but there's a part of the derivation which I don't really get. Here's what I got:
Facts:
$\mathbb{E}(\hat{\beta})=\hat{\beta}\space$ (unbiased estimator)
$\text{Cov}(\...
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Spatial effects competing for variance with error term?
I am simulating a dataset from a spatial model. Each data point is distributed as follows:
$$
y_i \sim \mathcal{N}(\mu + \phi_i, \sigma^2)
$$
Here $\mu$ is a fixed value, estimated as an intercept. ...
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