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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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How to estimate the variance of the regression coefficients via Variance-Covariance Matrix?

everyone I am not used to the matrix algebra. I know the maximum likelihood method to get the point estimation of the regression coefficients well. However, I don't understand the mathematical method ...
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Per-Item inter rater reliability with multiple values and raters

I am trying to find the best statistical calculation to measure the agreement between 72 different raters on one item. My goal is to convey in a statistic how spread the raters are on their rating and ...
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Conditional variance of random walk with given start points and ending points

If I have a random walk with 0 drift and I observe that $X_1 = x_1$ and $X_k = x_k$, bu I don't have all the points from $X_i$ for $i \in \{2, ..., k-1 \}$, how do I estimate them and given an CI? I ...
The One's user avatar
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Covariance of multivariate negative binomial with random effects

I am fitting a negative binomial-2 regression model where there is a multivariate normal random effects term. I would like to find an equation for the covariance of two outcomes. In "the ...
Nick Link's user avatar
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Understanding Volatility Clustering: Conditional or Unconditional Variance?

A stylized fact observed in financial time series is volatility clustering. Volatility clustering is commonly described as the fact that large changes in asset prices are followed by large changes, ...
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Can I include a variable related to the outcome variable into statistical analysis?

My research question is about the contact patterns during the pandemic and what characteristics of people who contacted more person during the national lock down. The outcome variable is a variable ...
Chao's user avatar
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Is the variance of the mean of a set of possibly dependent random variables less than the average of their respective variances? [closed]

Is the variance of the mean of a set of possibly dependent random variables less than or equal to the average of their respective variances? Mathematically, given random variables $X_1, X_2, ..., X_n$ ...
HappyFace's user avatar
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Why can the standard error of the weighted mean be smaller than the standard errors of the individual measurements?

I am combining two independent measurements with their respective standard errors using a weighted mean. The measurements are: It seems counterintuitive to me that the standard error of the weighted ...
Francesco 's user avatar
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3 answers
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What does it mean for observations to be uncorrelated and have constant variance?

I am learning about linear regression from the textbook Elements of Statistical Learning by Friedman, Tibshirani, and Hastie. In this section they suppose we have a set of training data $(x_1, y_1), \...
CBBAM's user avatar
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central moments of random variable from _estimates_ of draws from the distribution function

I am trying to estimate the first two central moments of random variable $r$. The information I have about $r$ is a set of estimates $\hat{r}_i$ for $i \in \mathcal{I}$, each with corresponding ...
daydaybroskii's user avatar
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Measurement error R in Kalman Filter [duplicate]

I want to calculate the measurement error R for Kalman filter if I have such data: True value of the golden bar is 18 g. A tool was used to measure the weight of the bar: 17.7, 17.8, 18.1, 17.8. How ...
Max Heron's user avatar
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Variance around true value, not mean

The water temperature is 19 C, which is true value. I have measured the temperature of the water and I received such results: 18.7, 18.8, 19.1, 18.8. Can I calculate variance here around true value (...
Max Heron's user avatar
1 vote
1 answer
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Estimate sample variance of return-on-ad-spend (ROAS)?

I'm trying to make sense of the correct method to calculate the variance of ad-revenue for my marketing company. During an a/b test we need to estimate the sample variance to compute our confidence ...
Zach Cuddihy's user avatar
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2 answers
34 views

Calculating variance between paired samples, where one sample is constrained to always be the lower bound?

I'm sure this is a solved question, but I haven't been able to hit on the right search terms. Suppose I have paired samples A and B. A represents a derived variable (say distance "as-the-crow-...
Danielle McCool's user avatar
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Unbiased and consistent estimator with positive sampling variance as n approaches infinity? (Aronow & Miller) [duplicate]

In Aronow & Miller, "Foundations of Agnostic Statistics", the authors write on p105: [A]lthough unbiased estimators are not necessarily consistent, any unbiased estimator $\widehat{\...
user24465's user avatar
2 votes
1 answer
148 views

Expected Value Chi Square distribution

I'm trying to simulate the distribution from the sample variance $s^2$ and compare it with the theoretical distribution. Therefore, I perform a fairly simple simulation (upfront, I'm not a ...
Mexx's user avatar
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In Regression Through the Origin, why do the CIs of the slope depend on datapoints with zero x value?

I'm working with a Regression Through the Origin model as described in this reference. The model is $Y_i = \beta X_i + \epsilon$ and the least squares estimate of $\beta$ is $\hat\beta = \frac{\sum ...
Ryan Moulton's user avatar
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Emtrends pairwise comparisons all have same standard errors. 3 way interaction

I have created a linear mixed model and am using emtrends to determine the impact of a dichotomous variable on the effect of a continuous variable, across levels of a categorical variable. Is it ...
Jackson's user avatar
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Expected value of a decreasing function of two random variables

My question is exactly equal to the question posted at Expected value of decreasing function of random variable versus expected value of random variable with just one extra assumption: the two random ...
irodr's user avatar
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3 votes
2 answers
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What is the variance of a regression after t generations?

Suppose we have a regression: $$x_{t+1} = b x_t + e_t.$$ Taking the variance of each side we get $$\operatorname{Var}(x_{t+1}) = b^2 \operatorname{Var}(x_t) + \operatorname{Var}(e_t). $$ Now suppose ...
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Variance Component Estimation of Weighted Total Least Squares

Note: I'd like to make the cited document accessible to everyone but I am unsure how to do this. I am a bit confused by this 2014 article "Variance components in errors-in-variables models: ...
A Friendly Fish's user avatar
1 vote
1 answer
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How to analyze between-group differences in within-group variances over time in a 3-level model?

The data I am using is collected within the physical fitness surveillance program in schools. In these schools, either no intervention, healthy lifestyle intervention, healthy schools network ...
Antonio Martinko's user avatar
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Constrained Cholesky Decomposition

Suppose that I have an $(n\times 1)$ vector of random variables, $\varepsilon$. However, I know that $k$ linear combinations of $\varepsilon$ are 0. Specifically, I know that for a $(k\times n)$ ...
Leland's user avatar
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2 votes
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Time series and separating variance by time scale

There is a single-variable time series wich can be thought as being stationary in the long run. The observations are taken at irregular time intervals. The values of observations can be assumed to ...
Maciej Tomczak's user avatar
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Estimating variance from several samples

If several samples are taken from a distribution, say Gaussian, each sample having size n1,n2,n3,... and the SD of the underlying distribution is estimated from each of the samples, how can those ...
Maciej Tomczak's user avatar
1 vote
1 answer
82 views

Distribution of a spread of observations in triplicate sample taken from Gaussian distribution

Suppose random triplicate samples are taken from a Gaussian distribution with known mean and SD. What should be the distribution of the maximum absolute difference between 3 possible pairs of ...
Maciej Tomczak's user avatar
1 vote
1 answer
32 views

What statistical method for assessing the effect of a known measurement error variable?

I have lots of repeated measures data for a dataset of 95 subjects. The data concerns medical-imaging measures of morphology. medical-imaging is a tricky kind of data - the same body part imaged on ...
Maks Hall's user avatar
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Derive the expectation and variance of squared sample correlation: delta-method or else?

I would like to obtain the expectation and variance of the squared Pearson sample correlation ($\operatorname{E}(R_{lk}^2)$ and $V(R_{lk}^2)$) between two random variables $l$ and $k$ following a ...
CafféSospeso's user avatar
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Can I test if a difference for a single subject is large enough to consider that subject an outlier from a population of subjects?

I have measurements of vegetation bed size for four beds before and after an event. Three of the beds are unaffected by the event and all changed in size. One of the beds may have been affected by the ...
Joe_P's user avatar
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Retrieving beta distribution parameters, alpha and beta, from mode and variance

Is it possible to decide the parameters of beta distribution ,alpha and beta, when mode and variance are given? I know the two parameters can be decided from mean and variance as: $E[X] = \dfrac{a}{a+...
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Average Variance Extracted and Factor loading cutoff not aligning

The cutoff for factor loadings is generally around 0.4 (Stevens 1992), Fidell (2007), 0.32 (poor), 0.45 (fair), 0.55 (good) by follow Comrey and Lee (1992). But for convergent validity you require ...
Rahul Kiroriwal's user avatar
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1 answer
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In blmer, is sigma variable random-effect covariance, and why would cov(r,c)var(r) = var(c)?

As the title says, I have two questions regarding the blmer() models in R. I have tried to get firm understanding about the ...
Imsa's user avatar
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2 answers
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In linear regression, what's the asymptotic distribution of the error variance estimator?

Suppose $$Y_i=X_i'\beta+\epsilon_i$$ with $E(\epsilon_i|X_i)=0$ and $E\epsilon^2_i=\sigma^2$ and I estimate $\sigma^2$ using $s^2=\frac{1}{n}\sum_{i=1}^n (Y_i-X_i'\widehat{\beta})^2$, where $\widehat{...
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3 votes
2 answers
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Didactic example of mean-variance dependency in linear models

I'd like to illustrate the importance of accounting for the dependency between mean and variance in inference with linear models. Is my example below a good one? Do you agree with my comments on it? ...
dariober's user avatar
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2 votes
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Variance ratio below 3

Can it be assumed that the repeated measures (RM) ANOVA is robust, even after having a significant Levene test for a variable? What about if the ratio between the maximum and minimum variance is below ...
mdscience's user avatar
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1 answer
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Calculate Levene test in R

I'm trying to calculate the Levene tests with multiple interactions. ...
Minia's user avatar
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18 views

What is the distribution of sampled variance from a finite population?

Suppose there are certain sample mean x and sampled standard deviation sigma given N, then n number of data is sampled from this finite sample without replacement . The variance of the resampled ...
Ryan's user avatar
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Decompose variance explained in sequential mediation in lavaan

I am using sequential mediation analyses (aka serial mediation) in lavaan in R. Below is my model ...
Courtney's user avatar
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What is the standard deviation/uncertainty of a single observation in a meta-analysis?

I am running a simulation with parameters based on an existing random-effects meta-analysis. I would like to draw individual patients in the treatment group from a normal distribution with µ=the ...
bumble.bee's user avatar
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Testing for Homoscedasticity - should Levene's and Brown-Forsythe use Welch's t-test/ANOVA?

This question just came up and I haven't seen any literature on the subject. Background: When testing homoscedasticity for, say, a two-sample t-test, the F-test for equal variances is deprecated due ...
Steven Ouellette's user avatar
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0 answers
11 views

Analyze the variance of one adaptive process?

I'm currently interested in analyzing the variance of one adaptive process. To be more specific, suppose I have done some, let's say $n$ times, experiments where the results depend on some unknown ...
narip's user avatar
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1 answer
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Proving an Estimator of the sample variance to be MVUE

Question: Prove that $\hat{\sigma}_x^2=\displaystyle\frac{1}{N-1}\sum_{i=1}^N(X_i-\overline{X})^2$, with $\overline{X}=\frac{1}{N}\sum_{i=1}^N X_i$ is an unbiased, minimum variance estimator of the ...
Subhasis Biswas's user avatar
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Consequences of ignoring correlation on standard error

I want to know the mathematical reason why between-individual standard error is under-estimated, and conversely, why within-individual standard error is overestimated if we fail to take correlation ...
user1211188's user avatar
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41 views

Beta-binomial relationship between dispersion and correlation parameters

Context: I have created a beta-binomial model using glmmTMB() from the glmmTMB package and I am now trying to simulate a beta-...
Reid's user avatar
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1 vote
1 answer
54 views

Applying the law of total variance

Say we have a sample of 100 normally distributed payments, with mean=1000 dollars and standard deviation= 100 dollars. 10% of these payments were made in error and should be refunded their full ...
duke's user avatar
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What is known about the (in)efficiency of true score variance estimation?

In classical test theory, an observed score $X$ is defined as $$ X = T + E $$ where $T$ represents the individual true score and $E$ represents the individual error score. In this context $T$ may be ...
LJ Beinhauer's user avatar
1 vote
0 answers
39 views

Variance of ARMA$\left(2,2\right)$ model

Find $Var(∇Y_t)$ if $Y_t = 5 + 2Y_{t-1} - 1.7Y_{t-2} + 0.7Y_{t-3} + e_t - 0.5e_{t-1} + 0.25e_{t-2}$. I've reduced this down to $∇Y_t = 5 + ∇Y_{t-1} - 0.7∇Y_{t-2} + e_t - 0.5e_{t-1} + 0.25e_{t-2}$. ...
Random user33's user avatar
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Standard practice to show Biased CRBs

I have a problem with four-parameter estimation. I have derived the variances for the estimated parameters using Monte Carlo simulations (numerical ones) and theoretical ones using the inverse of the ...
CfourPiO's user avatar
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Is there an easy way to mentally calculate mean an variance? [closed]

Giving a generic numerical data is there an easy way to calculate mean an variance mentally or at least some easy formula that minimize the error with the correct mean and variance?
pgiacome's user avatar
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1 answer
26 views

Does the intuitive sense of overfitting in this mechanism design context exemplify bias-variance tradeoff?

Suppose the (we can say unanimous) preference of each individual in a society is to select roads for travel by placing 95% weight on the objective of minimizing travel time, and the remaining 5% ...
user10478's user avatar
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