Questions tagged [variance]

The expected squared deviation of a random variable from its mean; or, the average squared deviation of data about their mean.

Filter by
Sorted by
Tagged with
1
vote
0answers
11 views

How do you calculate variance for percentages?

I know this seems like a simple questions but I am trying to wrap my head around calculating variance for percentages (e.g. 15%, 16%). I know that 15% is equivalent to 0.15, but when I try to ...
0
votes
0answers
7 views

What statistical method deals with a continous predictor characterized by low variance?

I would like to run a study in which my predictor is a continuous variable. I already know that the distribution is normal but most of the points fall close to the center. I think that small ...
1
vote
1answer
21 views

How does pooling affect variance?

Suppose you are looking at the prevalence of a certain disease and you can detect this disease in fecal samples. How does having a bunch of pooled fecal samples (i.e., taking a fecal sample from 5 ...
0
votes
1answer
14 views

How much will the variance change in this scenario?

Imagine that a firm decides to increase the salary of every single of its employees by 10% of their current salary. The average of the salaries will increase by 10% too. But, how will the variance of ...
1
vote
0answers
21 views

Explanation for Bessel's correction [duplicate]

In textbooks and online the explanation for Bessel's correction is that the sample points are closer to the sample mean than the population mean.This is true for sampling with replacement as well. So, ...
0
votes
0answers
28 views

Unbiased estimator for Variance

So basically I have a survey where for each unit 1, ..., N in the population, we flip a fair coin to decide whether this person will be included in the survey or not. Let S be the r.v. denoting the ...
0
votes
0answers
23 views

Mean and variance of a function of random multivariate vector

Let's assume to have a scalar function $Y=f(X)$, that is function of a multivariate normally-distributed random variable $X\sim\mathcal{N}(\mu, \Sigma)$. Is there a general way to compute, even in an ...
1
vote
0answers
48 views

Is the $\sigma$ estimator more efficient than the $\mu$ estimator?

Are my empirical findings correct? How to get the same result analytically? I studied the efficiency of the mean and standard dev estimators: $$\mu_n=\sum \frac {x_i} {n}\space\space\space\space\...
0
votes
0answers
36 views

Don't understand how pseudo-R-squared results for mixed model are even possible (MuMIn in R)

We're using MuMIn in R to look at the delta R-squared when adding a term into a mixed model like this: ...
2
votes
0answers
18 views

How Does Variance Propagate From Likelihood Function To MCMC Posterior?

Suppose we are trying to obtain the posterior distribution of three parameters that influence a discretely observed population. The likelihood function is unfortunately intractable, as it is a mix of ...
1
vote
1answer
122 views

How to compute Variability Independent of the Mean (VIM)

Although I find this reading regarding the interpretation of the Coefficent of Variation (CoV) very interesting, I did not found hints regarding the Variability Independent of the Mean (VIM) which is ...
2
votes
2answers
84 views

Moments of truncated Student's $t$-distribution

I performed random sampling on a Student's $t$-distribution. I used SciPy to calibrate my parameters and then truncated my allowable values to the maximum and minimum observation in the data for ...
0
votes
0answers
9 views

Aggregating variance from many variables for Levene's test? [closed]

I am interested in finding out whether the composition of students has become more heterogeneous over time. People vary by several important variables: age, gender, ethnicity etc. I have large cross-...
0
votes
0answers
23 views

Fitting environmental variables to an ordination (artificially replicating data?)

I collected five samples of animal tissue from each of 3 different sampling sites (15 samples total). For each sample, I determined bacterial community composition, so I have a standard multivariate ...
0
votes
1answer
27 views

Changing only one point of a discrete distribution to maximize variance augmentation

X has a discrete distribution with support $x1, x2, ...$ in $ {]}0,1{[}$. You have the right to change only one of the $xi$ to lead to the highest increase in variance (or, at least, a systematic ...
0
votes
0answers
18 views

Is there an alternative to Box's M test for data that is not multivariate normally distributed?

My research question is to test whether two groups have a difference in variance-covariance across multiple measures. However, the data do not follow the multivariate normality assumption required for ...
0
votes
0answers
9 views

How to determine the accuracy and variance in categorical survey data responses?

I've conducted a survey where I have shown citizens images of transect squares placed in a field. For each image of a transect square, I've asked citizens to i) count the number of beetles (a ...
2
votes
1answer
36 views

PCA; variance, interpretability, and scaling

I've been going through threads about PCA and the predictive power of various axes, but since I cannot comment, I am opening a new question. There is a lot of discussion whether PCA components with ...
0
votes
0answers
22 views

Relation between bias and R-square

I am trying to understand relation between bias and R-squared value in linear regression. High bias means that the model is underfit. By this I am assuming that the R-square d will be less. So my ...
0
votes
0answers
23 views

Relation between Variance of one variable and variance of two independent variable

Is the following statement correct? If $X$ and $Y$ are independent then $\operatorname{Var}(X)\lt \operatorname{Var}(XY)$ and $\operatorname{Var}(Y)\lt \operatorname{Var}(XY).$
3
votes
0answers
57 views

Variance of integral of Poisson variables

I have a stochastic quantity (not sure if it is a proper stochastic process), defined as follows: $$I = \int d x f(x) X(x)$$ $f(x)$ is a positive function of real variable, defined over the integral ...
1
vote
1answer
17 views

Error in Derivation for Control Variate Variance?

I'm trying to derive the variance for a control variate estimator, but I seem to be missing a term that allows me to end up with the covariance in the final answer. Let $f(x)$ be my function and let $...
0
votes
0answers
15 views

Limiting distribution of sample variance and standard deviation

I have a centered Gaussian sample of $n$ elements $X_i,\,i=1,..,n$, with variance $\sigma^2$. I would like to find the limiting distribution of the sample variance $\sigma_n^2=\frac 1n \sum_{i=1}^n ...
2
votes
1answer
54 views

Negative Adjusted $R^2$ in twoway effects within model

I am having serious trouble understanding the results of my Fixed Effects panel regression. I am using two fixed effects (on year and regions) and I get a negative Adjusted R2 (i am using the plm ...
4
votes
0answers
29 views

Is it possible to show that this estimator has minimum variance?

Doing some exercises I stumbled upon this tricky one: Suppose we have an independent random sample $(X_1, ... , X_n)$ with $X_i \sim Poisson(\lambda)$. Define $\theta = e^{-\lambda}$. Let $$ \...
1
vote
1answer
51 views

Mean and variance of a Random Walk with lower boundary

Consider a random walk $S_n$ that starts at $S_0$ and terminates if it hits a lower boundary of $0$. $$ S_n=\begin{cases} 0, & \text{if } S_{n-1}=0\\ 0, & \text{if } S_{n-1}+x_n\le0\\ S_{n-...
0
votes
1answer
36 views

Can I predict the variance of a random variable using a machine learning regression model that predicts expected outcomes?

For example, suppose I'm using some machine learning model like gradient boosting that, given some input $x_i$ predicts the expected output $f(x_i) = y_i$. However, I'm also interested in estimating ...
0
votes
0answers
20 views

Variance estimator that is optimal under absolute loss

Given a random i.i.d. sample from a population with a finite variance $\sigma^2<\infty$, what estimator of $\sigma^2$ is optimal under absolute loss? $$ \arg\min_{\hat\sigma^{2}\in F}\mathbb{E}(|\...
0
votes
0answers
10 views

mixing absolute or relative error with standard deviation for error propagation

I have an equation $$A = \frac{B \cdot C}{D}$$ where I want to know the error of $A$. As the variables are independent, the variance of this should be: $$\mathrm{Var}(A)=\sqrt{\left(\frac{\partial A}{\...
1
vote
0answers
16 views

Two Factor ANOVA with different sample sizes but similar variances

I gave an educational intervention to Spanish speaking and English speaking students. I gave a pre and post test to these students. Due to certain issues I was not able to identify students with their ...
3
votes
2answers
85 views

Is $\hat{\sigma^2}=\hat{\sigma}^2$?

In simple linear regression $$Y_i=b_0+b_1X_i+\varepsilon_i$$ where $$\varepsilon_i\sim N(0, \sigma^2)$$ is it true to say that the estimator for variance and the estimator for SD squared are equal? I ...
0
votes
2answers
47 views

How are $n$ and $Var(\varepsilon)$ affecting to Variance of Estimation of Slope Parameter $\beta_1$ in Simple Linear Regression

Once I have derived the variance of $\hat{\beta_1}$ as: $\text{Var}(\hat{\beta_1})= \frac{\sigma^2}{\sum(x_i-\overline{x})^2}$ I would like to know how are affecting to this formula: the size of ...
1
vote
0answers
23 views

How to Calculate Observed Variance in a Random-Effects Meta-Analysis

I've received a revise and resubmit on a meta-analysis investigating the effects of a positive psychology intervention on depression and anxiety symptoms. I used Hedges' g as the effect size with a ...
3
votes
0answers
21 views

how to pick the daily volatility component in Multiplicative Components GARCH modelling?

Recently I've been drawn to the rather interesting Multiplicative Components GARCH model for intraday volatility modelling, a draft paper written on it can be found here: Chanda, Engle, Sokalska, 2005 ...
5
votes
1answer
89 views

Parameter estimation in the linear mixed effects model

In Parameter estimation and inference in the linear mixed effects model, page 1923, the variance \begin{equation} \begin{aligned} \text{var}(\tilde{u} - u) & = \sigma^2G - \text{var}(\tilde{u}) \...
2
votes
2answers
92 views

Mean and variance of a non-standard pdf

I have tried to compute the variance and the mean for $\mu=0.5$ of the following PDF using Wolfram cloud but I failed $$ F(z,\mu,\sigma)=\frac{2 (z-\sigma )^2 \exp \left(-\frac{(z-\sigma )^2 \...
7
votes
2answers
108 views

Linear Mixed Effects Model Variances

Consider the following model: \begin{equation} Y_i = X_i\beta + Z_ib_i + \varepsilon_i, \end{equation} where $b_i \sim N(0, D)$, and $\varepsilon_i \sim N(0, R_i(\gamma))$. The variance of $Y_i$ ...
0
votes
0answers
14 views

What conclusions can we draw from different correlations between IQ scores between subjects belonging in different groups?

I was reading a presentation where research was quoted according to which children and parents who live together have IQs that are correlated with a correlation coefficient of 0.42 while children and ...
0
votes
0answers
27 views

Why do some people say that an asymptotically unbiased estimator “satisfies a strong law of large numbers”?

If $x\in\mathbb R$, an estimator for $x$ is an integrable random variable $X$. We say that $X$ is unbiased if $\operatorname{Bias}(x,X):=x-\operatorname E[X]=0$. Now, in the context of Markov chain ...
1
vote
1answer
23 views

How to identify periods of high variance in temporal data [closed]

I have a dataset with concentration of a chemical (continuous) as the dependent variable plotted against time (continuous). I expect that certain periods during the year (e.g. summer) will have ...
1
vote
0answers
25 views

Why do regression estimates provide lower relative error than averaged values?

I am trying to estimate the per-cell protein concentration for some samples. I have performed a series of protein extractions for each of my samples, with each extraction using an increased (and known)...
5
votes
0answers
48 views

Keeping track of the variance of a Metropolis-Hastings estimator

Let $(E,\mathcal E,\lambda)$ and $(E',\mathcal E',\lambda')$ be measure spaces, $p,q$ be probability densities on $(E,\mathcal E,\lambda)$, and $\varphi:E'\to E$ be bijective and $(\mathcal E',\...
5
votes
1answer
357 views

Large Numerical difference in variance calculation : Unable to decipher

For the below pdf, I've calculated variance by two methods and observe a large difference (2.1477 vs 2.9100). Wondering why is this difference right at the first decimal? Is it just loss of precision ...
1
vote
0answers
25 views

How to bootstrap a statistic calculed in a meta-analyis?

I have calculated a statistic in a meta-analysis of individual data and I want to bootstrap it to obtain the variance (no analytic expression is available) to make a test. First, I was naively ...
1
vote
1answer
20 views

Variance Estimation for Least Squares with Probability Weights

I'm running a simulation study and finding that the nominal SEs of the estimated coefficients when using weights in lm in R are an underestimate of the simulation SE. I have confirmed that $\hat{\beta}...
0
votes
0answers
9 views

How can I compare the performance of two measurement modalities?

Let's say given some 3D images of the brain, I have two methodologies to measure the brain's volume. I'll call these two methodologies M1 ...
0
votes
0answers
33 views

Mean and covariance of Bernouilli

I am given probability distribution here for a multinomial bernoulli: $p_{x}(x|z=j; \mu^{j}) = \prod^{d}_{i=1}(\mu^{j})^{x_{i}}(1-\mu^{j})^{1-x_{i}}$ where $x_{i}$ takes value 1 or 0, $\mu_{j}$ is ...
1
vote
1answer
30 views

$X$ has distribution function $F(x) = e^{-e^{-x}}$. Justify that such a probability measure on $\mathbb{R}$ exists

How can I prove a probability measure exists? If $F(x) \rightarrow 1$ as $n \rightarrow +\infty$, does that mean $F(x)$ does exist? And how should I calculate $\mathbb{E}(F(X))$ and $Var(F(X))$?
2
votes
0answers
68 views

What is the estimate of $\mathrm{Var}\left(\frac{nM}{X}\right)$ where $X$ is hypergeometric?

Consider the classical capture-recapture method, where we are to estimate the number of deer (say) in a sanctuary. So a certain number of deer is captured, tagged and released. Then a random sample is ...
0
votes
0answers
16 views

Question on variance on finding the variance

I have a question on finding the variance of the giving problem: On an auto collision coverage, there are two classes of policyholders, A and B. 60% of drivers are in class A and 40% in class B. The ...