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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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Bias and Variance in underspecified models

Galit Shmueli (2012) introduces in her paper "To Explain or to Predict" the biases and variances of correctly and underspecified predictive models. The correct model is $f(x)=\beta_1x_1+\beta_2x_2+\...
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Finding variance normal distribution problem [on hold]

Can anybode help me to understand this? I've tried to solve this problem but can't get the right answer. "For controlling purposes, 1000 packages of rice are sampled from the production output and ...
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AR(1)/ARCH(1) Variance computation

I've tried to compute the unconditional variance of an AR(1)/ARCH(1) model, so an AR(1) in which the noise is modelled as an ARCH(1). I've computed the variance of the ARCH(1) as (w/1-α), then I've ...
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What does the angle bracket mean in variance formula?

When I check the formula of variance in Mathworld which is $$ \sigma^2 \equiv \langle\ (X - \mu)^2 \rangle\ $$ Though I'm more familiar with the other formula, I just wanted to know what does the ...
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Calculate variance between two groups

I would like to ask some fairly basic questions so please bear with me. I have a group audience who rated video A and video B. I would like to know if the variance (or should I be looking at ...
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Two Distributions, One a Sum: Discerning likelihood given error

Given $X, Y$ independent and non-normal, I'm recording histograms of $X$ and of $Z = X + Y$, sampled when $Y$ is not present and when it is, respectfully. I'm trying to figure out $Var(Y)$ and its ...
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One-sided variance test in r [duplicate]

I would like to compare variances of two independent samples (of different sizes) from two unknown distributions. It seems I should use a one-sided nonparametric test. Bartlett's and Fligner's tests ...
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$V(X|Y)=\Sigma_{XX}-\Sigma_{XY}\Sigma_{YY}^{-1}\Sigma_{YX}$

We know that the conditional variance of a multivariate normal vector $(X,Y)$ is equal to the Schur complement: $$V(X|Y)=\Sigma_{XX}-\Sigma_{XY}\Sigma_{YY}^{-1}\Sigma_{YX}$$ However, $\Sigma_{XX}-\...
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Why do we take `(Bias) ^2` in total error in a model? [duplicate]

I was recently studying some book and few blogs and come to note that : Total error = Bias^2 +Variance + irreducible error Also, I know that these are the errors ...
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1answer
24 views

Conditional covariance of a multivariate normal vector

We know that the conditional variance of a multivariate normal vector $(X,Y)$ is the Schur complement: $$V(X|Y=(y_1,...,y_n))=\Sigma_{XX}-\Sigma_{XY}\Sigma_{YY}^{-1}\Sigma_{YX}$$ I have the intuition ...
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How to interpret MANOVA results after adding gender, splitting the file?

I am analyzing my 2x3 between subject design with MANOVA in SPSS at the moment. In the main model, there is 2 IV's and 2 DV's. Result of the test is 1 main effect and no interaction effect. In an ...
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Total variance calculation in hierarchical clustering

I've clustered my data variables using ClustOfvar in R and got three clusters. How would I calculate total (global) variance explained by these three clusters for the dataset? ?
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Why does the variance of the OLS estimator goes to zero as n increases while it is a random variable?

I have a question regarding the OLS estimator. In my class, the teacher asked us to critic this comment: “We write the unconditional variance of the OLS as $V(\hat{b}^{ols}) = 1/N 𝜎^2 E(X_i'X_i )^{−...
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Multinomial logit with ridge penalization and value of time

I am fitting a multinomial logit model with ridge penalty and in turn estimating the value of time (VOT) or availability to pay (WTP). I want to work with real and simulated data. For the real data I ...
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Calculate the variance of $\sum\limits_{i=1}^{n-1} \sum\limits_{j=i+1}^n S(X_i - X_j)$ for $X_1,\ldots,X_n$ i.i.d. random variables

In p.88 of Wand & Jones (1995), they asked to show the following result. Let $X_1,\ldots,X_n$ be a set of i.i.d. random variables and define $$U=2n^{-2}\sum_{i=1}^{n-1} \sum_{j=i+1}^n S(X_i - ...
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how can we differentiate if the mean, variance of a distribution is finite or infinite?

For X with random variable distribution, can anyone please share an example, how can we differentiate if the mean, variance of that distribution is finite or infinite. Is there any easier way to ...
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Multiple correlation in the sampling variance of slope coefficient in multiple regression

Let's say we have the following multiple regression model, $$Y_i = \alpha + \beta_1 x_{i1} +\beta_2x_{i2} + ... + \beta_kx_{ik} + \varepsilon_i$$ with $ \varepsilon_i$ is $iid$ ~ $N(0,\sigma_{\...
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Negative variance, what is wrong?

I am trying to obtain the variance of a function of two random variables $$f(\boldsymbol x):= x_A (e^{k(x_A+x_B)}-1)$$ where $\boldsymbol x = [x_A, x_B]^T$. Additionally, I know that $\operatorname{...
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1answer
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Standard error of a proportion on a 2 x 2 contingency table

Why on a 2 x 2 table such as where $p = \frac{a}{a+b}$ the standard error of $p$ is $$\left(\frac{(a+c)(b+d)}{(a+b+c+d)^2(a+b) }\right)^{1/2}$$ ?
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Are variances within a group always larger than between groups? When is this not true?

A good example of this is the genetic difference within Africa, which are larger, than the genetic differences between Africa and Europe. From what I understand, on a mathematical level it means that ...
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Negative values for OLS variance

I am currently writing some code which performs regression and have noticed that when I calculate variance of $c\hat{\beta}$ I am sometimes on some datasets getting negative values. The variance is ...
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1answer
66 views

Time varying random variable

I am studying the water surface elevation in the presence of waves, at one location over time $\eta(t)$ as seen in the following figure.           &...
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Heteroskedasticity testing

Im estimating the carhart 4 factor model. Im testing for heteroskedasticity to see whether i need to use adjusted standard errors, but i am finding conflicted results. All but one test (ARCH) are ...
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1answer
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Difference between pooled variance equations

I'm currently doing A-level Further Maths A2. I've seen two different equations to calculate the estimate of pooled variance. I do not know when to use which and what makes each significantly ...
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Seeking origin of variance equation

In my data science textbook, it says that the variance of a variable $Y$ can be written as: $v_y = \frac{1}{n-1} \sum_{k=1}^{n} y_k^{T} y_k$, I have never seen variance defined like this before. ...
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55 views

In GLMs are the Scale and Dispersion parameters the same?

Given a data set and a genralized linear model I am asked to find the estimation of the scale parameter obtained with the Pearson statistic. But I am a bit confused: I know that ${\rm Var}(Y)=\phi\...
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2answers
63 views

Variance inhomogeneity in time series when forecasting

I am using a time series for monthly temperatures to predict future temperatures. To this I am using the seasonal ARIMA model and Holt Winters forecast, and my results seems fine. However, my data ...
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2answers
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Calculating the variance of sample, knowing the mean of population

Suppose that I somehow know the mean of the population. And I want to calculate the variance of a sample. Should I subtract population mean or sample mean? Is there any situation in which I should use ...
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Variability metric for Top 3 sports teams in a league

**I am a bit unsure what to mark this as/title this as. We refer to this type of phenomena as 'volatility' but this apparently has a specific context with regards to statistical phenomena so any ...
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Error variance estimation with weights

I am using data which include a (sample-)weight for each observation, i.e. the data is from a survey that has weights to make the sample representative for the US-population. I perform OLS to get some ...
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1answer
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Variance of ATE (Average Treatment Effect) from log-linked gamma model

I have matched my sample using propensity score matching such that each individual has an estimated propensity score of being assigned to a treatment group. Let $T_i$={0,1} be the actual treatment ...
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Intuitive understanding of variance of sum vs variance of difference

$\newcommand{\Var}{\operatorname{Var}}\newcommand{Cov}{\operatorname{Cov}}$Mathematically, $\Var(X + Y) = \Var(X) + \Var(Y) + 2\Cov(X,Y)$ and $\Var(X - Y) = \Var(X) + \Var(Y) - 2\Cov(X,Y)$ This ...
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Mean and variance of the median estimator [duplicate]

We are given an i.i.d sample of size n, $X_{1},...,X_{2}$. We also know that for all i, $EX_{i}=\mu,Var{X_{i}}=\sigma^{2}$. Let us define $\hat{X}_{median}$ as the median of these samples: $\hat{X}...
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Can anyone explain the case of the probit model where we can identify the variance of the error term?

I was told that the variance of the error can be identified in a probit model in a specific case, and cannot find anything about it online.
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coefficient of variance's significance

As far as I know, the coefficient of variance (CV) is used for measuring consistency of any variable. But should one always depend on CV for taking decisions, especially when means the are different? ...
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Random variates: Why is $Var(\bar{X}_A)+Var(\bar{X}_b) \approx (S_A^2+S_B^2)/N$?

Random variates: Why is $Var(\bar{X}_A)+Var(\bar{X}_b) \approx (S_A^2+S_B^2)/N$? Since I read that $S_A,S_B$ are sample variances which have $/N$ in them as well. So $/N$ would cancel? However, how ...
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1answer
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PCA influence of duplicates

I am using sklearn IPCA decomposition and surprised that if I delete duplicates from my dataset, the result differs from the "unclean" one. What is the reason? As I think, the variance is the same. ...
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1answer
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A question about pca and gene function analysis

I'm new to bioinformatics, and I have a pretty basic question. Let's say I have a bunch of genes {Xi} and I want to know which one has the most significant on some measurable phenotypic trait Y. Now I ...
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What is the correct formula for Bayesian update for normal distribution with known variance [duplicate]

As question title states, I'm interesting in Bayesian update of normally distributed data with known variance. I compared three sources and they seems to contradict each other. I use some kind of ...
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Understanding Rao-Blackwell [duplicate]

From Casella and Berger: Let $W$ be an unbiased estimator of $\tau(\theta)$ and let $T$ be a sufficient statistics for $\theta$. Define $\phi(T) = E[W|T]$. Then $E_{\theta}[ \phi(T)] = \tau(\theta)$ ...
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38 views

Estimating sample variance

Suppose that we have 2 independent samples $X_{11}, X_{12},.., X_{1n_1}$ and $X_{21}, X_{22},.., X_{2n_2}$ from a normally distributed population with $n_1<n_2$. Does that mean that the sample ...
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Question on a particular step in the Paule-Mandel 'Consensus Values and Weighting Factors' paper

I am preparing to use the Paule-Mandel method for determining the weighting factors in a meta-analysis. The paper I'm reading is the original one available here. I believe only those who are ...
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How to compute the variances of quotients of normal variables?

$x$ and $y$ are independent normal random variables. $z1=x/(x+y)$ and $z2=y/(x+y).$ How to obtain the variances for $z1$ and $z2$? I understand through the delta method, $\operatorname{Var}(z1)$ ...
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Sigma interpretation in Bayesian Linear Model?

I have two question concerning my output of my bayesian linear regression. 1) I have all beta posterior and obviously, having used a prior for Sigma, i have a posterior for Sigma too, but what can i ...
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Testing for Causality in variance

I have read a couple of papers which mention causality in variance. For example Cheung and Ng (1996, Journal of Econometrics), "A causality-in-variance test ands its applications to financial markets"....
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Range of population variance [duplicate]

I have a set of numbers between 0 and 1, for instance, {0.4, 0.1, 0.0, 0.8}. What are the minimum and maximum values of population variance on such set?
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Negative variance of linear combination of regression coefficients

I'm going crazy over this so I hope someone can help me.. First a presentation of my case: I have a complex multiple regression model with 4 predictors (some terms that don't concern this issue are ...
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Calculate target variance contionaly to continuous variable

I'm trying to get the conditional variance of my target Y conditional to my inputs X. To do this I first discretized my inputs variable into 1 qualitativ variable and then I computed the variance of Y ...
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Variance Co-Variance of a single column data

I am totally new to statistics, leastsquares methods and linear regression. But in to research using GPS data. I have a particular observation collected from GPS. It is a huge data with 30sec sample ...