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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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Standard variance of bivariate normal distribution plus normal distribution

Problem: $W = -27 + 0.3X + 0.45Y + E$ The pair $\begin{bmatrix} X \\ Y \end{bmatrix}$ behaves like a bivariate normal with vector of averages $\begin{bmatrix} 156 \\ 86 \end{bmatrix}$ and ...
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1answer
29 views

Variance of sum of dependent random variables

Can you guys help me prove the following: $$ Var[\frac{1}{m}\sum_{i=1}^my_i]=\frac{1}{m}(1-\rho)\sigma^2+\rho\sigma^2 $$ where the sampled predictions ($y_is$) have variance $\sigma^2$ and ...
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1answer
35 views

Variance of linear combination of Normal distributions

A company that develops software received an order for a service to be performed within a week and, in order to decide on the profile of the team of programmers to be used, it should take into account ...
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10 views

Renormalizing a distribution to reduce variance

I have a predictive model $M$ that generates an empirical predictive distribution $P_M$ via a set of samples. I cannot change the predictive model. I can evaluate the predictive performance using ...
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16 views

Equation (3.23) GP for ML book

This is the computation of the variance when we do Laplace Approximation for inference in binary classification. I do not understand why the variance is decomposed into these two terms.
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31 views

Are vanishing bias and variance enough for pointwise consistency for KDE-based estimation?

Question: Is the condition that asymptotic bias and asymptotic variance goes to zero for infinite samples sufficient to guarantee the pointwise consistency of an estimator based on plug-in kernel ...
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14 views

How to find the variance and SD using the raw score formula? And what is raw score formula

I read in the book of Statistics in Plain English by Thimothy Urdan (DOI: 10.4324/9780203851173) that you can find the standard deviation and variance using the raw ...
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Would like a double check on expected value & variance problem

If a student randomly chooses the answer to two multiple choice questions, where the first question has 3 possible answers and the second has 5, find: 1) $E(X)$ 2) $Var(X)$ For 1, I believe the ...
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1answer
26 views

Expectation, variance and autocorrelation of a “complex” AR(1) function

I'm preparing the exam for "stochastic models" and I encountered this exercise which is giving me a lot of problems: Let $$X_t=\phi X_{t-1}+\epsilon_t, ~~~~~~~~~~\epsilon_t \sim WN(0, \sigma^2)$$ ...
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9 views

Three Factor Multiple Comparison Post-Hoc Test for Levene's Test

My research question is to find out whether or not my samples are exhibiting any significant differences in their variance in response to three possible treatments. Here are my possible groups: ...
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14 views

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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11 views

Finding variance normal distribution problem [closed]

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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40 views

What's the variance of an AR(1)/ARCH(1)

The main question is: an AR(1)/ARCH(1) process has the variance of the ARCH(1)? 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 ...
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2answers
594 views

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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2answers
24 views

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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3answers
37 views

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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26 views

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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1answer
42 views

$V(X|Y)=\Sigma_{XX}-\Sigma_{XY}\Sigma_{YY}^{-1}\Sigma_{YX}$

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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26 views

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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1answer
10 views

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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29 views

Total variance calculation in hierarchical clustering [closed]

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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3answers
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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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23 views

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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0answers
32 views

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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1answer
35 views

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
28 views

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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1answer
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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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12 views

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
20 views

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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1answer
32 views

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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1answer
57 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
104 views

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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0answers
19 views

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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21 views

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
23 views

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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2answers
80 views

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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33 views

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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2answers
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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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1answer
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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
37 views

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
25 views

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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31 views

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 $E_{\theta}[ \phi(T)] = \tau(\theta)$ ...