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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Variance explained - equivalent statistics for categorical data?

I have a multinomial response variable and a multinomial "independent" variable. Is there an equivalent statistics or method for calculating the variance explained by the independent variable?
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8 views

Difference in expressions of variance and bias between MSE and MSPE

We all know the following relationship from a basic course in statistics: $MSE(\hat{\theta})=Var(\hat{\theta}) + Bias(\hat{\theta},\theta)^2$ But we read on Wikipedia that for the MSPE we have the ...
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27 views

Unbiased estimator variance of sample variance

I was reading the section on k-statistics on wolfram alpha. It was known to me that for the sample variance $k_2 = \frac{1}{n-1}\sum_{i=1}^n (x_i - \overline{x})^2$ it holds that its variance ...
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1answer
22 views

How to test for enough variance in Logistic regression?

I would like to find out if there's enough variance in my dependent variable which is binary. Which techniques would be best for this?
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3 views

A specific way to minimise the variance when importance sampling

Consider the following problem. We are interested in approximating from samples the expectation of $h$: $$ \int_t p(t) h(t) d(t) $$ We seek to obtain a lower-variance estimate by using importance ...
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1answer
4 views

How can I quantify the multivariate variances of several characters in different groups?

I have a multivariate dataset of linear measurements. Where I measured several characters (e.g. skull length, skull width, skull height, ...) for several different species. My questions is, if the ...
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1answer
37 views

Help Beginner Q: Explanation on pooled variance and when it is used

If I am conducting a difference in means hypothesis test, when do we use the pooled variance and why? Lets say the population variance was unknown for two samples, the sample sizes for the two means ...
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2answers
31 views

Is this controversial that in PCA, we want the variance as large as possible, while in bayesian, a large variance means a low precision?

I am wondering about the variance. We say the variance is inverse proportional to precision, then we also say the variance is proportional to the information, which means that a large variance means ...
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1answer
98 views

Why is my kalman filter trusting so much my observations?

This question follows the one asked there. I am trying to filter an equity index (Stoxx 600) time series using kalman filter. I'm using the R package dlm and my code is inspired from the dlm ...
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15 views

Higher variance in sample mean or sample median? [duplicate]

The variance of the sample median depends on the distribution you are sampling from. This is also true for the variance of the mean. But can one say that the variance of the sample mean is always ...
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7 views

Compare GLM with different dependent variables (that have not the same variance)

I would like to know if it is possible to compare the effects of one predictor on different response variables that follow e.g. a Poisson distribution. I have already read this topic with excellent ...
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5answers
615 views

How can we ever know the population variance?

In hypothesis testing, a common question is what is the population variance? My question is how can we ever know the population variance? If we knew the entire distribution, we might as well know the ...
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22 views

Meta-analysis: Calculating variance/ standard error of a mean difference for a within-subject design

I'm currently doing a random-effects meta-analysis. The studies that I'm analyzing come from a within-subject design where the same participants complete both the experimental and the control ...
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11 views

Repeated measures anova in R

I have a dataset containing percentage scores for 15 participants. There are two observations for every participant, one with an intervention and one with a placebo in a double-blind design. Each ...
3
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1answer
40 views

Proving a property of $(n-1)s^2$

I would appreciate your help as I climb the stats learning curve! I want to prove the following: "Let $x_1, x_2, ... , x_n$ be any numbers and let $\overline x = (x_1 + x_2 + ... + x_n)/n$ Then ...
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14 views

Weibull, Gumbell and Extreme Value: from mean and variance to shape, scale and location parameter

I need to sample random numbers from Weibull, Gumbel and Generalized extreme value distributions. Of all of these distributions I know mean and variance. My question is: how can I determine these ...
6
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2answers
109 views

Covariance of order statistics

I'm a researcher in social science and I have encountered the following math formulation of a problem in my field. Note that I'm relatively new to stack exchange and I have already posted this on ...
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2answers
24 views

What is the variance of the sum of Yi's

Seems a simple enough question, and I presume that, if Yi are normally distributed, Var(Sum(Yi)) = Sum(Var(Yi)) This feels like I'm jumping to the wrong conclusion though. Any help would be ...
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2answers
51 views

How can I test for differences in variation between groups in a mixed model (lme4)?

I would like to test for differences in variation, not in means, between two sites. By looking at a boxplot of my data I see that bird song in one site look much more variable in length than in ...
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1answer
35 views

Variance Estimation of MA(1) with known autocovariance function

I haven't worked with time-series in a while now and stumbled upon them in a different setting. Given $X_t\sim\mathcal{N}(0,\sigma^2)$ for $t=1,\ldots,n$ and the process $Y_t$ for $t=1,\ldots,n-1$ ...
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1answer
22 views

Forecasting next value range based on variance and historical values

If I know next variance from GARCH(1,1) model, can I get $X_{i+1}$? For example: $$ \sigma^2_n = \frac{1}{N} \sum_{i=1}^n(X_i-\mu_i)^2 $$ where $$ \mu_i = \frac{1}{n} \sum_{i=1}^nX_i. $$ So $$ ...
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7 views

One sample t-test with variance not assumed to represent the population?

Let's say you had a hypothetical study where you believe the sample standard deviation might be different from the population standard deviation. With a Welch's t-Test, you could work around this if ...
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16 views

Express analysis of deviance table as ANOVA

How can I express the following analysis of deviance in an ANOVA table , by hand not with R..
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1answer
29 views

Finding the MSE Using the Delta Method

I don't get the step in the solution for b) can someone please fill in the missing steps between going from eqn (1) to the solution. Thanks. Question: Solution:
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11 views

Leverages and effect of leverage points

I just got some question about the hat matrix in linear models. My first question is Why in a balanced one-way layout $(n_1=...=n_c=n_0)$, all leverages $h_{ii}$ have the same value $\frac{1}{n_0}$? ...
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1answer
25 views

Variance Explanation

I'm trying to learn statistics and I've been introduced to Variance, say I have the following... ...
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1answer
25 views

Prove that $Var(\hat {Y_i})=\sigma^2h_{ii}$

I just got a simple question. In general linear model, we have $$\hat Y=HY$$ where $H=X(X^TX)^{-1}X^T$ and the residual $$E=Y-\hat Y.$$ Now I want to prove that $$Var(\hat {Y_i})=\sigma^2h_{ii}$$ ...
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16 views

Testing for differences in variation between variables

I am trying to find out whether it is true that variation in expenditure is greater, for more narrow subsets. e.g. is it more likely that an individual buys an orange instead of an apple, than it is ...
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0answers
21 views

How does the fraction of retained PCA variance affect the accuracy of a model?

I was checking various tools for classification and optimisation; I trained a sample dataset using KNN. I got 100% accuracy with 95% PCA explained variance and 99.2% accuracy with 5% PCA explained ...
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2answers
59 views

What are the error distribution and link functions of a model family in R?

When building models with the glm function in R, one needs to specify the family. A family specifies an error distribution (or variance) function and a link ...
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59 views

Variance of a Cumulative Distribution Function of Normal Distribution

Suppose, $X\sim N(\mu,\sigma^2)$. Can anyone help in finding the following : $\text{Var } \bigg(\Phi\big(\frac{X + c}{d}\big) \bigg)$ ? Here, c and d are positive. Here, $\Phi(x)$ is the ...
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1answer
9 views

Variance of estimated sample mean

On Page 65 of the book - Introduction to Statistical Learning (https://web.stanford.edu/~hastie/local.ftp/Springer/ISLR_print1.pdf#page=80), I got a little confused on the Standard Error formula of ...
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16 views

Variance of subsample?

Total sample = subsample 1 + subsample 2 I have the mean and variance of total sample and subsample 1. I have n for total, subsample 1 and subsample 2. I can calculate the mean of subsample 2 ...
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23 views

Applying finite-population correction to the variance-covariance matrix of regression estimates

How would one modify the FPC to apply it to a regression coefficients covariance matrix rather than the $\hat{\sigma}$ vector? The conventional FPC is used a scalar on the vector of regression ...
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1answer
21 views

transformation for non-constant variance?

This is from my textbook I don't understand what does the content in red mean, for example, what does $y^2_i \infty \sigma_i$ mean? How can we tell the relationship between $y^2_i$ and $\sigma_i$ ...
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1answer
19 views

Share of variance explained by individual predictor [duplicate]

I am interested in how to calculate portion of explained variance of each individual independend variable in regression equation. So regression model is $y=b_{0}+b_{1}x_{1}+...b_{n}x_{k}+\epsilon$ ...
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13 views

Variance separation Theorem

I found the variance separation theorem in a book about Time Series Analysis. However, it does not give any explanation of where is this coming from. Anyone can give me an intuitive explanation or ...
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4answers
151 views

Something wrong with my implementation of the bias/variance diagnostic in polynomial regression

I'm trying to diagnosing bias/variance so I have the below Octavecode: ...
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1answer
32 views

Why is are unbiased statistics used more commonly than statistics with lower MSE?

I understand the difference between consistency and bias; one converges as the sample size increases, and the other converges as the number of estimates increases, respectively. But, I don't ...
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13 views

In testing Heteroscedasticity, when should I use Park Test or Glejser Test?

I am currently running a data analysis on survey data. In testing the heteroscedasticity assumption in Multiple Linear Regression, using Park Test, the research actually passed the test. However, when ...
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22 views

Fourier transform of white noise - Phase and magnitude?

Assume that $X(t)$ describes white noise in time, with $\langle X(t) \rangle =0 $ and $\langle X(t) X(t') \rangle = \sigma^2 \delta(x-x')$. I want to know the distribution of it's Fourier transform. ...
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16 views

Variance Reduction by Conditioning

Say that given Y=y, (edit->) a R.V. (edit end) N have a probability function of $f_N$ and Y have a distribution function $F_Y\in(0,1)$. We want to estimate the the probability p for when N is larger ...
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2answers
186 views

If $\text{Var}(X) < \infty$, is $\text{Var}(XY) < \infty$ for $0 \le Y \le 1$?

I have a variable $X$ that I know has finite variance (and therefore also finite mean). Is it always true that its variance remains finite after scaling by $0 \le Y \le 1$? Note that $X$ and $Y$ are ...
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1answer
17 views

How to calculate variance contribution in a Zero-Inflated Poisson regression?

I was wondering if anyone has an idea on how to calculate the contribution to variance of each independent variable in a Zero-Inflated Poisson. How would it even work if you actually have two models ...
0
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0answers
15 views

Test for equal variance for 2-way ANOVA

Forgive a novice in statistics for asking a perhaps very simple question, but I am running a two-way ANOVA with unbalanced design and want to test for homoscedasticity using Levene. For a one-way ...
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17 views

Variance explained $R^2$ by separate fixed effects (and interactions)

I am currently assessing the effect of five environmental variables (A, B, C...) on a trait (Y). I would like to estimate how much variance in Y each environmental variable explains. Previously I had ...
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39 views

What is zero mean and unit variance in terms of image data?

I am new to deep learning. I am trying to understand some concepts. I know "mean" is an average value and "variance" is deviation from mean.I have read some research papers, all say that we ...
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1answer
38 views

What's up with this variance computation?

I'm trying to re-implement the Ckmeans.1D.DP algorithm in Python. I have the actual dynamic optimization part down, but I'm a little confused by the BIC computation they use for selecting the number ...
3
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1answer
47 views

Negative variance result when calculating standard deviation

Please note, I am still in secondary school so please keep your answers simple. A question on my homework states to calculate the standard deviation from a given frequency table with several class ...
3
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1answer
69 views

If X~Exp(λ), what is the expected value of Y=X²?

I am trying to compute this using the integral definition of expected value but I don't think I am doing it right as I am getting a very hard integral that I can not solve. When computing ...