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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1answer
27 views

bias-variance decomposition and independence of $X$ and $\epsilon$

I took a look at a couple of derivations of this decomposition and I think they all require that $E[\epsilon \hat{f}] = 0$. The most transparent one I found was from Wikipedia here. I reproduce the ...
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0answers
4 views

Permanent and temporary shock income, variance decomposition

I have a balanced panel data (N= 190, T=5). It's about income and personal characteristics of the householder. I would like to find the coefficients of a temporary and of a permanent income shock. I ...
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0answers
10 views

Two-way ANOVA - discrepancy between main result and model parameters

I am running a two-way ANOVA examining the influence of both school and gender on Likert scale answers. The Type III SS results show school significant (p=0,001), but gender or gender*school not ...
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0answers
22 views

Calculate Var(X/Y) for dependent variables?

I understand that you can calculate Var(X*Y) through Bienayme, whether variables are dependent or not. I am wondering if there is a similar way of calculating Var(X/Y) when variables are dependent? ...
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0answers
15 views

What can be deduced from the variance and cramer rao bound?

I have computed the cramer rao bound of the estimates of the coefficients $\mathbf{h^T}$ for a moving average model (MA) involving 2 different process noise : (1) when the process noise is a random ...
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0answers
7 views

What is the best way to analyse data comparing one by one and stipulate the accuracy?

Follow the example: The first line is the data I got. The second line is the target data. | 154.0 | 784.4 | 854.1 | 789.3 | | 153.5 | 789.7 | 892.3 | 903.2 | I ...
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0answers
8 views

Statistically verifying distribution of users within an A/B Test

Hoping you can help me determine the best way to statistically verify that an A/B test was set up in an unbiased way. The A/B test was set up to split users on my website 50/50 into a test/control ...
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0answers
30 views

How to analyze survey data, interval or ordinal, and how to account for nonresponse bias?

I have a question regarding a survey. I gave a test to people and they were asked to rate the tester on a scale of 1 to 5, 5 being they liked it and gave it the highest rating, with 1 being the ...
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1answer
32 views

RBF transformation on a Normally Distributed Random Variable

I have a random vector $\mathbf{X} \sim \mathcal{N}(\mathbf{m,\Sigma})$ which is transformed by a Gaussian Radial Basis Function into the random variable $\mathbf{Y} = K(\mathbf X) = \exp(-\lambda ...
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0answers
12 views

Variance of sum of datasets with different sampling intervals

I have two randomly distributed datasets which are to be added together element-wise, and I am looking to calculate the uncertainty of the mean of the result. One dataset had a sampling rate of 1 ...
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0answers
14 views

conditional/unconditional expectation and variance for an AR(1) process

We have an AR(1) process, $X_t=\alpha X_{t-1}+\varepsilon_t$ with $\varepsilon\sim(0,\sigma^2)$, $X_0=0$ and $|\phi|<1$. We have the conditional expected a value with respect to $X_{t-1}$: ...
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8 views

Variance of the logarithm of a binomial distributed random variable

What is the variance of $\log(1+X)$, where $X \sim Bin(n,p)$. I am looking for an approximate solutions depending on n and p. I have tried Taylor expanding the logarithm, but it didn't lead to a ...
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1answer
32 views

Estimating population variance through simulation in R

I want to estimate the variance of the exponential distribution with a rate of $\lambda=0.2$. I'm drawing a sample of 5 exponentials 1000 times, and know that the theoretical variance of my ...
1
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1answer
35 views

What is the origin of squaring centred data as way to model variances instead of means?

I recently came across this Answer by @mpiktas wherein he suggested a transformation of $y_i \rightarrow y_i^{\prime}$ $$y_i^{\prime} = (y_i - \overline{y})^2$$ followed by fitting a model for ...
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1answer
134 views

Estimate variance of a population if population mean is known

I know that we use $\frac1{n-1}\sum\limits_i(x_i - \bar{x})^2$ to estimate the variance of a population. I remember a video from Khan Academy where the intuition given was that our estimated mean is ...
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0answers
25 views

Estimating the prediction variance in kernel ridge regression

I'm trying to estimate the variance of predictions for a kernel ridge regression model. The model is simply kernel ridge regression: $$\hat{y} = K(K+\lambda I)^{-1}y = A y$$ $K$ is the $n \times n$ ...
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1answer
79 views

Find standard deviation of arbitrary game with multiple payouts

This earlier question asked how to get a 5.76 standard deviation for a single number bet on Roulette. The answer gave the formula, but unfortunately, the formula doesn't easily generalize to more than ...
2
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1answer
44 views

Kriging with individual errors

When evaluating a Kriging prediction, it is possible to include a hyperparameter $\lambda$ to account for noise in the data. $\lambda$ can be estimated as a parameter in a maximum likelihood ...
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0answers
6 views

Is there a quantifiable way to find the optimize the minimization of variance in our sample without increasing our bias too much?

Due to the bias-variance trade off, whats the best way to test to see whether decreasing your variance has increased our bias too much? Or is there a way? Since we cannot quantify the bias of the ...
4
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1answer
42 views

Partition data into two sets such that the difference of their variance is minimal

Suppose there are $n$ data values $x_1<x_2<\ldots<x_{n-1}<x_n$,and I've found a partition number $k$, such that $$ ...
5
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0answers
45 views

why use diagonal $\Sigma$ when working with Bayes decision theory?

My prof. said in the class that for Bayes decision rule, the likelihood is Gaussian and in practice, we will almost always work with a diagonal $\Sigma$. Why is that? I know that a diagonal $\Sigma$ ...
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0answers
14 views

How to interpret Realized Volatility and TSRV using R

I am looking at some high frequency data and I would like to know how to interpret and compare Realized volatility (RV) and Two Scale Realized Volatility (TSRV). References below. Given X is the log ...
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1answer
31 views

Sum of variances law

I am currently trying to grasp the concept of Variance Sum Law where variance(x + y) = variance(x) + variance(y) I am not even sure if I understand it correctly ...
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23 views

Estimation of variance: How to bring Bessel's correction together with degrees of freedom?

I have been considering multiple textbooks to find out the reason that the denominator of the estimation of the population variance is n-1 rather than n. Depending on the book, two reasons are given: ...
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1answer
40 views

Variance of the $\hat{\sigma^2}$ of a Maximum Likelihood estimator

Given some normally distributed observations $x_1,x_2,...,x_n$ $\forall i\ x_i\sim\mathcal{N}(\mu, \sigma^2)$ the ML estimator decides that the variance that maximizes the likelihood function is ...
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48 views

Why does my p-value = 0?

I created a vector that is 329 rows long, with each row containing a z-score. I derived my degrees of freedom by counting up the number of rows (329) and subtracting 1. Then, I computed a test ...
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0answers
14 views

Relative Variance

Is there a standard definition of the Relative Variance? Wikipedia defines it as the square of the coefficient of variation, but some articles define it as the variance divided by the absolute value ...
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1answer
26 views

Hierarchical Bayesian Regression, Can an Inverse-Gamma distributed Variance look Normal or t?

Using Peter Hoff's book, A First Course in Bayesian Statistical Methods, I used some of my own data to fit a Hierarchical Bayesian Regression following his example. In his book, he utilized a Gibbs ...
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0answers
45 views

CLT and 2 variables

Okay so there are 2 variables $D_i$ and $V_i$. Now $D= D_1 + D_2 + ... + D_N$ and $V = V_1 +.. +V_N$ Now I know the relationship is such that $E[D_i - a*V_i] = 0$ and $Var[D_i - a*V_i] = E[D_i]$ ...
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1answer
20 views

Share of variance explained by one variable

I have two independent variables, x1 and x2. If I fit a linear model using only x1, I get this result Model 1: R^2 = 0.66, p value = 4.34E-10 (***) If I fit a linear model using both x1 and x2, ...
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1answer
31 views

Given a set of numbers from 0 to 100, what's the chance that the next number will be less than 10?

I performed a set of trials. Every trial returned a number 0<=N<100. What's the chance that in the next trial, the picked number will be less than 10?
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1answer
32 views

Usage of Plus-minus sign

I have a question concerning statistical conventions. I want to report the classification rate of a 3-fold cross validated machine learning experiment. Of course I report the mean and some measure of ...
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1answer
15 views

Partitioning of variance

Why do Mathematicians like to think about partitioning variances into different components -- the basis of ANOVA? In contrast, why is it not correct to partition the SD into components?
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45 views

R not plotting observations with leverage one

I am building a really simple linear model. I want to test if the frass I got over 3 days from butterfly larvae depend upon the food they ate (diet), the butterfly family (the mother line) and ...
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0answers
16 views

non parametric analysis of variance in small, unbalanced data set

I'm facing a data set composed of five different dependent (1,2,3,4,5) and three independent (I,II,III) variables. 1,2,3,4,5 are continuous but not normally distributed. I,II,III are qualitative, I ...
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0answers
10 views

A strange R limma voom function mean-variance trend [duplicate]

I am opening a long silent question here because I cannot understand my mean variance trend produced by limma. I am new to RNA-Seq analysis and tried using limma on my data. After voom transformation, ...
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4answers
40 views

Variance of linear combinations of correlated random variables

I understand the proof that $$(aX+bY) = a^2Var(X) +b^2Var(Y) + 2abCov(X,Y), $$ but I don't understand how to prove the generalization to arbitrary linear combinations. Let $a_i$ be scalars for ...
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1answer
25 views

A comprehension question to conditional heteroscedasticity/GARCH

I have a time series with strong seasonality. At specific time periods/seasons there is also a stronger Variance than in other time periods/seasons. Is that an example of conditional ...
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2answers
35 views

Is it fair to say that most real-life distributions have finite variance?

In most real scenarios I know the random variable X isn't unbounded.
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14 views

Why does GEE produce the same parameter estimates as OLS?

The quasi-likelihood function optimized under GEE is: $S_k(\beta)=\sum_{i=1}^{K}\frac{\partial\mu_i}{\partial\beta_k}\nu_i^{-1}(y_i-\mu_i)=0,$ where $\mu_i=h(\textbf{x}_i,\beta)$ is the conditional ...
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0answers
46 views

4 cases of Maximum Likelihood Estimation of Gaussian distribution parameters

Let $x_1,x_2,...,x_n$ some normally distributed observations. So $\vec{x}=\begin{bmatrix}x_1 & x_2 & ... & x_n\end{bmatrix}^{T}$ In the context of my research I am trying to estimate ...
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4answers
697 views

Inverse function of variance

For a given constant number $r$ (e.g. 4), is it possible to find a probability distribution for $X$, so that we have $\mathrm{Var}(X)=r$?
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1answer
19 views

Cross-validating the tbats/bats function in forecast

Is there a way to cross validate the tbats/bats function in the forecast package in R? I have been trying to get CV weighted parameters which then I can pass to a function for revised estimates. ...
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0answers
5 views

Estimate variance of an arbitrary estimator using cross validation

Ron Kohavi's paper "A Study of Cross-Validation and Boostrap for Accuracy Estimation and Model Selection" explains very well how to compute the variance of the estimated accuracy when using CV (or ...
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0answers
15 views

Robust Estimators - Winsorized Variance degree of freedom (df)

this is my first question on this site. So, I'm currently working on my final year thesis, and it was on Robust statistics. In my work, I will use Trimmed Mean, Winsorized Mean and Winsorized ...
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1answer
46 views

How to estimate a chance of getting in the first positions, given previous tries?

I perform a series of experiments that return a number N that is between 1 and MAX. MAX varies between experiments. For example: ...
2
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1answer
45 views

Variance of compound distribution

The binomial distribution describes the probability of $k$ 'success' events given $N$ independent trials, each with a probability $p$ of being a success. The distribution is described by the formula ...
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0answers
12 views

Calculate the dispersion between of the sample variances and the population variance

Suppose that I have one population and 30 samples of these population. One variable of the population is the income. I would like to compare the variance of the income of the population with the ...
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0answers
13 views

Noninformative prior for variance, understanding and coding

I have three questions regarding the understanding behind and implementation of a noninformative prior for variance. I'm attempting to build a Metropolis sampler and I'm trying to sample from a ...
2
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1answer
38 views

Testing whether variance across 6 values is significantly above zero

We estimated a network via the Ising model procedure. The network contains 11 variables, and therefore 55 pairwise associations (these are called edges). We estimated this network in 6 different ...