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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6 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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0answers
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 ...
6
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3answers
149 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
9 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 ...
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0answers
14 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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0answers
12 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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0answers
20 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
33 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
42 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
64 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 ...
2
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0answers
13 views

Difference between volatitlity of Annualized return and Annualized volatility of returns

I have a series of monthly returns on financial data. My goal is to estimate the volatility of 10 year rolling returns. I am a bit confused on two options. a) Calculate 10 year rolling returns, ...
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0answers
35 views

Volatility of investment (/w currency hedging)

I´ve been trying to compute volatility of investment with currency hedging, and I have a question. Let's take this example. We have our money in a fond copying the S&P500 index, which has 16% ...
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0answers
8 views

What is the difference between R2 and variance score in Scikit-learn?

I was reading about regression metrics in the python scikit-learn manual and even though each one of them has its own formula, I cannot tell intuitively what is the difference between R2 and variance ...
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1answer
17 views

Statistical analysis for replication in very small experimental datasets

A colleague does replication on a quite coslty experiments. There are four different conditions, each one duplicated. The outcome with $4\times 2 = 8$ points is illustrated below: The analysis is ...
-1
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0answers
22 views

There are many statistical erros in this results and discussion. Can someone help me locate them? [closed]

Results: Data Coding and Exploratory Data Analysis All data were entered into a single SPSS data file for analysis. Seven variables were coded: 1. Sex 2. Total amount of television viewing hours ...
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0answers
16 views

How many boxes have balls?

I have N boxes, each of which may or may not contain a ball. I want to know how many boxes have balls by sampling the boxes in the following way. For each box in the N boxes: I open this box with ...
1
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0answers
10 views

Variance estimation for Levy process

Let $(X_t)$ be a Levy process. It then holds that $$ E(X_{t+\Delta} - X_t) = \Delta \nu, \\ V(X_{t+\Delta} - X_t) = \Delta \mu, $$ under sufficient regularity conditions in terms of moments. For ...
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0answers
12 views

Assessing overall variation for each case in panel data

I have a panel data set - a score on a single measure for hundreds of people, taken once per day for all 365 days of a year. I'm looking for the best method to assess overall variation within each ...
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0answers
37 views

How to change your data to be homoscedastic?

I want to use a linear discriminant analysis and need homoscedasticity. I'm wondering how to get this assumption correct with the data that I have. I have in total over 7000 samples, but I'm ...
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0answers
20 views

Choosing Predictor values to minimize Variance of Least Squares Estimator

Suppose the values of $-1≤ x(i) ≤ 1$ are at your disposal in the simple linear regression model $Y(i) = α + βx(i) + ε(i)$, where the $ε(i)$ are i.i.d. $N(0, σ^2)$. How would you choose the $x(i)$ if ...
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2answers
68 views

How do the means of $X^2$ and $X$ compare?

If $X$ has an exponential distribution with mean $\theta$, does $X^2$ have mean $\theta^2$? If not, how would I find the variance of $X^2$? I tried this: $$V(X^2) = E[X^4] - E[X^2]^2$$ But I'm ...
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1answer
23 views

Data violates homogeneity of variances and is not normally distributed. Can I still run the t-test?

I have two categorical, independent groups, and a continuous dependent variable. The data violates homogeneity of variances, and the dependent variable is not normally distributed for each of the two ...
2
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0answers
24 views

Does rounding introduce variance into estimates?

It is often recommended to round parameter estimates to avoid suggesting more precision than the data really have, e.g. here. I understand rounding does not introduce bias, as long as an unbiased ...
4
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2answers
77 views

What is $V(X^t)$ for any $t$ when only $E(X)$ and $Var(X)$ are known and $X$ is assumed normal?

Summary I'm trying to calculate $Var(X^t)$ where $t$ is the number of periods using only the following known parameters: $E(X)$ and $Var(X)$. $X$ is a random variable and is the return factor $(1 + ...
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4answers
84 views

Odds of a number appearing only one time in 500 spins on roulette

I recently observed a roulette wheel where one number appeared only once in five hundred spins. This is an American roulette wheel with 0 and 00, so the odds of any number hitting should be 1/38. I ...
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0answers
12 views

Computing SD for function of two RV's in R gives wrong results [duplicate]

I have 2 random variables, all independant, discrete and uniform I want to compute standard deviation for Z = X - Y Here is the R code: ...
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0answers
4 views

Evaluate (user-defined) variance estimators in simulation environment?

I'd like to examine how a variance estimator that I constructed for complex surveys behaves in simulation environments, in a manner similar (and perhaps much simpler) to what Li and Levy (2009) at the ...
4
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1answer
179 views

What is meant by the variance of *functions* in *Introduction to Statistical Learning*?

On pg. 34 of Introduction to Statistical Learning: Though the mathematical proof is beyond the scope of this book, it is possible to show that the expected test MSE, for a given value $x_0$, can ...
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1answer
28 views

Variance of estimator(exponential distribution)

I have exponential distributed data $Exp(\lambda)$ with sample n = 50. Also, The sample mean = 2.17. I need to find the estimator of parameter $\lambda$ by the method of moments and to build 95% ...
0
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1answer
18 views

$LDL^T$ decomposition from Cholesky decomposition

Suppose we have a covariance matrix $\Sigma$. I know that the Cholesky decomposition $A^T A$ can be found from the LDL decomposition using $$ \Sigma = LDL^T = (LD^{\frac 1 2})(LD^{ \frac 1 2 })^T = ...
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1answer
29 views

Learning Statistics [closed]

I am new to statistics and I am trying to get my head around 'why' some of these are calculated the way they are and what they mean, or were they just made a preference that stuck? - the statistics ...
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29 views

ANOVA : mean or variance?

I am confused about the ANOVA method in Statistics. ANOVA stands for analysis of variance. It is used to compare the mean between several groups. We use a test of variance (Fisher) for ANOVA. So, is ...
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0answers
7 views

Error estimation in a two parameter non-linear model

With a dataset of $N = 26$ values for $n = 7$ different species (some species with 3-4 data points, one or two with 5)I've found the average value $y_i$ and standard deviation $\sigma _i$ for the $n$ ...
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0answers
27 views

Variance of Distributions from the Exponential Family

I want to understand how the variance of an exponential family behaves. To take a very concrete example. Let consider the unit ball $B$ in d dimensions. Consider the following distribution over unit ...
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0answers
20 views

What's the relationship between covariance, shared variance, and common variance?

I've generally assumed that shared variance and common variance were the same thing. However, here it is written that "Common variance is the realm of total collinearity. On the other hand, the term ...
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0answers
4 views

Comparing absolute error of prediction with variance of original score distribution

I have a dataset of images and their aesthetic ratings. It's basically a set of images, and each image has a set of human ratings. To predict the aesthetic rating of an image I have trained a model ...
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0answers
37 views

Definition of asymptotic variance

Upon studying the ML estimator this concept still confuses me. First define an asymptotic covariance matrix for the MLE estimator (just as an example, we have two parameters $\beta$ and $\sigma^2$, ...
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0answers
31 views

Good algorithm to compute the sample mean and variance [duplicate]

I am looking for good (fast, memory efficient, ideally one-pass) algorithms to compute the sample mean and variance. I have found a technical report by Chan, Golub, and LeVeque from 1983 with ...
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0answers
33 views

What are the bias and variance of a model returning the observed mean for a training set?

It seems to me that bias = variance = 0 but MSE > 0, possibly very high, so clearly my intuition, and math, are wrong. For a training set $T$ and a regression problem let $M(T) = \text{Ave}(y(T))$. ...
7
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2answers
75 views

Why aren't we simply using $R_j^2$ instead the VIF?

After all we calculate the VIF by $1/(1-R_j^2)$. A VIF of $5$ corresponds to an $R_J^2$ of $0.8$. To me, the information given by $R_j^2$ just becomes more obscure when I apply the VIF formula. Why ...
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0answers
19 views

Variance of the difference of two random variables compared to the difference of conditional expectation

Fix a probability space $(\Omega,\mathscr{F},\mathbb{P})$. Let $Y$ be a square integrable random variable $\mathbb{E}Y^2 < \infty$ and let $\mathscr{G}$ be a sub-$\sigma$-algebra of $\mathscr{F}$. ...
2
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1answer
57 views

what is bias and variance of an estimator?

I know what Variance is. But what is Bias? I just have problems to understand this what is written!
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1answer
30 views

If two stats have same stdev but different distribution will their variance be the same?

So if two distributions are, say, normally distributed and have the same standard deviation, they should have the same variance, right? How about if they aren't both normally distributed?
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0answers
33 views

Splitting up the variance of Z for Z = X*Y

$Z$ is a function of two dependent random variables, e.g. $X \cdot Y$. Here it is shown that $$var(Z) = var(XY)=(cov(X^2,Y^2)+E[X^2]E[Y^2])-(cov(X,Y)+E[X]E[Y])^2$$ I am interested in a metric that ...
1
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1answer
26 views

Expectation of $\mathbb{E}(Tr(X^T A X))$ and $Var(Tr(X^T A X))$?

What is the expectation: $\mathbb{E}(Tr(X^T A X))$ and $Var(Tr(X^T A X))$ when $X_{i,j} \sim N(\mu, \sigma^2)$ and $X \in \mathbb{R}^{n \times k}$ where $n>k$ and $A$ is a given p.s.d matrix (not ...
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0answers
11 views

Systematic component variation

The appendix of the paper of McPherson et al (1982) contains a derivation of the systematic component variation SCV. I understand the derivation with exception of the first step. Here are the ...
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1answer
14 views
0
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0answers
6 views

Multilevel modelling - similar level1 and level2 coefficients, but small level 2 variance

I have a random intercept MLM with healt predicted from individual level trust and aggregate trust at the neighbourhood level. The coefficient for individual level is .235 and for neighbourhood level ...
4
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1answer
15 views

Estimate weighted variances in mixture models

Given a generic mixture model $X$ of $k$ components, with distribution $$ f(x)=∑_i\pi_if_i(x), $$ It is easy to show that the $k-th$ moment is just the weighted mean of the $k-th$ moments of the ...
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1answer
31 views

Compute confidence interval for univariate Kernel Density Estimator

I've got a univariate dataset (timeseries) for two kind of simulated systems, and I want to explore the differences between the two. To do that, I can build a univariate gaussian KDE for each dataset ...