The expected squared deviation of a random variable from its mean; or, the average squared deviation of data about their mean.

learn more… | top users | synonyms

0
votes
1answer
21 views

Comparing two means (randomized experiment)

I'm kind of new to science :) for my thesis I worked on some study on health related behavior. There was an intervention for the experimental group and none for the control. So that seems to be a nice ...
-3
votes
0answers
19 views

I need to prove this relation [on hold]

show that Var(y)= 1/N{σyy [0] + 2 (_L=1^(N-1))∑(1-((|L|)/N))σyy[L]} Where ; σyy=Auto co variance function Var(y) = variance of y
0
votes
0answers
18 views

What is the variance of a normally distributed random variable minus the sample mean of the data it came from?

If $Y_i \sim N(\beta, \sigma^2), i = 1,2,\ldots,n$ and $U_i = Y_i - \bar{Y}$, then what is the distribution of $U_i$? I know that $\bar{Y} \sim N(\beta, \sigma^2/n)$ and that the sum (or difference) ...
0
votes
1answer
16 views

How can an intentional timing pattern be demonstrated in temporal data?

I dispose of data showing when a public authority issues different kinds of permits, say, planning permissions and liquor licences. I am interested in finding out whether the timing of one type of ...
1
vote
0answers
19 views

Bound on the variance of a product

Let $Z$ be a positive $\mathbb R$-valued random variable bounded above by $M>0$, and $H$ an $\mathbb R^d$-valued random variable (seen as a column vector) such that $\mathbb E[H_i^2]=1$. Define the ...
0
votes
0answers
14 views

mean preserving spread preserve mean

I have a set of samples (interpreted as probabilities) in the range [0,0.2] with mean =0.1 and sd=0.03. I want to expand them to the range [0,1] while preserving the mean. I have no restrictions on ...
0
votes
1answer
18 views

Showing that $\sum_{i=1}^{n}\sum_{j=1}^{n}(a_{i} - a_{j})^2 = 2n \sum_{i=1}^{n}(a_{i} - \bar{a})^2$

I wish to show $\sum_{i=1}^{n}\sum_{j=1}^{n}(a_{i} - a_{j})^2 = 2n \sum_{i=1}^{n}(a_{i} - \bar{a})^2$ for any numbers $a_1, a_2, ..., a_n$. I assume the first step $+\bar{a}$ and $-\bar{a}$ in the ...
3
votes
2answers
90 views

Find Variance of AR(2) process $X_i = 0.3X_{i-2} + u_i$

Full question: $X_0,X_1, …., X_n$ are distributed according to the following AR(2) process $$X_i = 0.3X_{i-2} + u_i$$ for $i=1,...,n$, $X_0=X_1=0$, and $u_i$ are iid $N(0,3^2)$. Have no idea ...
0
votes
0answers
19 views

How to compute the variance-covariance of log binomial distributions

I have some problems computing the variance and covariance of log binomial distributions. If $A \thicksim binomial(\theta,n)+1 $ and $B \thicksim binomial(p,A)+1$ (where $+1$ is added to avoid ...
1
vote
0answers
16 views

Average conditional variance

Related to Explanatory power of variable. Given a data for 1d variable $Y$ and multidimensional variable $X$, what is the best way to compute average conditional variance of $Y$ given $X$: $$ \Bbb ...
0
votes
0answers
29 views

Proof of $Var(Y_i - \bar{Y})=Var(\bar{Y})$

I saw a result recently that stated $Var(Y_i - \bar{Y}) = Var(\bar{Y})$ but haven't been able to derive it. \begin{align} Var(Y_i - \bar{Y}) &= Var(Y_i) -2 Cov(Y_i, \bar{Y}) + Var(\bar{Y}) \\ ...
1
vote
2answers
45 views

Estimating unconditional variance in time series

Consider a time series process with a well-defined, finite unconditional variance. Given a realization of the process (a time series) and a model for it, there are at least two ways of estimating the ...
1
vote
1answer
236 views

Is the following statement for variance true?

I know: Let be $X$ a random variable and $c\in\mathbb{R}$. Then is $$Var(cX)=c^2Var(X).$$ But is it true that $$Var(cX)=\underbrace{Var[Var[\ldots Var}_{c \text{ times}}[X]\ldots]]?$$
0
votes
0answers
18 views

Use R to explore the properties of the sample variance [migrated]

I am attempting to learn statistics and R. I want to try the following question, and I think I need some guidance. Generate 1000 samples of size 5 from the standard normal distribution and compute ...
0
votes
0answers
18 views

Compare variance components between populations

I am interested in determining if there are differences in variance components between two populations and wanted to ask for feedback on potential strategies. I can compare total variance between two ...
2
votes
2answers
78 views

Why does the parameter variance change when control variables are added to a regression model?

If I add a control variable to my regression, this changes the variances of the parameter estimates. Why is this the case? Is this because SSE increases and therefore the SSR decreases? So basically ...
4
votes
1answer
36 views

Cramér-Rao Lower Bound for Exponential Families

I am having a problem with applying the Cramér-Rao inequality to identify the lower bound for the variance of an unbiased estimator and hoped that you guys could help me. The problem is the following: ...
1
vote
0answers
22 views

Comparing variances of forecast errors

I am forecasting a weekly commodity price series. I use a rolling window for estimating my model, and from each window I make point forecasts for one and two steps ahead. I want to investigate ...
0
votes
0answers
7 views

Estimating variance or coefficient of variation for population given total and count for four segments of population

My goal is to estimate the coefficient of variation for a population, but the data we have been given is very limited. All we have is the total and count for four segments of the population. The ...
1
vote
0answers
36 views

simple statistics of aggregated posterior data after ensemble data assimilation

I have $N$ "4-dimensional" arrays $(x,y,t,c)_{i=1:N}$ containing greenhouse gas emission data, where $(x,y)$ are the spatial coordinates $t$ is the time coordinate (discrete time points) $c$ is the ...
0
votes
1answer
41 views

How to interpret my learning curve

I created the following learning curve in order to diagnose my Random Forest model. As I can see the curve indicates high variance and 'underfitting' (not overfitting), because cross-validation ...
1
vote
0answers
29 views

Hint for problem including function of random variable?

If $Y=\frac{\ln(U_1)}{\ln(U_1)+\ln(1-U_2)}$ where $U_1,U_2$ are independent $U(0,1)$ random variables, then variance of Y equals. I usually use Jenson's inequality to underestimate or overestimate ...
2
votes
1answer
55 views

How should I calculate the variance of a circular random variable?

Consider the following function being the PDF of a circular random variable (orientation angle from the zenith) ...
1
vote
1answer
53 views

Variance of $a^TX$ for MVN X

How do you show that the variance of $a^TX$ for multivariate normal X is $a^T\Sigma a$? I have $V(a'X)=E(a'X-E[a'X])^2$, but it seems like the dimensions get messed up or something after that. So I'm ...
5
votes
2answers
61 views

Removing outliers from a dataset [duplicate]

EDIT: Background: I need to (lin) scale a big dataset to e.g [0,10]. Outliers (in example below 1 and 10000 get (non lin) mapped to resp 0 and 10, the rest (50,51 in this case) is scaled over 0 to 10 ...
4
votes
2answers
60 views

Sample mean and variance independence in the case of correlated observations

Are the sample mean and sample variance of correlated normal observations independent? The classic theory relies on the independence of observations, but this is not the case. So as an example I ...
0
votes
0answers
26 views

help with computing standard score for scarce discretely quantized data

I'm not a stats major and I'd appreciate any help I can get. I've got data with each point defined by a score (between 0-1) and a frequency (0-100%). At 100%, the score is most reliable, at 1% the ...
0
votes
1answer
23 views

How does Anscombe transformation stabilize the variance of a Poisson R.V.?

I was taught that a transformation f(X) is said to be a variance-stabilizing transformation if $[f'(E(X))]^2*Var(X)$ is independent of E(X). For a Poisson-distributed random variable X, E(X) = Var(X) ...
3
votes
0answers
34 views

Bias-variance decomposition

In section 3.2 of Bishop's Pattern Recognition and Machine Learning, he discusses the bias-variance decomposition, stating that for a squared loss function, the expected loss can be decomposed into a ...
1
vote
0answers
10 views

Decomposition of variation into cross-sectional and time series variation

I have a panel dataset covering 20 counties and I have 150 monthly datapoints for each country. Specifically, my data consists of stock returns from each individual country. I want to dig deeper into ...
4
votes
0answers
34 views

How to check if a distribution has undefined variance?

How can I determine if experimental data comes from a distribution where the variance is undefined (e.g. the Cauchy distribution)? I honestly have no idea how to attack this problem in a sensible ...
1
vote
1answer
15 views

“weigh” different variance covarance matrixes

so my question if I have a set of weights which sums to 1 (say: [0.2,0.2,0.6]) which would represent my states of the world and I have forecasted 3 different variance covariance matrixes (all of which ...
0
votes
1answer
31 views

calculating mean of a random variable raised to a power

Given the mean & variance of a dataset of linear measurements X ... N~(14,2), I want to find the mean of X^3. So by taking mean as being expected value, & rearranging: - ...
0
votes
2answers
42 views

Variance of Gaussian linear combination

I have two independent gaussian distributions to combine and I have a doubt. Let's say we have $X \sim N(\mu_x,\sigma^2_x)$ and $Y \sim N(\mu_y,\sigma^2_y)$. I want to mix the two variables with a ...
1
vote
1answer
61 views

Variance in estimating p for a binomial distribution

how can I calculate the variance of p as derived from a binomial distribution? Let's say I flip n coins and get k heads. I can estimate p as k/n, but how can I calculated the variance in that ...
1
vote
0answers
18 views

Proof for Irreducible Error statement in ISLR page 19

This section of Introduction to Statistical Learning in R (page 19 in v6, statement 2.3) is motivating the difference between reducible and irreducible error (that is noted by $\epsilon$ and has mean ...
0
votes
2answers
38 views

Variance calculation [duplicate]

Can someone explain why: Given a set of n independent observations Z1...Zn, each with variance K. The variance of the mean is K/n?
1
vote
1answer
32 views

distribution of sample variance of correlated observations

It is well known that if we have n i.i.d. observations of a normal random variable, then Cochran's theorem tells us that: $\frac{(n-1)s^2}{\sigma^2} \widetilde{} χ^2_{n-1}$ But what if the samples ...
1
vote
0answers
6 views

3 biological groups, 30 subjects (total), measured on 10 days - how to correct for day-to-day variation?

We've run an experiment in which we included 90 subjects and have measured several variables. My question specifically goes to the way we can correct for day-to-day variations. So, here is the setup ...
0
votes
0answers
28 views

ANOVA with Zero Variance

I have four sites. I would like to run ANOVA with Tukey's HSD post hoc test to show that an average hydrological variable (in this case peak runoff rate) is different across the sites. My issue is ...
3
votes
1answer
127 views

Distribution of variance of Gaussian variable

I have a Gaussian random variable, which I can use to generate a sequence of values. So, I've generated a sequence of values of arbitrary length, and each set of 50 data become a sample. Now, consider ...
3
votes
2answers
66 views

Conditional variance in OLS regression

Consider the linear regression model: $$y_{it}=x_{it}\beta+\epsilon_{it}$$ where $x$ is single regressor. The conditional mean of any specific observation is:$$E[y_{it}|x_{it}]=x_{it}\beta$$ ...
0
votes
0answers
11 views

How to assess similarity of two sets of Principal Component Analysis loadings

A predictive model that I currently use relies on PCA with varimax rotation to reduce the dimensionality of the data (whether this is appropriate is a separate question). The dataset consists of ...
1
vote
1answer
35 views

When would you want to reduce variance?

In a sampling-estimation context, low variance of the estimate is a goal. Several things I've read suggest (though I can't quite connect the dots) that lowering variance in the data will improve the ...
0
votes
1answer
33 views

Does multicollinearity affect performance of a classifier?

I know that wikipedia references are sometimes frowned upon here, but this one has me puzzled: Wikipedia - Multicollinearity I know what multicollinearity is, and ...
0
votes
1answer
85 views

Negative variance in a log normal distribution

I'm currently trying to solve a maximum likelihood estimation of a random variable which is assumed to be log normal distributed. For this I compute the log of all sample values I have in order to ...
3
votes
3answers
79 views

Why does a regression tree not split based on variance?

When choosing each split, recursively, in a regression tree, I understand that you want to measure the spread, in each side of the split, essentially. So, in some sources, including this one at 6 ...
0
votes
0answers
7 views

Evaluating the reliability of binary observations by members of a group of observers

If there are N observers who each make binary observations, e.g. pass/fail, what is the suggested statistical approach to evaluate the reliability of each observer? There are a large number of ...
1
vote
2answers
48 views

Covariance of linear combinations of correlated random variables

I am trying to predict the covariance of two linear combinations of normal random variables: $\newcommand{\N}{\mathcal N}$ \begin{align} X &= w\N(u_1,\sigma^2_1)+(1-w)\N(u_2,\sigma^2_2) \\ Y ...
1
vote
1answer
49 views

Time series of variance

If the mean or total of a variable studied over time displays seasonality, should I expect that the variance of that variable should display seasonality similar to the mean? Why or why not? The data ...