The expected squared deviation of a random variable from its mean; or, the average squared deviation of data about their mean.
4
votes
1answer
35 views
Justifying the distribution for the maximum likelihood estimator in a linear regression example
Data $(x_1, y_1), \dots, (x_n, y_n)$ is modelled with $x_i$ being non random and $y_i$ being observed values of $$Y_i = \alpha + \beta (x_i - \bar x) + \sigma \epsilon_i$$ with $\epsilon_i \sim ...
3
votes
2answers
54 views
Finding the variance of the estimator for the maximum likelihood for the Poisson distribution
If $K_1, \dots, K_n$ are i.i.d. Poisson distributions with parameter $\beta$ I have worked out that the maximum likelihood estimate is $$\hat\beta (k_1, \dots, k_n) = \frac{1}{n} \sum_{i=1}^n k_i$$ ...
2
votes
0answers
29 views
Model variance and bias in cross validation
his question is partly inspired about the answer to this other question: Number of folds for K-fold.
The fundamental question I have is the following: How do different cross-validation methods ...
1
vote
0answers
39 views
How do I create a random variance matrix (x'x)/N with confidence that it will be invertible?
I see some similar threads, but no answer that I know how to apply to this question. I wish to create a variance matrix for a (pseudo)random matrix $X$ with dimensions $K \times N$, where each row $k$ ...
2
votes
1answer
26 views
Are these possible LeveneTest results?
I have experimental data of response times that differ according to the factor TrialType: Regular or ...
3
votes
1answer
46 views
Testing change in variance over 5 time points and regression to the mean
Good morning
I searched regarding change in variance over time, but everything I saw was about relatively long time series. I have a series of 5 time points, equally spaced, but with different ...
2
votes
1answer
57 views
Estimating the population variance [duplicate]
I'm trying to understand the emphasized phrase in the following passage:
The usual method of determining the probability that the mean of the population lies within a given distance of the mean of ...
3
votes
0answers
51 views
Variance of marginal posterior distribution
Suppose $Y_1,\dots,Y_n\mid\mu,\sigma^2 \sim \text{ iid } N(\mu,\sigma^2)$ and suppose the priors $\mu \mid \sigma^2 \sim N(\mu_0, \sigma^2 / \kappa_0)$ and $1/\sigma^2 \sim \text{gamma}(\nu_0/2, \nu_0 ...
3
votes
1answer
34 views
Are degrees of freedom $n-1$ for both the sample standard deviation of the individual observations and for the standard error of the sample mean?
I collect $n$ ($<20$) i.i.d. observations from any distribution. In order to compute the sample variance, I take
$$s^2=\sum_i \frac{(\bar{X}-X_i)^2}{n-1}$$
If I want to build a confidence ...
0
votes
1answer
34 views
How to understand the variance in this setting?
All -
I have a dataset originated from a practical setting, but it is not clear to me how to interpret it. Let me try to frame the setting and see if it makes sense:
A manufacturer produces a type ...
0
votes
0answers
19 views
Variance of the forecasting error of the model: $y_s = \beta + u_s$
I want to derive the var of the forecasting errors of the model: $y_s = \beta + u_s$
the conditional forecast: $$\hat y_s=\hat\beta$$
the forecasting error is: $$\hat y_0 - y_0=\hat\beta - \beta - ...
2
votes
1answer
44 views
hypothetical measure of variability similar to entropy
Variance has the following properties:
$Var(cX)=c^2Var(X)$
For independent variables $Var(X+Y)=Var(X)+Var(Y)$.
Range of a rv has the following properties:
$Range(cX)=|c| Range(X)$
For ...
0
votes
0answers
42 views
Is the squares of the coefficients of variation of (Z^c)-1 ascending in c?
In my previous question we consider whether CV^2(Z^c) is ascending in c, where Z is a random variable with positive values larger than 1 and c>0. The given answer was right. Now, assume that Y=(Z^c)-1 ...
2
votes
1answer
35 views
Variance of product of k correlated random variables
Does somebody know an equality/inequality about the variance of
product of k correlated random variables?
With many thanks.
0
votes
0answers
26 views
Is the square of coefficient of variation an ascending function of exponent c? [duplicate]
Suppose that $x$ is a random variable with any distribution that takes only positive values. If $z=x+1$, can the following inequality hold for constants $c_2>c_1>0$?
...
2
votes
0answers
36 views
Variance in a known population
I am working on a problem that is similar to the standard radioactive decay rate experiment, but with a twist. In the normal experiment, one takes several different measurements of the decay rate, ...
2
votes
0answers
33 views
Measuring parameter sensitivity and variability (standard-error) in k-fold cross-validation
I mainly use k-fold cross-validation for parameter tuning and model selection for prediction problems. Now, is there a standard or if not a less-known way to measure the sensitivity of the parameters ...
3
votes
2answers
109 views
Question about squares of the coefficients of variation
Suppose that $X$ is a random variable with any distribution that takes only positive values. Can the following inequality hold for constants $c_2 >c_1 >0$?
...
1
vote
1answer
50 views
Proof: Linear Regression
I am at a loss how might one prove $\text{Var}{(\hat{y}_h)} = \sigma^2 \left(\frac{1}{n} + \frac{(x_h-\bar{x})^2}{S_{xx}}\right)$. Note that $\hat{y}_h$ = $b_0 + b_1X_h$ which is a regression line ...
6
votes
0answers
58 views
Standard Deviation of Binned Observations
I have a dataset of sample observations, stored as counts within range bins. e.g.:
min/max count
40/44 1
45/49 2
50/54 3
55/59 4
70/74 1
Now, ...
1
vote
1answer
53 views
Constrained mean variance optimization
I have some numbers $X={x_1,x_2,...,x_n}$. I add some small numbers to them and get $Y={y_1,y_2,...,y_n}$ where $y_i=x_i+\epsilon_i$. How can I find $Z={z_1,z_2,...,z_n}$ to minimize ...
0
votes
1answer
32 views
If I can simplify the equation [closed]
I have an equation where it is divided by $\sqrt{(c_1 var(x_1)+c_2 var(x_2) + 2 c_1 c_2 cov(x_1,x_2)}$. If I can simplify it (without sqrt).
-4
votes
0answers
25 views
Please show me that with which formula, I can calculate pooled variance for unequal population variance? [closed]
I know it not legal and valid for faq but I cannot put a photo here because of reputation and not logged in here. Sorry. This is last question. After this, I never put link here. Sorry.
My question ...
0
votes
0answers
34 views
How to transform $Var(X-Y)^{2}$
I have something like that:
$$ Var\left( \frac{1}{2n-2} \sum_{i=1}^{n-1} \left( X_{i+1}-X_{i}\right)^{2} \right) $$
and I transformed it to something like that (I hope it is correct):
$$ ...
0
votes
1answer
31 views
Consistent estimator with var=0
I'm trying to think of an example of a consistent estimator with var=0 but I'm having a hard time.
I pretty sure it exists but I'm unable to find one.
Any help\hints would be much appreciated.
0
votes
0answers
12 views
ANOVA as Comparision of Means and Regression [duplicate]
ANOVA, ANalysis Of VAriance, is a method to compare means of several variables. At the same time it falls under G(eneral)LM in a sense that it a method for regression and used for regressing ...
0
votes
0answers
20 views
Variance of superset from variance of subsets [duplicate]
Let's say I want to estimate $var(A)$ of a list of numbers $a_i \in A, i\in [0,N]$.
However, I only have the variance of the non-overlapping, and complete ($B \cup C = A)$ subsets $B$ and $C$.
...
1
vote
1answer
42 views
need derivation of join-count variance (spatial autocorrelation stat), know where it is?
I am using interlibrary loan to get Cliff and Ord's book Spatial Processes, but the semester just ended and it is slow now. On page 18ish of this book, Cliff and Ord show how the variance for the ...
0
votes
1answer
103 views
Which variables have too much variation?
So I have 1000 variables (different lakes), each with 12 observations (each lake was tested once a year for 12 years). Some of the lakes are really small, so we think they have way too much variation. ...
2
votes
1answer
87 views
F test for equality of variances
I know that the test statistic is $$F=S_1^2/S_2^2 $$
But I am looking at some example questions from my lecturer and some have confused me. For example:
For a certain game, individual game scores ...
0
votes
0answers
75 views
Want to evaluate how uniform my data is?
I have a feature vector of size nx3 where n = no. of data points and no. of features = 3.
So the mean is a 3x1 vector.
The data actually is a set of pixels of an image segment(not a whole image). and ...
4
votes
0answers
42 views
How to test whether mean and variance is the same in two small samples?
I would like to test two relatively small samples against the null hypothesis that both their means and variances are the same. The alternative would be that they in fact differ. I saw a post on this ...
0
votes
1answer
53 views
Var(AZ)=A Var(Z) A^T?
I am learning linear models, and I do not understand the following:
$\text{Var}(AZ)=A \text{Var}(Z) A^T$ where $A$ is a constant matrix. I want to know the variance $\widehat{\beta}$ in a linear ...
1
vote
0answers
17 views
Are the sequential sum of squares appropriate when treatments must be applied in sequence?
I'm working with some modeled future stream flow data that was created in two steps. First, future precipitation predictions (at certain points in a watershed) were created by running historical ...
1
vote
1answer
50 views
NMDS and variance explained by vector fitting
I just ran a non metric multidimensional scaling model (nmds) which compared multiple locations based on benthic invertebrate species composition. After running the analysis, I used the vector fitting ...
4
votes
3answers
121 views
Why it is natural to expect equality of variances?
When conducting various statistical test why do we expect equality of variances/ homoscedasticity/sphericity etc.?
1
vote
0answers
32 views
What coefficient could I use to calculate the relative difficulty of a test in relation to others using only mean and population standard deviation?
I have a series of tests, all of them of different difficulty, and from each of them I get an average score and a population standard deviation; e.g:
...
2
votes
2answers
80 views
Correlation not significant because there is not enough variance?
I have a question about correlations again.
I have a dichotomous variable that I want to correlate with the another one (metric) by using the point-biserial correlation coefficient. I get a ...
1
vote
0answers
45 views
Interpretation of Variance and Covariance
I am totally new to statistics and I have to create a variance and covariance analysis.
I am using SPSS for this.
I have created the covariance table:
Hopefully it is the right thing. The first 3 ...
1
vote
2answers
76 views
Why is the k-means algorithm minimizing the within cluster variance?
I have read that the k-means algorithm tries to minimize the within cluster sum of squares (or variance). With some brainstorming, a question popped up. Why is it that k-means or any other clustering ...
4
votes
2answers
82 views
What does the Semivariance tell me?
I am looking at a Semivariogram. I know it shows me the relationship between distance and semi-variance. I also know that at the end of the range the distance no longer auto correlates. What I am ...
6
votes
1answer
127 views
What does the residual higher level variance tell me?
I have a multilevel logistic regression model predicting the probability of item nonresponse, where the random intercept variance at country level takes on the following distribution for the different ...
0
votes
1answer
60 views
How to calculate the variance of the GED distribution?
The density of the GED distribution is given by
\begin{align}
GED(l;\mu,\beta,\nu)&=\frac{\nu \exp\left[-(\frac{1}{2}) \left|\frac{l-\mu}{\beta \lambda}\right|^\nu \right]} {\lambda ...
1
vote
1answer
28 views
ANOVA determining percentage of variation
The Financial Review wished to estimate the amount of annual government spending using tax revenue and level of nationwide debt. Data from 1958-2008 (inclusive) was used. All variables were measured ...
2
votes
0answers
42 views
Can the OLS residual variance suggest a polynomial relationship?
I am trying to figure out whether from the following graph of the OLS residuals that the linear relationship does not hold, and that probably a cubic relationship would do better? Since both in the ...
1
vote
0answers
30 views
calculating variance of sum of predicted costs from two-part model
I have a question regarding the calculation of the variance of the sum of predicted health care costs using a two-part regression model. Details are below, but it boils down to how to calculate the ...
0
votes
0answers
24 views
How to prepare variance matrix in Statistica (or different tool)?
I have data which describe measurments in four different point for few days.
Four water parameters have been measured.
In other words, data contains following columns:
point name - we have four ...
3
votes
1answer
90 views
Variance of a time series fitted to an ARIMA model
I think this is a basic question, but maybe I am confusing the concepts.
Suppose I fit an ARIMA model to a time series using, for example, the function auto.arima() in the R forecast package. The ...
2
votes
0answers
33 views
Bound on the variance for [0,1] RVs as a function of the mean
I noticed that if $X$ is a RV in $[0,1]$ then $V[X] \leq E[X](1-E[X])$, which also implies that the bernoulli distribution maximizes variance (one of many solutions).
For interest's sake consider ...
0
votes
1answer
37 views
What's the difference between bias in model error in regression?
Is model error the same as bias in regression? For example, if I construct data by $y_i=N^{\text{th}}$ degree polynomial plus uncorrelated noise, and do a regression with the $M^{\text{th}}$ degree ...
