All Questions
1,569 questions with no upvoted or accepted answers
3
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Is the following property for positive random variables fulfilled in general?
[I have cross-posted this from math.stackexchange: https://math.stackexchange.com/questions/476466/is-the-following-property-for-positive-random-variables-fulfilled-in-general ]
Suppose we have a ...
- 179
3
votes
0
answers
114
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Test for equal variability in mixed model setting
I have a setting where I normally would model the variability in measurements by a linear mixed model which would look in R as follows.
...
user29057
3
votes
0
answers
110
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t-test on two variance calculations
I have survey data that was recorded in a many different towns. I want to see for which variables is the data significantly more or less variable within towns than across all towns.
Currently, I'm ...
- 1,312
3
votes
0
answers
409
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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 ...
- 2,545
3
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2k
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Variance associated with factors in GLS (nlme)
First time posting here, so thank you ahead of time for your help. I'd like to estimate the variances associated with two factors in a relatively simple, but unbalanced GLS model, and I am unsure how ...
- 101
3
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1k
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Confidence intervals for extreme value distributions
I have wind data that i'm using to perform extreme value analysis (calculate return levels). I'm using R with packages 'evd', 'extRemes' and 'ismev'.
I'm fitting GEV, Gumbel and Weibull distributions,...
- 951
3
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0
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142
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Distribution of variable
How to find the distribution of $$\sum_{i=1}^n (X_i - X_{1:n}),$$ where $X_i$ are i.i.d. random variables and $X_{1:n} = \min(X_1,X_2,...,X_n)$?
I need to find the distribution in a particular case, ...
- 31
3
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610
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Online algorithm to compute variance with a decay
Could somebody point me to an online algorithm that computes the variance, but gives a higher weight to more recent values?
3
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answers
4k
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Accurate estimates of the variance of maximum likelihood estimators
According to various sources, the variance of ML estimators can be obtained from the Hessian matrix of the likelihood function. If $H$ is the Hessian of the negative log-likelihood function, then $H^{-...
- 2,392
3
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352
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Correct variance for minimum detectable difference
I have a question regarding variance, paired testing and minimum detectable difference (MDD).
Paired samples:
$$
MDD (δ) = \sqrt{ \frac{σ^2}{n} (t_{(α/2,n-1)} + t_{(1-β, n-1)})}
$$
I have a set of ...
- 31
3
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1
answer
1k
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How to minimize Chi-Square using the CDF instead of the PDF?
Suppose one has data that is suspected to obey a normal distribution. One computes a histogram of the data, and performs Pearson's Chi-Squared Test. To perform this test, one must compare the observed ...
user146123
3
votes
1
answer
2k
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Almost sure convergence and limiting variance goes to zero
Say an estimator converges with probability one and at the same time its variance goes to zero in the limit. How is it different than an estimator that converges with probability one but its variance ...
- 185
3
votes
1
answer
766
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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 ...
- 1,113
2
votes
0
answers
57
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Learning to do the parametric bootstrap
I learned about the parametric bootstrap (Can we bootstrap regression coefficients instead of data?) and I am interested in applying this method to determine the confidence interval on the ratio of ...
- 667
2
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0
answers
48
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Understanding Volatility Clustering: Conditional or Unconditional Variance?
A stylized fact observed in financial time series is volatility clustering. Volatility clustering is commonly described as the fact that large changes in asset prices are followed by large changes, ...
- 1,465
2
votes
1
answer
32
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Time series and separating variance by time scale
There is a single-variable time series wich can be thought as being stationary in the long run. The observations are taken at irregular time intervals. The values of observations can be assumed to ...
- 152
2
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0
answers
23
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Variance of a single measurement
Say that I have a collection of $n$ data points: $x_i, y_i, i = 0, \ldots, n-1$, and $x_0 < x_1 < \cdots < x_{n-1}$. The $x_i$ are the independent data, and the $y_i$ are the dependent data (...
- 121
2
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27
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Understanding proof of variance of mean of random effects model and relationship to E[MS_treatments]
My textbook makes the following proof:
But I cannot understand how it arrives.
The variance of $y_{ij} = \sigma^2 + \sigma_t^2$ by assumption
this leads to:
$MS_e = \sigma^2$
$MS_{treatments} = \...
2
votes
0
answers
42
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Is the Between-Groups Variance a Covariance?
I am currently working through a book/class in quantitative genetics, and in Falconer and Mackay's Introduction to Quantitative Genetics, the following line stumped me:
"The between-group ...
2
votes
0
answers
128
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Independent Component Analysis (ICA): Why rotate whitened data by principal components instead of right singular vectors?
I have a data matrix $ X $ that is $n \times m$, where $n$ is the number of features and $m$ is the number of samples and $ n < m$. Let the Singular Value Decomposition (SVD) of $X$ be $$ X = U \...
- 51
2
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answers
28
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Variance partitioning when using a response from 1st study as a predictor in 2nd study
I use linear mixed-effects models to analyze my data, where I have a variable C that is used as a response and an explanatory variable in separate studies.
In the first study C ~ A + (1|B),
I found ...
- 23
2
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0
answers
99
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How can I find the unconditional variance of this process?
Let $y_t = \Delta p_t$ denote a time series of asset returns, where $p_t$ are logarithmic prices. $y_t$ is generated by a heteroskedastic MA(1) process
\begin{aligned}
y_t &= z_t+\theta z_{t-1}, \\...
- 115
2
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answers
53
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Count distribution in which the mean is equal to the standard deviation?
I have a data set with counts that exhibit the sample property that
$$\hat \sigma_x \approx \bar x$$
which is to say that the sample standard deviation (with Bessel's correction) appears to ...
- 9,680
2
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answers
75
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Bias and Variance of a Honest Random Forest
I am trying to read the paper Estimation and Inference of Heterogeneous Treatment
Effects using Random Forests. In the section 3.1(Theoretical Background), page 13 paragraph 2, The authors have ...
- 137
2
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0
answers
124
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Statistically comparing the variance of two dependent samples
I have two dependent samples of data. Each sample contains N = 800 values (data points) and stem from the same human subjects, that is, sample one is the pre-experimental and sample two the post-...
- 307
2
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0
answers
158
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Definition of exponent measure (extreme value theory)
Let $F$ be a distribution function on $\mathbb{R}^2$, and let $U_i$ be the left continuous inverse of $\frac{1}{1-F_i}$, where $F_i$ is the marginal distribution of $F$.
In my textbook, there is the ...
- 656
2
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answers
72
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$1-F$ is rapidly varying if and only if there exists $b_n$ such that $\frac{\max X_i}{b_n} \to 1$ in probability
The following is a problem from Extreme Values, Regular Variation and Point Processes by Resnick.
We will say $1-F$ is rapidly varying as $x \to \infty$ if $\lim_{t \to \infty} \frac{1-F(tx)}{1-F(t)} =...
- 656
2
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75
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Special PCA which minimizes the variances explained
Lets say I want to do a different version of PCA, in which I minimize the variances explained.
So lets say I find the first such variance minimizing axis $PC^{'}_1$. Then I impose the orthogonality ...
- 21
2
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0
answers
30
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Measuring group homogeneity
I am trying to answer a hypothesis wherein companies with more heterogenous boards are more compliant and less likely to attempt fraud than companies with homogenous boards.
So in effect I have a ...
- 51
2
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0
answers
43
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on the variance of sample mean times estimated coefficient
Consider a simple regression model $Y_i = \alpha + \beta X_i + u_i, (i=1,...,n)$ where $(Y_i,X_i)$ is a random sample. Let $\hat{\beta}$ be the OLS estimator of $\beta$ and $\bar{X}$ be the sample ...
- 387
2
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0
answers
61
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How to compute sample variance and/or mean square error as a percentage?
Say I have a set of measurement values $y_\text{m} = (y_{\text{m},1}, \dots y_{\text{m},N}) $, and compare these with some ground truth $y = (y_1, \dots y_N)$. Then, if I understood correctly, I can ...
- 21
2
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0
answers
59
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Variance Homogeneity for a mixed model
I have run the model:
model2 <- lmer(tas ~ station + (1 | date), data = all5)
where station is a categorical variable with 4 ...
- 139
2
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0
answers
117
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Covariance of a vectorized random matrix
I am looking for an answer to the following question. Assume a random matrix $\mathbf{A}$ of dimension $n\times n$ such that each row $\mathbf{A}_i$ of the matrix $\mathbf{A}$ is a realization of a ...
- 23
2
votes
1
answer
28
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Create dataset by sampling from near-boundary of binary classifier to improve accuracy
Say I have some binary classifier $f: X \to [0, 1]$. I think the following bi-stage training method is straightforward to reduce error.
Step1. Sample uniformly from $X$ and create dataset with ...
- 211
2
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0
answers
84
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Calculating confidence Interval for a return time curve, via non-parametric bootstrapping
I have some precipitation data (yearly extremes), which I have fit with a Gumbel distribution (CDF), from which I have calculated a return time distribution. I want to calculate the 95% confidence ...
- 21
2
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0
answers
133
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Is there any intuitive explanation for MoM in estimating parameters?
I found from some literature that when we use the method of moments to fit the Gumbel distribution, the estimated
(On page 24) A comparison of the variance formulas in (1.66) with the CramBr-Rao ...
- 747
2
votes
1
answer
248
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Extreme value theory for detrended series
I'm reading "An Introduction to Statistical Modeling of Extreme Values" by Stuart Coles, and using the pyextremes package for exploring the data which is time to return (in days). After ...
- 21
2
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0
answers
15
views
How to determine the variation of influences?
I need to investigate a chain of influences which can be described as following: First, a deliverer sends barrels of oil. These will be connected to a certain system and purified. Next, the oil will ...
- 3,493
2
votes
0
answers
76
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How to Calculate the Variance of the Aggregate of a Bernoulli Process Given Known False Positive and False Negative Rates
I have $n$ sensors which output either $0$ or $1$. These sensors have known measurement error reflected by a false positive rate, $fpr$ and false negative rate, $fnr$. In my case, $fnr > fpr$.
...
2
votes
0
answers
177
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Limit distribution of the joint distribution of maximum and minimum of a sequence of random variables
Assume we have a sequence $\mathsf{X}_1,\mathsf{X}_2,\mathsf{X}_3,...$ of iid random variables. Then the Fisher-Tippet-Gnedenko theorem shows that
$$ \mathbb{P}\left(\frac{\max\{\mathsf{X}_1,\mathsf{X}...
- 167
2
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0
answers
452
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Variance-stabilizing transformation on a simple linear regression
I am currently working with variance-stabilizer method and readed something about it from my textbook. I want to understand it better so I would like to consider a case where I for instance have a ...
- 181
2
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0
answers
76
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Tail-equivalence implying same domain of attraction
Suppose two distributions F and G that have the same extreme point ($x^F = x^G$) and
$$\lim_{x \to x^F}\frac{\bar{F}(x)}{\bar{G}(x)} = c \in (0, \infty)$$
Show that F and G belongs to the same domain ...
- 21
2
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0
answers
94
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Finding Variance of Proportional Hazards Regression Coefficient Estimates in Weibull Regression
So I am doing Weibull regression in R with the exponential relative risk function. The proportional hazards model formulation assumes that the hazard rate is given by $$\alpha(t;a,\sigma, \boldsymbol ...
- 331
2
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0
answers
764
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Lower RMSE but worse model prediction
I am using a KNN model to predict quantity sold for a highly seasonal business. I chose KNN because I thought that using nearest neighbors would inform my model about said seasonality better than a ...
- 21
2
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0
answers
54
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If variance of overlapping sums > variance of underlying?
Starting with a sample series $x_1, ..., x_n$, I generate overlapping sums $y_i = \sum(x_i,...,x_{i+9})$.
If $X$ ~ Normal then it appears that $Var(Y) \approx 10 \times Var(X)$.
But for samples from ...
- 1,176
2
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37
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Variance sensitivity of dataset with scaling
What I have is 3 datasets scaled with RobustScaler, MinMaxScaler and StandardScaler. However ...
- 21
2
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0
answers
313
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Variance of von Mises-Fisher Distribution
As a follow up to this previous question on the expectation of the von Mises-Fisher distribution, what is the variance of a von-Mises Fisher distribution as a function of the mean direction $\mu$ and ...
- 1,057
2
votes
0
answers
166
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Variance in variance-weighted variance estimate?
Apologies for the confusing title, but I couldn't resist.
Much can and has been said about computing the unbiased variance using a sample of points, weighting by the variances of each point (for ...
- 78
2
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92
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When would one need to be able differentiate Var(X)?
Reading Blitzstein and Hwang’s introduction to probability http://probabilitybook.net (really good so far!).
On page 172, they discuss why $E[|X-E[X]|$ isn’t used as the definition of variance. They ...
- 311
2
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0
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32
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Proportion of explained variance for a probability model(binary logistic regression)
in the article written by Frank Harell ,Statistically Efficient Ways to Quantify Added Predictive Value of New Measurements,(https://www.fharrell.com/post/addvalue/)
Harell is writing:
For a ...
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