Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [scale-invariance]

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Scale-invariant analysis of time series

When developing a general purpose time-series software, is it a good idea to make it scale invariant? How would one do that? I took a time series of around 40 points, and then multiplied by factors ranging from 10E-9 to 10E3 and then ran through the…
Samik R
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Why feature scaling only to training set?

I was following the book "Hands-On Machine Learning with Scikit-Learn & TensorFlow" by "Aurelien Geron". The following remark was made about feature scaling : - As with all the transformations, it is important to fit the scalers to the training…
Upendra01
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Choice of weight function in Moran's I

I'm doing an autocorrelation analysis for a spatially distributed collection of observations. To perform my analysis, I am using Moran's I statistic. My questions are: (1) What are the implications and benefits of using different weighting…
pariser
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Is there a "central distribution" for distributions for which the CLT doesn't apply?

The central limit theorems state roughly that under a certain set of properties of a sampling process, the distribution of a statistic from that sample will converge in distribution to the normal distribution. As the canonical example, let me take…
user56834
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Parametrisation invariance/covariance of the Jeffreys prior

I've been trying to understand what exactly is meant by parametrisation invariance of the Jeffreys prior. Already I've read here that invariance is technically not the best term to use, and that it's more a case of covariance. My understanding of…
Timsey
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RMSE is scale-dependent; is RMSE%?

I've got a graph of RMSE% vs. unit size and it declines nicely. Is this scale-dependence or does the "%" compensate for that? $$ \text{RMSE%} = 100\% \cdot \frac{\sqrt{\frac{1}{n}\Sigma_{i=1}^n (y_i - \hat{y}_i)^2}}{\bar{y}} $$
J Kelly
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The meaning of scale and location in the Pearson correlation context

According to wikipedia, pearson correlation is scale and location invariant. Does scale refer to "variance" and location refer to "mean" ? Thanks.
johnny
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Inconsistent delta.chisq.scaled using Lavaan and semTools?

I've recently been using Lavaan and semTools to test for measurement invariance in confirmatory factor analysis (CFA) models and I noticed an (apparent) inconsistency in a calculation that confused me. When you use the "measurementInvariance"…
Jeremyjaytaylor
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Showing $\mathbb{E}[T_n] = \theta \mathbb{E}_1[T_n]$ is scale equivariant?

This is question 5 is from Staudte and Sheather (1990), Robust estimation and testing. Let $X_1,\ldots , X_n$ be i.i.d with $$ F_\theta = F(\frac{x}{\theta}),\quad x>0;\theta>0.$$ Assume that $T_n = T_n(X_1,\ldots ,X_n)$ is scale equivariant. Show…
user7045
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Linear regression - results depending on the scale of the inputs

Why is there a difference in p-values for the following model $$ y = a + b_1x_1 + b_2 x_2 + b_{12}x_1x_2 + \epsilon $$ depending on the scale of the x's? > # response variable > y <- rnorm(8, mean=17, sd=1.2) > > # model 1 > x1 <- c(1, -1, -1, -1,…
user7064
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What does it mean to say that a regression method is (not) "scale invariant"?

I was just studying partial least squares regression, and I read that it is "not scale invariant". What does "scale invariant" mean, and why is partial least squares, and why would a regression methodology in general be, not "scale invariant"? Some…
The Pointer
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Are confidence intervals scale-invariant?

Suppose I estimate a mean and construct some sort of confidence intervals (e.g. based on normal approximation or bootstrapped) around the mean. I now wish to rescale my mean from, say, the mean number of infections per hundred persons to the mean…
user3614648
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Do parameters stay unchanged when GARCH is scaled?

Let's say we have a GARCH($1,1$) process specified as follows: $y_t = \epsilon_t \sqrt h_t, \quad \epsilon_t \sim N(0,1) \quad \text{i.i.d.}$ $h_t = a_0 + a_1 y^2_{t-1} + b_1 h_{t-1}.$ If we were trying to estimate the parameters $\Theta = (a_0,…
Vykta Wakandigara
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Why can scale invariance cause a loss of explanatory power?

Gary King made the following statement on Twitter: scale invariance sounds cool but is usually statisticians shirking responsibility & losing power by neglecting subject matter info What is an example of this phenomena, where scale…
Shane
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Invariance of maximum likelihood estimates to rearrangements of parameters/constants in the model?

I know that maximum likelihood estimates are invariant to re-parametrization (https://stats.stackexchange.com/a/335368/267430). Is the MLE also invariant to rearrangements of the constants and parameters in the statistical model? Is this somehow…
Mon2
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