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I am reading the paper on consistency and sparsity for sliced inverse regression in high dimensions (https://doi.org/10.1214/17-AOS1561). … What I only know is the classical sliced inverse regression conclusion that $E(x|y)$ satisfies $$ E(x|y) = \Sigma\beta(\beta^{T}\Sigma\beta)^{-1}\beta^T E(x|y). $$ Is there a similar conclusion when we …

And that is exactly what ordinary least squares regression does. … The use of 45 degree angles makes it easier to compare differences (see also this question and answer about slopegraphs) Related questions Inverse Regression vs Reverse Regression Effect of switching …

This question was motivated by the sliced inverse regression method of Duan and Li, where you regress $X$ on $Y$ to learn about $Y|X$ …

I don't have enough reputation to comment, but I've heard it referred to as calibration or inverse regression. Hope that gives you something to start. …

This is a 'calibration' or (perhaps more descriptively) an 'inverse regression' problem. That should guide you to some useful theoretical treatments. …

"B", "C", "D", "E"), height = c(2, 4, 6, 10, 12), gene1 = c(0.2, -0.3, -0.6, -0.7, -0.8), gene2 = c(0.4, -0.2, -0.4, -0.2, -0.6), gene3 = c(-0.1, 0.1, 0.3, 0.5, 0.7)) I became interested in doing inverse … regression on gene 1, since the residual values I obtain from that gives different results than using height as response. …

This is a variant of calibration, or inverse regression/inverse prediction. One survey paper is this at JSTOR but it does not look explicitly at predicting the peak location. … Some stored google searches that looks promosing: peak detection and confidence intervals and response surface, inverse regression. …

This is what I mean by inverse regression. However I've seen since been playing with some toy models and I'm starting to see that the 'wrong' method produces much better predictions. … Are there other situations where inverse regression actually outperforms? …

This code implements Slice Inverse Regression (SIR) in an unusual way. I notice that, when I compare it to the standard algorithm, the modified algorithm does better. … import numpy as np import matplotlib.pyplot as plt from sliced import SlicedInverseRegression # sliced inverse regression # X - NxM matrix of M inputs and N observations # Y - vector of responses of length …

If I regress y on x and the beta is less that one, shouldn't the beta from a regression of x on y be greater than one. … And if that's the case should the inverse regression yield a beta greater than one? What am I missing? Is there an easy way to conceptualize this? …

I've been using sliced inverse regression for my work and I use the dr package in R to estimate the parameter vector. … I really appreciate it if someone can direct me to a link or an R package that can handle the p>n case for sliced inverse regression. Or if you can explain why we can't use it when p>n. …

I will do this by using a multiple regression. First question: Is a simple multiple regression sufficient or is there something "advanced" more suitable? … Despite from that, I wonder if a calibration is the same as an inverse regression? …

Magno, “A statistical overview on univariate calibration, inverse regression, and detection limits: application to gas chromatography/mass spectrometry technique”, Mass Spectrometry Reviews 26 (2007) 1 …

Typically this is done with inverse regression techniques (i.e. after-fitting / reparameterisation), but sometimes these impose constraints or come with a greater degree of uncertainty. …

$$A=\frac{1}{1-\left(\frac{V}{\theta_0} \right)^{\theta_1}}+\theta_2 \tag 1$$ The inverse function is : $$V=\theta_0\left(1-\frac{1}{A-\theta_2} \right)^{1/\theta_1} \tag 2$$ The problem is to evaluate … ADDITION after comments Cubic Polynomial Regression works very well with log-log variables : Even quadratic polynomial regression is sufficient as shown on the next figure : But the polynomial regression …