Skip to main content

Questions tagged [influence-function]

a measure of how strongly the model parameters or predictions depend on a training instance.

Filter by
Sorted by
Tagged with
1 vote
1 answer
39 views

How to actually use the Empirical Influence Function for BCa Bootstrap Intervals?

In the course of seeking reassurance for another part of a hobby analysis* I found a stack answer which mentioned The Jackknife, the Bootstrap and Other Resampling Plans (Efron, 1980). Having managed ...
Vonvorv's user avatar
  • 51
0 votes
0 answers
14 views

How to ues Conjugate Gradients (CG) to computes Inverse-Hessian vector products(IHVP)?

I do not understand the conjugate gradients(CG) in computing the Inverse-Hessian vector products(IHVP) of this paper https://arxiv.org/abs/1703.04730, does someone know about the calculation process ...
Hongbo Zhu's user avatar
0 votes
0 answers
21 views

How to show that the influence function of minimum density power divergence estimator with positive tuning parameter is bounded?

In the linked paper, in the influence function section, the term ${u_{\theta}(y)}{f_{\theta}(y)}^\alpha$ is directly called bounded which i do not get the explanation of? Here $\alpha > 0$ is the ...
Amlan Dey's user avatar
1 vote
0 answers
45 views

Recentered influence function and OLS interpretation

I am working with Recentered Influence Functions (RIF) to estimate regressions in distribution. We have the following regression $RIF(F_y, \nu (F_y)) = \beta_0 + \beta_1X + \varepsilon$ where $\nu(F_y)...
Valentina Andrade's user avatar
1 vote
0 answers
92 views

Variance of Influence Functions, Cross-fitting, and the Propensity Score

Following example 2 in this paper, suppose I wanted to estimate $\psi = E[E[Y|X,A=a]] $ and I had an influence function follows: $$ IF(\psi) = \frac{A}{\pi(X)}\{Y-\mu(X)\} - \psi $$ where $\pi(X)$ is ...
Roy Z's user avatar
  • 33
1 vote
0 answers
31 views

Influence function of the IQR

In class I am told the influence function of the IQR should be a constant times the difference between the influence function for the 75th percentile and the influence function for the 25th percentile,...
Satoshi Nakamoto's user avatar
0 votes
1 answer
148 views

Intuition of Influence Function and Score function: $E[IF(X)S_{\beta}(X; \theta_0)]$

Question I find a theorem regarding influence function and score function \begin{align*} E\left\{IF(Z) S_\beta\left(Z, \theta_0\right)\right\}&=1\\ E\left\{IF(Z) S_\eta^T\left(Z, \theta_0\right)\...
mayu's user avatar
  • 1
2 votes
0 answers
45 views

Deriving Influence Function for variance estimator

In chapter 2 of Tsiatis (2006), the following is stated After some straightforward algebra, we can express the estimator $\hat{\sigma}_n^2$ minus the estimand as $$(\hat{\sigma}_n^2 - \sigma_0^2) = ...
pzivich's user avatar
  • 2,542
0 votes
0 answers
123 views

Influence function of conditional quantile

I'm trying to derive the influence function of the estimand $\Psi$ $$\Psi(P) = P(Y > y | X = x)$$ Following tutorials for deriving the influence function of the average treatment effect here. Has ...
dogs4ever's user avatar
1 vote
0 answers
156 views

Influence Function of M-Estimator

I know the following influence function for a M-Estimator: $IF(x_0,T,F_0)= $ $\frac{\psi(x_0)}{\mathbb{E}_{F_0}[\psi'(X)]}$ where $F_0$ is the centered model ($F_{\theta}(x)=F_0(x-\theta)$) I am ...
Jonathan Baram's user avatar
1 vote
0 answers
208 views

Intuitive understanding of influence function

This question asks about influence functions. Probabilityislogic's answer is a bit fuzzy to me, but I can make more sense of jayk's answer, as this was the way influence function was presented to me ...
AyamGorengPedes's user avatar
3 votes
1 answer
65 views

Influence function used in partykit for binary classification

What is the influence function used for binary classification in the R package partkit, specifically for the conditional tree (...
Kozolovska's user avatar
  • 1,355
3 votes
1 answer
237 views

How is the asymptotic justification of the "linearization by influence function method" for surveys established?

The survey R package recently adopted the "linearization by influence function" method of estimating covariances between domain estimates. The central ...
bschneidr's user avatar
  • 452
2 votes
0 answers
76 views

How to calculate the Influence function for the half variance

So we know that the influence function $IF$ for a functional $v$ at a point $y$ is roughly defined as: $$IF(v,F,y)=lim_{e\rightarrow 0} \frac{v(Y,G_y)-v(Y,F_y)}{e}$$ where $$G_y(y)=1(Y>y)*e + (1-e)...
Fcold's user avatar
  • 752
7 votes
0 answers
110 views

Is there a measure of the robustness of a statistic?

I got a question today when talking about mean and median, IQR and variance. Is there a numerical measure of the robustness of a statistic? I must confess that I had never thought about that before, ...
Luis's user avatar
  • 473
2 votes
0 answers
69 views

How to find influence function of $\lambda=\log(\mu)$ such that $\mu=E(X)$?

The original question is that $X$ is a random variable that $E(X)=\mu$. We are interested in statistical functionals $\theta=\int\log(x)dF(x)$ and $ \lambda=\log(\mu)$. The first part of the question ...
JoZ's user avatar
  • 699
4 votes
1 answer
1k views

How does an influence function-based estimator estimate a target functional for an unknown distribution?

How exactly does a "1-step" influence function-based estimator estimate a target functional (like average treatment effect) for an unknown distribution? As described in Aaron Fisher and Edward H. ...
RobertF's user avatar
  • 6,164
2 votes
0 answers
310 views

How to find Influence function?

Derive $IF(x;T,F)$ when $$\displaystyle T(F)=\int_{F^{-1}(\alpha)}^{F^{-1}(1-\alpha)}x ~dF(x)$$ Here $IF$ stands for Influence function. Trial: Here $$\begin{align}IF(x;T,F) &=\lim_{t\to 0}\frac{...
Argha's user avatar
  • 2,110
22 votes
3 answers
13k views

Influence functions and OLS

I am trying to understand how influence functions work. Could someone explain in the context of a simple OLS regression \begin{equation} y_i = \alpha + \beta \cdot x_i + \varepsilon_i \end{equation} ...
stevejb's user avatar
  • 423