# Questions tagged [influence-function]

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

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### 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 ...
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### 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 ...
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### 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 ...
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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 $\nu(F_y)... 1 vote 0 answers 92 views ### Variance of Influence Functions, Cross-fitting, and the Propensity Score Following example 2 in this paper, suppose I wanted to estimate$\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 ... • 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,... 0 votes 1 answer 148 views ### Intuition of Influence Function and Score function:$E[IF(X)S_{\beta}(X; \theta_0)]Question I find a theorem regarding influence function and score function \begin{align*} E\left\{IF(Z) S_\beta\left(Z, \theta_0\right)\right\}&=1\\ E\left\{IF(Z) S_\eta^T\left(Z, \theta_0\right)\... • 1 2 votes 0 answers 45 views ### Deriving Influence Function for variance estimator In chapter 2 of Tsiatis (2006), the following is stated After some straightforward algebra, we can express the estimator\hat{\sigma}_n^2$minus the estimand as $$(\hat{\sigma}_n^2 - \sigma_0^2) = ... • 2,542 0 votes 0 answers 123 views ### Influence function of conditional quantile I'm trying to derive the influence function of the estimand \Psi$$\Psi(P) = P(Y > y | X = x)$$Following tutorials for deriving the influence function of the average treatment effect here. Has ... 1 vote 0 answers 156 views ### Influence Function of M-Estimator I know the following influence function for a M-Estimator: IF(x_0,T,F_0)= \frac{\psi(x_0)}{\mathbb{E}_{F_0}[\psi'(X)]} where F_0 is the centered model (F_{\theta}(x)=F_0(x-\theta)) I am ... 1 vote 0 answers 208 views ### Intuitive understanding of influence function This question asks about influence functions. Probabilityislogic's answer is a bit fuzzy to me, but I can make more sense of jayk's answer, as this was the way influence function was presented to me ... 3 votes 1 answer 65 views ### Influence function used in partykit for binary classification What is the influence function used for binary classification in the R package partkit, specifically for the conditional tree (... • 1,355 3 votes 1 answer 237 views ### How is the asymptotic justification of the "linearization by influence function method" for surveys established? The survey R package recently adopted the "linearization by influence function" method of estimating covariances between domain estimates. The central ... • 452 2 votes 0 answers 76 views ### How to calculate the Influence function for the half variance So we know that the influence function IF for a functional v at a point y is roughly defined as:$$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)... • 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, ... • 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)$. The first part of the question ... • 699 4 votes 1 answer 1k views ### How does an influence function-based estimator estimate a target functional for an unknown distribution? How exactly does a "1-step" influence function-based estimator estimate a target functional (like average treatment effect) for an unknown distribution? As described in Aaron Fisher and Edward H. ... • 6,164 2 votes 0 answers 310 views ### How to find Influence function? Derive$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{...
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I am trying to understand how influence functions work. Could someone explain in the context of a simple OLS regression $$y_i = \alpha + \beta \cdot x_i + \varepsilon_i$$ ...