Weighted-average quantile regression

• URL: http://arxiv.org/abs/2203.03032v1
• Date: Sun, 6 Mar 2022 19:06:53 GMT
• Title: Weighted-average quantile regression
• Authors: Denis Chetverikov, Yukun Liu, Aleh Tsyvinski
• Abstract summary: We introduce the weighted-average quantile regression framework, $int_Y|X(u)psi(u)du = X'beta$, where $Y$ is a dependent variable. We develop an estimator of the vector of parameters $beta$, where $T$ is the size of available sample.
• Score: 1.0742675209112622
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we introduce the weighted-average quantile regression framework, $\int_0^1 q_{Y|X}(u)\psi(u)du = X'\beta$, where $Y$ is a dependent variable, $X$ is a vector of covariates, $q_{Y|X}$ is the quantile function of the conditional distribution of $Y$ given $X$, $\psi$ is a weighting function, and $\beta$ is a vector of parameters. We argue that this framework is of interest in many applied settings and develop an estimator of the vector of parameters $\beta$. We show that our estimator is $\sqrt T$-consistent and asymptotically normal with mean zero and easily estimable covariance matrix, where $T$ is the size of available sample. We demonstrate the usefulness of our estimator by applying it in two empirical settings. In the first setting, we focus on financial data and study the factor structures of the expected shortfalls of the industry portfolios. In the second setting, we focus on wage data and study inequality and social welfare dependence on commonly used individual characteristics.

Related papers

• OPORP: One Permutation + One Random Projection [37.6593006747285]
  OPORP uses a variant of the count-sketch'' type of data structures for achieving data reduction/compression. One crucial step is to normalize the $k$ samples to the unit $l$ norm. With OPORP, the two key steps: (i) the normalization and (ii) the fixed-length binning scheme, have considerably improved the accuracy in estimating the cosine similarity.
  arXiv  Detail & Related papers  (2023-02-07T14:45:34Z)
• The Projected Covariance Measure for assumption-lean variable significance testing [3.8936058127056357]
  A simple but common approach is to specify a linear model, and then test whether the regression coefficient for $X$ is non-zero. We study the problem of testing the model-free null of conditional mean independence, i.e. that the conditional mean of $Y$ given $X$ and $Z$ does not depend on $X$. We propose a simple and general framework that can leverage flexible nonparametric or machine learning methods, such as additive models or random forests.
  arXiv  Detail & Related papers  (2022-11-03T17:55:50Z)
• Spectral properties of sample covariance matrices arising from random matrices with independent non identically distributed columns [50.053491972003656]
  It was previously shown that the functionals $texttr(AR(z))$, for $R(z) = (frac1nXXT- zI_p)-1$ and $Ain mathcal M_p$ deterministic, have a standard deviation of order $O(|A|_* / sqrt n)$. Here, we show that $|mathbb E[R(z)] - tilde R(z)|_F
  arXiv  Detail & Related papers  (2021-09-06T14:21:43Z)
• Locality defeats the curse of dimensionality in convolutional teacher-student scenarios [69.2027612631023]
  We show that locality is key in determining the learning curve exponent $beta$. We conclude by proving, using a natural assumption, that performing kernel regression with a ridge that decreases with the size of the training set leads to similar learning curve exponents to those we obtain in the ridgeless case.
  arXiv  Detail & Related papers  (2021-06-16T08:27:31Z)
• Optimal Spectral Recovery of a Planted Vector in a Subspace [80.02218763267992]
  We study efficient estimation and detection of a planted vector $v$ whose $ell_4$ norm differs from that of a Gaussian vector with the same $ell$ norm. We show that in the regime $n rho gg sqrtN$, any spectral method from a large class (and more generally, any low-degree of the input) fails to detect the planted vector.
  arXiv  Detail & Related papers  (2021-05-31T16:10:49Z)
• CountSketches, Feature Hashing and the Median of Three [18.85876632959721]
  We revisit the classic CountSketch method, which is a sparse, random projection that transforms a (high-dimensional) Euclidean vector $v$ to a vector of dimension $(2t-1) s$. Our main contribution is a new analysis of Count-Sketch, showing an improvement in variance to $O(min|v|2/s2,|v|2/s2)$ when $t > 1$. This finding suggests that the Feature Hashing method, which is essentially identical to CountSketch but does not make use of the median, can be made
  arXiv  Detail & Related papers  (2021-02-03T18:45:21Z)
• The Sample Complexity of Robust Covariance Testing [56.98280399449707]
  We are given i.i.d. samples from a distribution of the form $Z = (1-epsilon) X + epsilon B$, where $X$ is a zero-mean and unknown covariance Gaussian $mathcalN(0, Sigma)$. In the absence of contamination, prior work gave a simple tester for this hypothesis testing task that uses $O(d)$ samples. We prove a sample complexity lower bound of $Omega(d2)$ for $epsilon$ an arbitrarily small constant and $gamma
  arXiv  Detail & Related papers  (2020-12-31T18:24:41Z)
• Sparse sketches with small inversion bias [79.77110958547695]
  Inversion bias arises when averaging estimates of quantities that depend on the inverse covariance. We develop a framework for analyzing inversion bias, based on our proposed concept of an $(epsilon,delta)$-unbiased estimator for random matrices. We show that when the sketching matrix $S$ is dense and has i.i.d. sub-gaussian entries, the estimator $(epsilon,delta)$-unbiased for $(Atop A)-1$ with a sketch of size $m=O(d+sqrt d/
  arXiv  Detail & Related papers  (2020-11-21T01:33:15Z)
• Optimal Sub-Gaussian Mean Estimation in $\mathbb{R}$ [5.457150493905064]
  We present a novel estimator with sub-Gaussian convergence. Our estimator does not require prior knowledge of the variance. Our estimator construction and analysis gives a framework generalizable to other problems.
  arXiv  Detail & Related papers  (2020-11-17T02:47:24Z)
• Computationally and Statistically Efficient Truncated Regression [36.3677715543994]
  We provide a computationally and statistically efficient estimator for the classical problem of truncated linear regression. Our estimator uses Projected Descent Gradient (PSGD) without replacement on the negative log-likelihood of the truncated sample. As a corollary, we show that SGD learns the parameters of single-layer neural networks with noisy activation functions.
  arXiv  Detail & Related papers  (2020-10-22T19:31:30Z)
• Optimal Robust Linear Regression in Nearly Linear Time [97.11565882347772]
  We study the problem of high-dimensional robust linear regression where a learner is given access to $n$ samples from the generative model $Y = langle X,w* rangle + epsilon$ We propose estimators for this problem under two settings: (i) $X$ is L4-L2 hypercontractive, $mathbbE [XXtop]$ has bounded condition number and $epsilon$ has bounded variance and (ii) $X$ is sub-Gaussian with identity second moment and $epsilon$ is
  arXiv  Detail & Related papers  (2020-07-16T06:44:44Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.