اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدScalable Estimation and Inference with Large-scale or Online Survival Data
71
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
With the rapid development of data collection and aggregation technologies in many scientific disciplines, it is becoming increasingly ubiquitous to conduct large-scale or online regression to analyze real-world data and unveil real-world evidence. In such applications, it is often numerically challenging or sometimes infeasible to store the entire dataset in memory. Consequently, classical batch-based estimation methods that involve the entire dataset are less attractive or no longer applicable. Instead, recursive estimation methods such as stochastic gradient descent that process data points sequentially are more appealing, exhibiting both numerical convenience and memory efficiency. In this paper, for scalable estimation of large or online survival data, we propose a stochastic gradient descent method which recursively updates the estimates in an online manner as data points arrive sequentially in streams. Theoretical results such as asymptotic normality and estimation efficiency are established to justify its validity. Furthermore, to quantify the uncertainty associated with the proposed stochastic gradient descent estimator and facilitate statistical inference, we develop a scalable resampling strategy that specifically caters to the large-scale or online setting. Simulation studies and a real data application are also provided to assess its performance and illustrate its practical utility.
قيم البحث
اقرأ أيضاً
In this article, motivated by biosurveillance and censoring sensor networks, we investigate the problem of distributed monitoring large-scale data streams where an undesired event may occur at some unknown time and affect only a few unknown data stre
ams. We propose to develop scalable global monitoring schemes by parallel running local detection procedures and by combining these local procedures together to make a global decision based on SUM-shrinkage techniques. Our approach is illustrated in two concrete examples: one is the nonhomogeneous case when the pre-change and post-change local distributions are given, and the other is the homogeneous case of monitoring a large number of independent $N(0,1)$ data streams where the means of some data streams might shift to unknown positive or negative values. Numerical simulation studies demonstrate the usefulness of the proposed schemes.
This paper considers fixed effects estimation and inference in linear and nonlinear panel data models with random coefficients and endogenous regressors. The quantities of interest -- means, variances, and other moments of the random coefficients --
are estimated by cross sectional sample moments of GMM estimators applied separately to the time series of each individual. To deal with the incidental parameter problem introduced by the noise of the within-individual estimators in short panels, we develop bias corrections. These corrections are based on higher-order asymptotic expansions of the GMM estimators and produce improved point and interval estimates in moderately long panels. Under asymptotic sequences where the cross sectional and time series dimensions of the panel pass to infinity at the same rate, the uncorrected estimator has an asymptotic bias of the same order as the asymptotic variance. The bias corrections remove the bias without increasing variance. An empirical example on cigarette demand based on Becker, Grossman and Murphy (1994) shows significant heterogeneity in the price effect across U.S. states.
Handling big data has largely been a major bottleneck in traditional statistical models. Consequently, when accurate point prediction is the primary target, machine learning models are often preferred over their statistical counterparts for bigger pr
oblems. But full probabilistic statistical models often outperform other models in quantifying uncertainties associated with model predictions. We develop a data-driven statistical modeling framework that combines the uncertainties from an ensemble of statistical models learned on smaller subsets of data carefully chosen to account for imbalances in the input space. We demonstrate this method on a photometric redshift estimation problem in cosmology, which seeks to infer a distribution of the redshift -- the stretching effect in observing the light of far-away galaxies -- given multivariate color information observed for an object in the sky. Our proposed method performs balanced partitioning, graph-based data subsampling across the partitions, and training of an ensemble of Gaussian process models.
Empirical researchers often trim observations with small denominator A when they estimate moments of the form E[B/A]. Large trimming is a common practice to mitigate variance, but it incurs large trimming bias. This paper provides a novel method of c
orrecting large trimming bias. If a researcher is willing to assume that the joint distribution between A and B is smooth, then a large trimming bias may be estimated well. With the bias correction, we also develop a valid and robust inference result for E[B/A].
We consider the problem of simultaneous estimation of a sequence of dependent parameters that are generated from a hidden Markov model. Based on observing a noise contaminated vector of observations from such a sequence model, we consider simultaneou
s estimation of all the parameters irrespective of their hidden states under square error loss. We study the roles of statistical shrinkage for improved estimation of these dependent parameters. Being completely agnostic on the distributional properties of the unknown underlying Hidden Markov model, we develop a novel non-parametric shrinkage algorithm. Our proposed method elegantly combines textit{Tweedie}-based non-parametric shrinkage ideas with efficient estimation of the hidden states under Markovian dependence. Based on extensive numerical experiments, we establish superior performance our our proposed algorithm compared to non-shrinkage based state-of-the-art parametric as well as non-parametric algorithms used in hidden Markov models. We provide decision theoretic properties of our methodology and exhibit its enhanced efficacy over popular shrinkage methods built under independence. We demonstrate the application of our methodology on real-world datasets for analyzing of temporally dependent social and economic indicators such as search trends and unemployment rates as well as estimating spatially dependent Copy Number Variations.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
