ترغب بنشر مسار تعليمي؟ اضغط هنا

Jackknife Model Averaging for Composite Quantile Regression

205   0   0.0 ( 0 )
 نشر من قبل Miaomiao Wang
 تاريخ النشر 2019
  مجال البحث الاحصاء الرياضي
والبحث باللغة English




اسأل ChatGPT حول البحث

Model averaging considers the model uncertainty and is an alternative to model selection. In this paper, we propose a frequentist model averaging estimator for composite quantile regressions. In recent years, research on these topics has been added as a separate method, but no study has investigated them in combination. We apply a delete-one cross-validation method to estimate the model weights, and prove that the jackknife model averaging estimator is asymptotically optimal in terms of minimizing out-of-sample composite final prediction error. Simulations are conducted to demonstrate the good finite sample properties of our estimator and compare it with commonly used model selection and averaging methods. The proposed method is applied to the analysis of the stock returns data and the wage data and performs well.



قيم البحث

اقرأ أيضاً

With the availability of high dimensional genetic biomarkers, it is of interest to identify heterogeneous effects of these predictors on patients survival, along with proper statistical inference. Censored quantile regression has emerged as a powerfu l tool for detecting heterogeneous effects of covariates on survival outcomes. To our knowledge, there is little work available to draw inference on the effects of high dimensional predictors for censored quantile regression. This paper proposes a novel procedure to draw inference on all predictors within the framework of global censored quantile regression, which investigates covariate-response associations over an interval of quantile levels, instead of a few discrete values. The proposed estimator combines a sequence of low dimensional model estimates that are based on multi-sample splittings and variable selection. We show that, under some regularity conditions, the estimator is consistent and asymptotically follows a Gaussian process indexed by the quantile level. Simulation studies indicate that our procedure can properly quantify the uncertainty of the estimates in high dimensional settings. We apply our method to analyze the heterogeneous effects of SNPs residing in lung cancer pathways on patients survival, using the Boston Lung Cancer Survival Cohort, a cancer epidemiology study on the molecular mechanism of lung cancer.
In this paper, we develop a quantile functional regression modeling framework that models the distribution of a set of common repeated observations from a subject through the quantile function, which is regressed on a set of covariates to determine h ow these factors affect various aspects of the underlying subject-specific distribution. To account for smoothness in the quantile functions, we introduce custom basis functions we call textit{quantlets} that are sparse, regularized, near-lossless, and empirically defined, adapting to the features of a given data set and containing a Gaussian subspace so {non-Gaussianness} can be assessed. While these quantlets could be used within various functional regression frameworks, we build a Bayesian framework that uses nonlinear shrinkage of quantlet coefficients to regularize the functional regression coefficients and allows fully Bayesian inferences after fitting a Markov chain Monte Carlo. Specifically, we apply global tests to assess which covariates have any effect on the distribution at all, followed by local tests to identify at which specific quantiles the differences lie while adjusting for multiple testing, and to assess whether the covariate affects certain major aspects of the distribution, including location, scale, skewness, Gaussianness, or tails. If the difference lies in these commonly-used summaries, our approach can still detect them, but our systematic modeling strategy can also detect effects on other aspects of the distribution that might be missed if one restricted attention to pre-chosen summaries. We demonstrate the benefit of the basis space modeling through simulation studies, and illustrate the method using a biomedical imaging data set in which we relate the distribution of pixel intensities from a tumor image to various demographic, clinical, and genetic characteristics.
Radiomics involves the study of tumor images to identify quantitative markers explaining cancer heterogeneity. The predominant approach is to extract hundreds to thousands of image features, including histogram features comprised of summaries of the marginal distribution of pixel intensities, which leads to multiple testing problems and can miss out on insights not contained in the selected features. In this paper, we present methods to model the entire marginal distribution of pixel intensities via the quantile function as functional data, regressed on a set of demographic, clinical, and genetic predictors. We call this approach quantile functional regression, regressing subject-specific marginal distributions across repeated measurements on a set of covariates, allowing us to assess which covariates are associated with the distribution in a global sense, as well as to identify distributional features characterizing these differences, including mean, variance, skewness, and various upper and lower quantiles. To account for smoothness in the quantile functions, we introduce custom basis functions we call quantlets that are sparse, regularized, near-lossless, and empirically defined, adapting to the features of a given data set. We fit this model using a Bayesian framework that uses nonlinear shrinkage of quantlet coefficients to regularize the functional regression coefficients and provides fully Bayesian inference after fitting a Markov chain Monte Carlo. We demonstrate the benefit of the basis space modeling through simulation studies, and apply the method to Magnetic resonance imaging (MRI) based radiomic dataset from Glioblastoma Multiforme to relate imaging-based quantile functions to demographic, clinical, and genetic predictors, finding specific differences in tumor pixel intensity distribution between males and females and between tumors with and without DDIT3 mutations.
Quantile regression is studied in combination with a penalty which promotes structured (or group) sparsity. A mixed $ell_{1,infty}$-norm on the parameter vector is used to impose structured sparsity on the traditional quantile regression problem. An algorithm is derived to calculate the piece-wise linear solution path of the corresponding minimization problem. A Matlab implementation of the proposed algorithm is provided and some applications of the methods are also studied.
179 - Takuya Ishihara 2020
In this study, we develop a novel estimation method of the quantile treatment effects (QTE) under the rank invariance and rank stationarity assumptions. Ishihara (2020) explores identification of the nonseparable panel data model under these assumpti ons and propose a parametric estimation based on the minimum distance method. However, the minimum distance estimation using this process is computationally demanding when the dimensionality of covariates is large. To overcome this problem, we propose a two-step estimation method based on the quantile regression and minimum distance method. We then show consistency and asymptotic normality of our estimator. Monte Carlo studies indicate that our estimator performs well in finite samples. Last, we present two empirical illustrations, to estimate the distributional effects of insurance provision on household production and of TV watching on child cognitive development.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا