Author: Alexandre BelloniPublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
High Dimensional Latent Panel Quantile Regression with an Application to Asset Pricing
Author: Alexandre BelloniHigh Dimensional Latent Panel Quantile Regression with an Application to Asset Pricing
Author: Essays on High-dimensional Nonparametric Smoothing and Its Applications to Asset Pricing
Author: Chaojiang WuPublisher:
ISBN:
Category :
Languages : en
Pages : 105
Book Description
Nonparametric smoothing, a method of estimating smooth functions, has gained increasing popularity in statistics and application literature during the last few decades. This dissertation has focused primarily on the nonparametric estimation in quantile regression (Chapter 1) and an application of nonparametric estimation to financial asset pricing (Chapter 2). In the first essay (Chapter 1), we consider the estimation problem of conditional quantile when multi-dimensional covariates are involved. To overcome the "curse of dimensionality" yet retain model flexibility, we propose two partially linear models for conditional quantiles: partially linear single-index models (QPLSIM) and partially linear additive models (QPLAM). The unknown univariate functions are estimated by penalized splines. An approximate iteratively reweighted penalized least square algorithm is developed. To facilitate model comparisons, we develop effective model degrees of freedom for penalized spline conditional quantiles. Two smoothing parameter selection criteria, Generalized Approximate Cross-validation (GACV) and Schwartz-type Information Criterion (SIC) are studied. Some asymptotic properties are established. Finite sample properties are investigated through simulation studies. Application to the Boston Housing data demonstrates the success of proposed approach. Both simulations and real applications show encouraging results of the proposed estimators. In the second essay (Chapter 2), we investigate whether the conditional CAPM helps explain the value premium using the single-index varying-coefficient model. Our empirical specification has two novel advantages relative to those commonly used in the previous studies. First, it not only allows for a flexible dependence of conditional beta on state variables but also modeling heteroskedasticity. Second, from a large set of candidate state variables, we identify the most influential ones through an exhaustive variable selection method. We have also developed statistics to test the functional form of conditional beta and alpha, which provides justifications for or against the practices of letting conditional beta depend linearly on state variables and assuming constant alpha. Consistent with the notion that the value premium tends to be riskier during business recessions than during business expansions, we find that its conditional beta co-moves with unemployment and inflation, the two most closely watched gauges of aggregate economy by the Federal Reserve, and the price-earnings ratio. Realized beta does not subsume all the other explanatory variables when we include the realized beta as a state variable. The alpha is smaller for the conditional CAPM than for the unconditional CAPM; nevertheless, neither model fully explains the value premium.
Handbook of Quantile Regression
Author: Roger KoenkerPublisher: CRC Press
ISBN: 1351646567
Category : Mathematics
Languages : en
Pages : 739
Book Description
Quantile regression constitutes an ensemble of statistical techniques intended to estimate and draw inferences about conditional quantile functions. Median regression, as introduced in the 18th century by Boscovich and Laplace, is a special case. In contrast to conventional mean regression that minimizes sums of squared residuals, median regression minimizes sums of absolute residuals; quantile regression simply replaces symmetric absolute loss by asymmetric linear loss. Since its introduction in the 1970's by Koenker and Bassett, quantile regression has been gradually extended to a wide variety of data analytic settings including time series, survival analysis, and longitudinal data. By focusing attention on local slices of the conditional distribution of response variables it is capable of providing a more complete, more nuanced view of heterogeneous covariate effects. Applications of quantile regression can now be found throughout the sciences, including astrophysics, chemistry, ecology, economics, finance, genomics, medicine, and meteorology. Software for quantile regression is now widely available in all the major statistical computing environments. The objective of this volume is to provide a comprehensive review of recent developments of quantile regression methodology illustrating its applicability in a wide range of scientific settings. The intended audience of the volume is researchers and graduate students across a diverse set of disciplines.
Quantile Regression
Author: I. Gusti Ngurah AgungPublisher: John Wiley & Sons
ISBN: 1119715180
Category : Mathematics
Languages : en
Pages : 496
Book Description
QUANTILE REGRESSION A thorough presentation of Quantile Regression designed to help readers obtain richer information from data analyses The conditional least-square or mean-regression (MR) analysis is the quantitative research method used to model and analyze the relationships between a dependent variable and one or more independent variables, where each equation estimation of a regression can give only a single regression function or fitted values variable. As an advanced mean regression analysis, each estimation equation of the mean-regression can be used directly to estimate the conditional quantile regression (QR), which can quickly present the statistical results of a set nine QR(τ)s for τ(tau)s from 0.1 up to 0.9 to predict detail distribution of the response or criterion variable. QR is an important analytical tool in many disciplines such as statistics, econometrics, ecology, healthcare, and engineering. Quantile Regression: Applications on Experimental and Cross Section Data Using EViews provides examples of statistical results of various QR analyses based on experimental and cross section data of a variety of regression models. The author covers the applications of one-way, two-way, and n-way ANOVA quantile regressions, QRs with multi numerical predictors, heterogeneous QRs, and latent variables QRs, amongst others. Throughout the text, readers learn how to develop the best possible quantile regressions and how to conduct more advanced analysis using methods such as the quantile process, the Wald test, the redundant variables test, residual analysis, the stability test, and the omitted variables test. This rigorous volume: Describes how QR can provide a more detailed picture of the relationships between independent variables and the quantiles of the criterion variable, by using the least-square regression Presents the applications of the test for any quantile of any numerical response or criterion variable Explores relationship of QR with heterogeneity: how an independent variable affects a dependent variable Offers expert guidance on forecasting and how to draw the best conclusions from the results obtained Provides a step-by-step estimation method and guide to enable readers to conduct QR analysis using their own data sets Includes a detailed comparison of conditional QR and conditional mean regression Quantile Regression: Applications on Experimental and Cross Section Data Using EViews is a highly useful resource for students and lecturers in statistics, data analysis, econometrics, engineering, ecology, and healthcare, particularly those specializing in regression and quantitative data analysis.
L1-Penalized Quantile Regression in High Dimensional Sparse Models
Author: Victor ChernozhukovPublisher:
ISBN:
Category : Regression analysis
Languages : en
Pages : 60
Book Description
We consider median regression and, more generally, quantile regression in high-dimensional sparse models. In these models the overall number of regressors p is very large, possibly larger than the sample size n, but only s of these regressors have non-zero impact on the conditional quantile of the response variable, where s grows slower than n. Since in this case the ordinary quantile regression is not consistent, we consider quantile regression penalized by the 1-norm of coefficients (L1-QR). First, we show that L1-QR is consistent, up to a logarithmic factor, at the oracle rate which is achievable when the minimal true model is known. The overall number of regressors p affects the rate only through a logarithmic factor, thus allowing nearly exponential growth in the number of zero-impact regressors. The rate result holds under relatively weak conditions, requiring that s/n converges to zero at a super-logarithmic speed and that regularization parameter satisfies certain theoretical constraints. Second, we propose a pivotal, data-driven choice of the regularization parameter and show that it satisfies these theoretical constraints. Third, we show that L1-QR correctly selects the true minimal model as a valid submodel, when the non-zero coefficients of the true model are well separated from zero. We also show that the number of non-zero coefficients in L1-QR is of same stochastic order as s, the number of non-zero coefficients in the minimal true model. Fourth, we analyze the rate of convergence of a two-step estimator that applies ordinary quantile regression to the selected model. Fifth, we evaluate the performance of L1-QR in a Monte-Carlo experiment, and provide an application to the analysis of the international economic growth. Keywords: median regression, quantile regression, sparse models. JEL Classifications: C13, C14, C30, C51, D4, J24, J31.
Penalized Model Averaging for High Dimensional Quantile Regressions
Author: Haowen BaoUsing Ordinary Least Squares Regression and Quantile Regression to Test the Capital Asset Pricing Model and the Fama and French Model in the Australian Equity Market
Author: Yixaun RuiPublisher:
ISBN:
Category : Capital assets pricing model
Languages : en
Pages : 162
Book Description
Large-dimensional Panel Data Econometrics: Testing, Estimation And Structural Changes
Author: Feng QuPublisher: World Scientific
ISBN: 9811220794
Category : Business & Economics
Languages : en
Pages : 167
Book Description
This book aims to fill the gap between panel data econometrics textbooks, and the latest development on 'big data', especially large-dimensional panel data econometrics. It introduces important research questions in large panels, including testing for cross-sectional dependence, estimation of factor-augmented panel data models, structural breaks in panels and group patterns in panels. To tackle these high dimensional issues, some techniques used in Machine Learning approaches are also illustrated. Moreover, the Monte Carlo experiments, and empirical examples are also utilised to show how to implement these new inference methods. Large-Dimensional Panel Data Econometrics: Testing, Estimation and Structural Changes also introduces new research questions and results in recent literature in this field.
Author: Toshio Honda