scholarly journals COMPLETE SUBSET AVERAGING FOR QUANTILE REGRESSIONS

2021 ◽  
pp. 1-43
Author(s):  
Ji Hyung Lee ◽  
Youngki Shin
Keyword(s):  
Asymptotic Optimality ◽  
Model Averaging ◽  
Prediction Method ◽  
Equal Weight ◽  
Finite Sample ◽  
Quantile Regressions ◽  
Usual Model ◽  
Conditional Quantile ◽  
Proper Size ◽  
Leave One Out

We propose a novel conditional quantile prediction method based on complete subset averaging (CSA) for quantile regressions. All models under consideration are potentially misspecified, and the dimension of regressors goes to infinity as the sample size increases. Since we average over the complete subsets, the number of models is much larger than the usual model averaging method which adopts sophisticated weighting schemes. We propose to use an equal weight but select the proper size of the complete subset based on the leave-one-out cross-validation method. Building upon the theory of Lu and Su (2015, Journal of Econometrics 188, 40–58), we investigate the large sample properties of CSA and show the asymptotic optimality in the sense of Li (1987, Annals of Statistics 15, 958–975) We check the finite sample performance via Monte Carlo simulations and empirical applications.

OPTIMAL MULTISTEP VAR FORECAST AVERAGING

2020 ◽  
Vol 36 (6) ◽  
pp. 1099-1126
Author(s):  
Jen-Che Liao ◽  
Wen-Jen Tsay
Keyword(s):  
Infinite Order ◽  
Asymptotic Optimality ◽  
Model Misspecification ◽  
Model Averaging ◽  
Finite Sample ◽  
Forecast Horizon ◽  
Simulation Experiments ◽  
Vector Autoregressive ◽  
One Step ◽  
Mallows Model

This article proposes frequentist multiple-equation least-squares averaging approaches for multistep forecasting with vector autoregressive (VAR) models. The proposed VAR forecast averaging methods are based on the multivariate Mallows model averaging (MMMA) and multivariate leave-h-out cross-validation averaging (MCVAh) criteria (with h denoting the forecast horizon), which are valid for iterative and direct multistep forecast averaging, respectively. Under the framework of stationary VAR processes of infinite order, we provide theoretical justifications by establishing asymptotic unbiasedness and asymptotic optimality of the proposed forecast averaging approaches. Specifically, MMMA exhibits asymptotic optimality for one-step-ahead forecast averaging, whereas for direct multistep forecast averaging, the asymptotically optimal combination weights are determined separately for each forecast horizon based on the MCVAh procedure. To present our methodology, we investigate the finite-sample behavior of the proposed averaging procedures under model misspecification via simulation experiments.

Model averaging with the hybrid model: An asymptotic study and demonstration

2022 ◽  
pp. 096228022110417
Author(s):  
Kian Wee Soh ◽  
Thomas Lumley ◽  
Cameron Walker ◽  
Michael O’Sullivan
Keyword(s):  
Cross Validation ◽  
Asymptotic Optimality ◽  
Model Averaging ◽  
Explanatory Variables ◽  
Model Average ◽  
Cross Validation Error ◽  
Validation Procedure ◽  
High Level ◽  
Leave One Out ◽  
Established Technique

In this paper, we present a new model averaging technique that can be applied in medical research. The dataset is first partitioned by the values of its categorical explanatory variables. Then for each partition, a model average is determined by minimising some form of squared errors, which could be the leave-one-out cross-validation errors. From our asymptotic optimality study and the results of simulations, we demonstrate under several high-level assumptions and modelling conditions that this model averaging procedure may outperform jackknife model averaging, which is a well-established technique. We also present an example where a cross-validation procedure does not work (that is, a zero-valued cross-validation error is obtained) when determining the weights for model averaging.

scholarly journals QUANTILE DOUBLE AUTOREGRESSION

2021 ◽  
pp. 1-47
Author(s):  
Qianqian Zhu ◽  
Guodong Li
Keyword(s):  
Time Series ◽  
Financial Time Series ◽  
Simulation Studies ◽  
Finite Sample ◽  
Conditional Quantile ◽  
New Model ◽  
Conditional Quantiles ◽  
Financial Time ◽  
Portmanteau Tests ◽  
Strict Stationarity

Many financial time series have varying structures at different quantile levels, and also exhibit the phenomenon of conditional heteroskedasticity at the same time. However, there is presently no time series model that accommodates both of these features. This paper fills the gap by proposing a novel conditional heteroskedastic model called “quantile double autoregression”. The strict stationarity of the new model is derived, and self-weighted conditional quantile estimation is suggested. Two promising properties of the original double autoregressive model are shown to be preserved. Based on the quantile autocorrelation function and self-weighting concept, three portmanteau tests are constructed to check the adequacy of the fitted conditional quantiles. The finite sample performance of the proposed inferential tools is examined by simulation studies, and the need for use of the new model is further demonstrated by analyzing the S&P500 Index.

WHAT DO QUANTILE REGRESSIONS IDENTIFY FOR GENERAL STRUCTURAL FUNCTIONS?

2014 ◽  
Vol 31 (5) ◽  
pp. 1102-1116 ◽  
Author(s):  
Yuya Sasaki
Keyword(s):  
Partial Derivative ◽  
General Class ◽  
Weighted Average ◽  
Causal Effects ◽  
Quantile Regressions ◽  
Conditional Quantile ◽  
Mild Conditions ◽  
Structural Functions ◽  
Partial Effects

This paper shows what quantile regressions identify for general structural functions. Under fairly mild conditions, the quantile partial derivative identifies a weighted average of heterogeneous structural partial effects among the subpopulation of individuals at the conditional quantile of interest. This result justifies the use of quantile regressions as means of measuring heterogeneous causal effects for a general class of structural functions with multiple unobservables.

scholarly journals CLT for single functional index quantile regression under dependence structure

2021 ◽  
Vol 13 (1) ◽  
pp. 45-77
Author(s):  
Nadia Kadiri ◽  
Abbes Rabhi ◽  
Salah Khardani ◽  
Fatima Akkal
Keyword(s):  
Asymptotic Properties ◽  
Likelihood Method ◽  
Dependence Structure ◽  
Finite Sample ◽  
Functional Index ◽  
Conditional Quantile ◽  
Index Model ◽  
Conditional Quantile Estimator ◽  
Pseudo Maximum Likelihood ◽  
Random Responses

Abstract In this paper, we investigate the asymptotic properties of a nonparametric conditional quantile estimation in the single functional index model for dependent functional data and censored at random responses are observed. First of all, we establish asymptotic properties for a conditional distribution estimator from which we derive an central limit theorem (CLT) of the conditional quantile estimator. Simulation study is also presented to illustrate the validity and finite sample performance of the considered estimator. Finally, the estimation of the functional index via the pseudo-maximum likelihood method is discussed, but not tackled.

Dynamic Sampling Allocation Under Finite Simulation Budget for Feasibility Determination

2021 ◽  
Author(s):  
Zhongshun Shi ◽  
Yijie Peng ◽  
Leyuan Shi ◽  
Chun-Hung Chen ◽  
Michael C. Fu
Keyword(s):  
Stochastic Systems ◽  
Asymptotic Optimality ◽  
Asymptotic Properties ◽  
Sampling Procedure ◽  
Allocation Rule ◽  
Finite Sample ◽  
Significant Difference ◽  
Finite Set ◽  
Dynamic Sampling ◽  
Sampling Allocation

Monte Carlo simulation is a commonly used tool for evaluating the performance of complex stochastic systems. In practice, simulation can be expensive, especially when comparing a large number of alternatives, thus motivating the need to intelligently allocate simulation replications. Given a finite set of alternatives whose means are estimated via simulation, we consider the problem of determining the subset of alternatives that have means smaller than a fixed threshold. A dynamic sampling procedure that possesses not only asymptotic optimality, but also desirable finite-sample properties is proposed. Theoretical results show that there is a significant difference between finite-sample optimality and asymptotic optimality. Numerical experiments substantiate the effectiveness of the new method. Summary of Contribution: Simulation is an important tool to estimate the performance of complex stochastic systems. We consider a feasibility determination problem of identifying all those among a finite set of alternatives with mean smaller than a given threshold, in which the means are unknown but can be estimated by sampling replications via stochastic simulation. This problem appears widely in many applications, including call center design and hospital resource allocation. Our work considers how to intelligently allocate simulation replications to different alternatives for efficiently finding the feasible alternatives. Previous work focuses on the asymptotic properties of the sampling allocation procedures, whereas our contribution lies in developing a finite-budget allocation rule that possesses both asymptotic optimality and desirable finite-budget properties.

Rates of Expansions for Functional Estimators

2021 ◽  
Author(s):  
Yulia Kotlyarova ◽  
Marcia M. A. Schafgans ◽  
Victoria Zinde-Walsh
Keyword(s):  
Convergence Rates ◽  
Mean Squared Error ◽  
Model Averaging ◽  
Finite Sample ◽  
Squared Error ◽  
Semiparametric Estimators ◽  
Asymptotic Mean Squared Error ◽  
The Impact ◽  
Nonconvex Model

AbstractIn this paper, we summarize results on convergence rates of various kernel based non- and semiparametric estimators, focusing on the impact of insufficient distributional smoothness, possibly unknown smoothness and even non-existence of density. In the presence of a possible lack of smoothness and the uncertainty about smoothness, methods of safeguarding against this uncertainty are surveyed with emphasis on nonconvex model averaging. This approach can be implemented via a combined estimator that selects weights based on minimizing the asymptotic mean squared error. In order to evaluate the finite sample performance of these and similar estimators we argue that it is important to account for possible lack of smoothness.

scholarly journals ON USING LINEAR QUANTILE REGRESSIONS FOR CAUSAL INFERENCE

2016 ◽  
Vol 33 (3) ◽  
pp. 664-690 ◽  
Author(s):  
Ryutah Kato ◽  
Yuya Sasaki
Keyword(s):  
Causal Inference ◽  
Unobserved Heterogeneity ◽  
Weighted Average ◽  
Quantile Function ◽  
Structural Function ◽  
Slope Parameter ◽  
Quantile Regressions ◽  
Conditional Quantile ◽  
Conditional Quantile Function ◽  
Linear Regressions

We show that the slope parameter of the linear quantile regression measures a weighted average of the local slopes of the conditional quantile function. Extending this result, we also show that the slope parameter measures a weighted average of the partial effects for a general structural function. Our results support the use of linear quantile regressions for causal inference in the presence of nonlinearity and multivariate unobserved heterogeneity. The same conclusion applies to linear regressions.

scholarly journals Gender differences in wage expectations: the role of biased beliefs

2021 ◽  
Author(s):  
Stephanie Briel ◽  
Aderonke Osikominu ◽  
Gregor Pfeifer ◽  
Mirjam Reutter ◽  
Sascha Satlukal
Keyword(s):  
Gender Differences ◽  
University Students ◽  
Gender Gap ◽  
Quantile Regressions ◽  
Conditional Quantile ◽  
Lower Wage

AbstractWe analyze gender differences in expected starting salaries along the wage expectations distribution of prospective university students in Germany, using elicited beliefs about both own salaries and salaries for average other students in the same field. Unconditional and conditional quantile regressions show 5–15% lower wage expectations for females. At all percentiles considered, the gender gap is more pronounced in the distribution of expected own salary than in the distribution of wages expected for average other students. Decomposition results show that biased beliefs about the own earnings potential relative to others and about average salaries play a major role in explaining the gender gap in wage expectations for oneself.

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