Partially Linear Support Vector Quantile Regression Using Asymmetric e-insensitive Loss Function

심주용,석경하,황창하 한국자료분석학회 2013 Journal of the Korean Data Analysis Society Vol.15 No.4

Quantile regression has been an popular method for estimating the quantiles of a conditional distribution on the values of covariates. Support vector quantile regression (SVQR) is capable of providing a good description of the linear and nonlinear relationships among random variables. The SVQR results in nonsparsity because of the zero- insensitiveness of check function. In this paper, we propose a partially linear SVQR (PSVQR) using an asymmetric e-insensitive loss function in SVQR in order to provide the efficient estimation and sparsity. The proposed loss function is designed to provide more sparsity by adjusting insensitiveness according the sign of residuals. The asymmetric e-insensitive loss function is used to increase the sparsity efficiently. We have a generalized approximate cross validation function for choosing hyperparameters which affects the performance of the proposed estimator. Experimental results are then presented which illustrate the performance of the proposed method by comparing with nonsparse partially linearly SVQR. Through the examples we showed that the proposed method provides the sparsity and better performance than partially linear support vector quantile regression using check function.

A study on a composite support vector quantile regression with varying coefficient model

Insuk Sohn,Jooyong Shim,Kyungha Seok 한국데이터정보과학회 2018 한국데이터정보과학회지 Vol.29 No.4

Varying coefficient models are widely used to explore dynamic patterns of regression parameters among regression models available to avoid the curse of dimensionality. In this paper we propose a new regression estimation of the varying coefficient composite support vector quantile regression which combines the formulations of the composite quantile regression and the varyng coefficient support vector quantile regression which is a nonparametric quantile regression with varying regression quantiles. We also consider a cross validation method for the optimal values of hyperparameters which affect the performance of the proposed method. Numerical studies with synthetic and real data are conducted to illustrate the performance of the proposed estimation of the regression functions.

Stochastic orders using quantile-based reliability functions

B. Vineshkumar,N. Unnikrishnan Nair,P. G. Sankaran 한국통계학회 2015 Journal of the Korean Statistical Society Vol.44 No.2

The concept of stochastic orders plays a major role in the theory and practice of statistics. It generally refers to a set of relations that may hold between a pair of distributions of random variables. In reliability theory, stochastic orders are employed to compare lifetime of two systems. In the present work, we develop new stochastic orders using the quantilebased reliability measures like the hazard quantile function and the mean residual quantile function. We also establish relationships among the proposed orders and certain existing orders. Various properties of the orders are also studied.

이항 회귀모형의 연결함수 오지정 문제에서 확률화된 분위수 잔차 사용에 대한 연구

양호진(Hojin Yang),이동혁(Donghyuk Lee) 한국자료분석학회 2022 Journal of the Korean Data Analysis Society Vol.24 No.5

반응변수가 베르누이 혹은 이항분포를 따를 때 공변량들로 관심사건이 발생할 확률을 예측하는 모형에 흔히 로지스틱 회귀모형이 사용된다. 이는 로지스틱 연결함수를 사용한 일반화 선형모형의 일종으로 실제 자료를 생성시키는 연결함수가 로지스틱 연결함수가 아닐 때 연결함수 오지정(link misspecification) 문제가 발생한다. 회귀모형을 진단하는 방법으로 잔차를 활용할 수 있지만, 반응변수가 범주형이면 잔차들의 활용도가 일반적인 선형회귀분석에 비하여 떨어지게 된다. 이를 보완하기 위하여 확률화된 분위수 잔차(randomized quantile residual)를 사용할 수 있는데 이들은 모형이 정확할 때 정규분포를 따르도록 정의되었다. 본 연구에서는 연결함수 오지정 문제를 진단하기 위한 확률화된 분위수 잔차의 활용도를 살펴보았다. 실제 자료를 생성시키는 연결함수가 로지스틱 연결함수가 아닐 때 로지스틱 회귀모형을 사용한 경우, 확률화된 분위수 잔차들의 정규성 검정을 통하여 연결함수의 오지정 유무를 진단할 수 있는지 다양한 모의실험을 통하여 검증하였다. 이를 통하여 로지스틱 연결함수가 실제 연결함수를 잘 근사하지 못하여 실제 연결함수가 적합된 로지스틱 연결함수와 차이가 클 때 확률화된 분위수 잔차들은 정규분포를 따르지 않게 됨을 확인하였다. Logistic regression model is usually used when the response is Bernoulli or binomial to predict the probability of event of interest. Specifically, the logistic model is a generalized linear model(GLM) where the assumed link function is the inverse CDF of the logistic distribution. The link misspecification often occurs when the true link is not the logistic link function. In addition, residuals in the binomial GLM model are of less practical use for diagnostics because the response is not continuous. Randomized quantile residuals are an alternative option because they are defined to follow the standard normal distribution. In this study, we investigated the usage of the randomized quantile residual to diagnose the link misspecification. When the logistic regression is fitted to the data where the true data generating process is irrelevant to the logistic link function, we consider the normality test on the randomized quantile residuals from the misspecified logistic regression model and explore whether the link misspecification can be detected or not via extensive simulation studies. We have found that the randomized quantile residual is far from the normality especially when the fitted logistic link function fails to approximate the true link function so that their gap is big.

Testing linearity in partial functional linear quantile regression model based on regression rank scores

Yu Ping,Du Jiang,Zhang Zhongzhan 한국통계학회 2021 Journal of the Korean Statistical Society Vol.50 No.1

This paper investigates the hypothesis test of the parametric component in partial functional linear quantile regression model in which the dependent variable is related to both a vector of fnite length and a function-valued random variable as predictor variables. A quantile rank score test based on functional principal component analysis is developed. Under mild conditions, we establish the consistency of the proposed test statistic, and show that the proposed test can detect Pitman local alternatives converging to the null hypothesis at the usual parametric rate. A simulation study shows that the proposed test procedure has good size and power with fnite sample sizes. Finally, an illustrative example is given through ftting the Berkeley growth data and testing the efect of gender on the height of kids.

Quantile based reliability aspects of partial moments

P. G. Sankaran,N. Unnikrishnan Nair,S.M. Sunoj 한국통계학회 2013 Journal of the Korean Statistical Society Vol.42 No.3

Partial moments are extensively used in literature for modeling and analysis of lifetime data. In this paper, we study properties of partial moments using quantile functions. The quantile based measure determines the underlying distribution uniquely. We then characterize certain lifetime quantile function models. The proposed measure provides alternate definitions for ageing criteria. Finally, we explore the utility of the measure to compare the characteristics of two lifetime distributions.

A study on a composite support vector quantile regression with varying coefficient model

손인석,심주용,석경하 한국데이터정보과학회 2018 한국데이터정보과학회지 Vol.29 No.4

Varying coefficient models are widely used to explore dynamic patterns of regression parameters among regression models available to avoid the curse of dimensionality. In this paper we propose a new regression estimation of the varying coefficient composite support vector quantile regression which combines the formulations of the composite quantile regression and the varyng coefficient support vector quantile regression which is a nonparametric quantile regression with varying regression quantiles. We also consider a cross validation method for the optimal values of hyperparameters which affect the performance of the proposed method. Numerical studies with synthetic and real data are conducted to illustrate the performance of the proposed estimation of the regression functions.

The Weight Function in the Bounded Influence Regression Quantile Estimator for the AR(1) Model with Additive Outliers

Jung Byoung Cheol,Han Sang Moon 한국통계학회 2005 Communications for statistical applications and me Vol.12 No.1

In this study, we investigate the effects of the weight function in the bounded influence regression quantile (BIRQ) estimator for the AR(l) model with additive outliers. In order to down-weight the outliers of X -axis, the Mallows' (1973) weight function has been commonly used in the BIRQ estimator. However, in our Monte Carlo study, the BIRQ estimator using the Tukey's bisquare weight function shows less MSE and bias than that of using the Mallows' weight function or Huber's weight function. Thus, the use of the Tukey's weight function is recommended in the BIRQ estimator for our model.

A study on a composite support vector quantile regression with varying coefficient model

Sohn, Insuk,Shim, Jooyong,Seok, Kyungha Korean Data and Information Science Society 2018 한국데이터정보과학회지 Vol.29 No.4

Varying coefficient models are widely used to explore dynamic patterns of regression parameters among regression models available to avoid the curse of dimensionality. In this paper we propose a new regression estimation of the varying coefficient composite support vector quantile regression which combines the formulations of the composite quantile regression and the varyng coefficient support vector quantile regression which is a nonparametric quantile regression with varying regression quantiles. We also consider a cross validation method for the optimal values of hyperparameters which affect the performance of the proposed method. Numerical studies with synthetic and real data are conducted to illustrate the performance of the proposed estimation of the regression functions.

Interdependence Modeling for the Major Stock Markets and the Stock Portfolio Risk Management

이호진 명지대학교(서울캠퍼스) 금융지식연구소 2020 금융지식연구 Vol.18 No.2

We employ a variety of dependence measures to test interdependence structure of the Korean and the US stock markets. We use daily returns on the KOSPI 200 and S&P 500. We measure a variety of dependence measures other than the linear correlation coefficient to characterize the copula function. The scale invariant dependence measure whose attribute can determine the form of the copula is a function of the ranks and is solely dependent upon the copula and not the marginal distributions of the data. Firstly, we calculate the quantile dependence which provides with the degree of asymmetric dependence in the extreme quantile by weighing the left tail to the right. Quantile dependence between the two variables is different from linear correlation or rank correlation whose values are scalars in the sense that it provides with varying degrees of asymmetric dependence from the center of the distribution to each extreme. Secondly, we compute the tail dependence which measures the synchronicity between extreme events and can be calculated as the population quantile dependence at the limit. Thirdly, we test for the existence of asymmetric and time-varying dependence. The time-varying conditional volatility of each series may induce time-varying conditional dependence. The test for time-varying dependence between the KOSPI 200 and S&P 500 standardized residuals is implemented. We then use the stationary bootstrap to construct the confidence intervals for the dependence measures. Lastly, we use the multi-stage GMM to estimate the constant parametric copula function and the time-varying copula function.