Jiancheng Jiang

Weighted Composite Quantile Regression Estimation of DTARCH Models

In modelling volatility in financial time series, the double‐threshold autoregressive conditional heteroscedastic (DTARCH) model has been demonstrated as a useful variant of the autoregressive conditional heteroscedastic (ARCH) models. In this paper, we propose a weighted composite quantile regression method for simultaneously estimating the autoregressive parameters and the ARCH parameters in the DTARCH model. This method involves a sequence of weights and takes a data‐driven weighting scheme to maximize the asymptotic efficiency of the estimators. Under regularity conditions, we establish asymptotic distributions of the proposed estimators for a variety of heavy‐ or light‐tailed error distributions. Simulations are conducted to compare the performance of different estimators, and the proposed approach is used to analyse the daily S&P 500 Composite index, both of which endorse our theoretical results.

Robust modelling of ARCH models

The autoregressive conditional heteroscedastic (ARCH) model and its extensions have been widely used in modelling changing variances in financial time series. Since the asset return distributions frequently display tails heavier than normal distributions, it is worth while studying robust ARCH modelling without a specific distribution assumption. In this paper, rather than modelling the conditional variance, we study ARCH modelling for the conditional scale. We examine the L[subscript 1]-estimation of ARCH models and derive the limiting distributions of the estimators. A robust standardized absolute residual autocorrelation based on least absolute deviation estimation is proposed. Then a robust portmanteau statistic is constructed to test the adequacy of the model, especially the specification of the conditional scale. We obtain their asymptotic distributions under mild conditions. Examples show that the suggested L[subscript 1]-norm estimators and the goodness-of-fit test are robust against error distributions and are accurate for moderate sample sizes. This paper provides a useful tool in modelling conditional heteroscedastic time series data. Copyright

Non- and Semi- Parametric Modeling in Survival Analysis

In this chapter, we give a selective review of the nonparametric modeling methods using Cox’s type of models in survival analysis. We first introduce Cox’s model (Cox 1972) and then study its variants in the direction of smoothing. The model fitting, variable selection, and hypothesis testing problems are addressed. A number of topics worthy of further study are given throughout this chapter.

On estimation of survival function under random censoring model

We study an estimator of the survival function under the random censoring model. Bahadur-type representation of the estimator is obtained and asymptotic expression for its mean squared errors is given, which leads to the consistency and asymptotic normality of the estimator. A data-driven local bandwidth selection rule for the estimator is proposed. It is worth noting that the estimator is consistent at left boundary points, which contrasts with the cases of density and hazard rate estimation. A Monte Carlo comparison of different estimators is made and it appears that the proposed data-driven estimators have certain advantages over the common Kaplan-Meier estmator.

Robust goodness-of-fit tests for AR(p) models based onL 1-norm fitting

A robustified residual autocorrelation is defined based onL1-regression. Under very general conditions, the asymptotic distribution of the robust residual autocorrelation is obtained. A robustified portmanteau statistic is then constructed which can be used in checking the goodness-of-fit of AR(p) models when usingL1-norm fitting. Empirical results show thatL1-norm estimators and the proposed portmanteau statistic are robust against outliers, error distributions, and accuracy for a given finite sample.

Risk-adjusted monitoring of surgical performance

We propose a nonparametric risk-adjusted cumulative sum chart to monitor surgical outcomes for patients with different risks of post-operative mortality due to risk factors that exist before the surgery. Using varying-coefficient logistic regression models, we accomplish the risk adjustment. Unknown coefficient functions are estimated by global polynomial spline approximation based on the maximum likelihood principle. We suggest a bisection minimization approach and a bootstrap method to determine the chart testing limit value. Compared with the previous (parametric) risk-adjusted cumulative sum chart, a major advantage of our method is that the morality rate can be modeled more flexibly by related covariates, which significantly enhances the monitoring efficiency. Simulations demonstrate nice performance of our proposed procedure. An application to a UK cardiac surgery dataset illustrates the use of our methodology.

Nearest neighbor estimates of regression

New nearest neighbor estimators of the nonparametric regression function and its derivatives are developed. Asymptotic normality is obtained for the proposed estimators over the interior points and the boundary region. Connections with other estimators such as local polynomial smoothers are established. The proposed estimators are boundary adaptive and extensions of the Stute estimators. Asymptotic minimax risk properties are also established for the proposed estimators. Simulations are conducted to compare the performance of the proposed estimators with others.

Failure time regression with continuous informative auxiliary covariates

AbstractIn this paper we use Cox’s regression model to fit failure time data with continuous informative auxiliary variables in the presence of a validation subsample. We first estimate the induced relative risk function by kernel smoothing based on the validation subsample, and then improve the estimation by utilizing the information on the incomplete observations from non-validation subsample and the auxiliary observations from the primary sample. Asymptotic normality of the proposed estimator is derived. The proposed method allows one to robustly model the failure time data with an informative multivariate auxiliary covariate. Comparison of the proposed approach with several existing methods is made via simulations. Two real datasets are analyzed to illustrate the proposed method.n Mathematics Subject Classification (MSC): 62G07, 62G20