Shaojun Guo

Least Absolute Relative Error Estimation

Multiplicative regression model or accelerated failure time model, which becomes linear regression model after logarithmic transformation, is useful in analyzing data with positive responses, such as stock prices or life times, that are particularly common in economic/financial or biomedical studies. Least squares or least absolute deviation are among the most widely used criterions in statistical estimation for linear regression model. However, in many practical applications, especially in treating, for example, stock price data, the size of relative error, rather than that of error itself, is the central concern of the practitioners. This paper offers an alternative to the traditional estimation methods by considering minimizing the least absolute relative errors for multiplicative regression models. We prove consistency and asymptotic normality and provide an inference approach via random weighting. We also specify the error distribution, with which the proposed least absolute relative errors estimation is efficient. Supportive evidence is shown in simulation studies. Application is illustrated in an analysis of stock returns in Hong Kong Stock Exchange.

Global Partial Likelihood for Nonparametric Proportional Hazards Models

As an alternative to the local partial likelihood method of Tibshirani and Hastie and Fan, Gijbels, and King, a global partial likelihood method is proposed to estimate the covariate effect in a nonparametric proportional hazards model, λ(t|x)=exp{ψ(x)}λ0(t) . The estimator, ψˆ(x), reduces to the Cox partial likelihood estimator if the covariate is discrete. The estimator is shown to be consistent and semiparametrically efficient for linear functionals of ψ(x) . Moreover, Breslow-type estimation of the cumulative baseline hazard function, using the proposed estimator ψˆ(x) , is proved to be efficient. The asymptotic bias and variance are derived under regularity conditions. Computation of the estimator involves an iterative but simple algorithm. Extensive simulation studies provide evidence supporting the theory. The method is illustrated with the Stanford heart transplant data set. The proposed global approach is also extended to a partially linear proportional hazards model and found to provide efficient estimation of the slope parameter. This article has the supplementary materials online.

Marginal regression models with time‐varying coefficients for recurrent event data

Recurrent event data arise frequently from medical research. Examples include repeated infections, recurrence of tumors, relapse of leukemia, repeated hospitalizations, recurrence of symptoms of a disease, and so on. In the analysis of recurrent event data, the proportional rates model assumes that the regression coefficients are time invariant. In reality, however, these parameters may vary over time, and the temporal covariate effects on the event process are of great interest. In this article, we formulate a class of semiparametric marginal rates models, which incorporate a mixture of time-varying and time-independent parameters, to analyze recurrent event data. For statistical inference on model parameters, an estimation procedure is developed and asymptotic properties of the proposed estimators are established. In addition, we develop tests for investigating whether or not covariate effects vary with time. The finite-sample behaviors of the proposed methods are examined in simulation studies. An example of application of the proposed methodology is illustrated on a set of data from a clinic study on chronic granulomatous disease.

Functional Graphical Models

ABSTRACT Graphical models have attracted increasing attention in recent years, especially in settings involving high-dimensional data. In particular, Gaussian graphical models are used to model the conditional dependence structure among multiple Gaussian random variables. As a result of its computational efficiency, the graphical lasso (glasso) has become one of the most popular approaches for fitting high-dimensional graphical models. In this paper, we extend the graphical models concept to model the conditional dependence structure among p random functions. In this setting, not only is p large, but each function is itself a high-dimensional object, posing an additional level of statistical and computational complexity. We develop an extension of the glasso criterion (fglasso), which estimates the functional graphical model by imposing a block sparsity constraint on the precision matrix, via a group lasso penalty. The fglasso criterion can be optimized using an efficient block coordinate descent algorithm. We establish the concentration inequalities of the estimates, which guarantee the desirable graph support recovery property, that is, with probability tending to one, the fglasso will correctly identify the true conditional dependence structure. Finally, we show that the fglasso significantly outperforms possible competing methods through both simulations and an analysis of a real-world electroencephalography dataset comparing alcoholic and nonalcoholic patients.

A Dynamic Structure for High-Dimensional Covariance Matrices and Its Application in Portfolio Allocation

ABSTRACT Estimation of high-dimensional covariance matrices is an interesting and important research topic. In this article, we propose a dynamic structure and develop an estimation procedure for high-dimensional covariance matrices. Asymptotic properties are derived to justify the estimation procedure and simulation studies are conducted to demonstrate its performance when the sample size is finite. By exploring a financial application, an empirical study shows that portfolio allocation based on dynamic high-dimensional covariance matrices can significantly outperform the market from 1995 to 2014. Our proposed method also outperforms portfolio allocation based on the sample covariance matrix, the covariance matrix based on factor models, and the shrinkage estimator of covariance matrix. Supplementary materials for this article are available online.

Double AR model without intercept: An alternative to modeling nonstationarity and heteroscedasticity

ABSTRACT This paper presents a double AR model without intercept (DARWIN model) and provides us a new way to study the nonstationary heteroscedastic time series. It is shown that the DARWIN model is always nonstationary and heteroscedastic, and its sample properties depend on the Lyapunov exponent. An easy-to-implement estimator is proposed for the Lyapunov exponent, and it is unbiased, strongly consistent, and asymptotically normal. Based on this estimator, a powerful test is constructed for testing the ordinary oscillation of the model. Moreover, this paper proposes the quasi-maximum likelihood estimator (QMLE) for the DARWIN model, which has an explicit form. The strong consistency and asymptotic normality of the QMLE are established regardless of the sign of the Lyapunov exponent. Simulation studies are conducted to assess the performance of the estimation and testing, and an empirical example is given for illustrating the usefulness of the DARWIN model.

Marginal Regression Model with Time-Varying Coefficients for Panel Data

In this article, we formulate a class of semiparametric marginal means models with a mixture of time-varying and time-independent parameters for analyzing panel data. For inference about the regression parameters, an estimation procedure is developed and asymptotic properties of the proposed estimators are established. In addition, some tests are presented for investigating whether or not covariate effects vary with time. The finite-sample behavior of the proposed methods is examined in simulation studies, and the data from an AIDS clinical trial study are used to illustrate the methodology.