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To eliminate the nonlinear error of phase generated carrier (PGC) demodulation in sinusoidal phase modulating interferometer (SPMI), an active linearized PGC demodulation with fusion of differential-and-cross-multiplying (PGC-DCM) and the arctangent (PGC-Arctan) schemes is proposed. In this method, the periodic integer multiple of π (π-integer phases) of PGC-Arctan without nonlinear error and the corresponding PGC-DCM results recorded at the same time are fused to obtain a calibration coefficient for PGC-DCM demodulation. Combining the accurate π-integer phases of PGC-Arctan and the calibrated fractional phase in the range of π of PGC-DCM, a linearized PGC demodulation result can be achieved, effectively eliminating the nonlinear error caused by drifts of phase demodulation depth (m) and carrier phase delay (θ). The distinct advantage of the proposed method is that it actively and linearly calibrates the fractional result of PGC-DCM without needing to measure or compensate m and θ. Simulation and displacement measurement experiments with different m and inherent arbitrary θ are performed to validate the proposed method. The experimental results show that nonlinear error of the proposed method can be reduced to about 0.1 nm with real-time linearization.

Summary In the literature, a discrepancy in the limiting distributions of least square estimators between the stationary and nonstationary cases exists in various regression models with different persistence level regressors. This hinders further statistical inference since one has to decide which distribution should be used next. In this paper, we develop a semiparametric partially linear regression model with stationary and nonstationary regressors to attenuate this difficulty, and propose a unifying inference procedure for the coefficients. To be specific, we propose a profile weighted estimation equation method that facilitates the unifying inference. The proposed method is applied to the predictive regressions of stock returns, and an empirical likelihood procedure is developed to test the predictability. It is shown that the Wilks theorem holds for the empirical likelihood ratio regardless of predictors being stationary or not, which provides a unifying method for constructing confidence regions of the coefficients of state variables. Simulations show that the proposed method works well and has favourable finite sample performance over some existing approaches. An empirical application examining the predictability of equity returns highlights the value of our methodology.

The considerable local dissolution of strengthening phases under gradient thermo-mechanical effects of friction stir welding leads to a noticeable decrease in material local hardness and tensile properties in friction stir welded Al-Li joints at the joint central area, known as the thermo-mechanical coupling zone, compared to its surrounding regions. Consequently, the resulting high gradient in joint local properties at borders of the joint center leads to high local stress concentration and tensile failure under relatively low loading values at this region. In this study, firstly, effects of joint center laser-peening-induced local compressive residual stresses evolution and work hardening are investigated on the enhancement in local hardness and tensile properties of AA2195-T6 friction stir welded joints. Then overall induced joint mechanical property homogeneity effects from these effects are evaluated on the improvement in joint global tensile properties. LP-induced local residual stresses are measured through the depth using the X-ray diffraction method. X-ray diffraction pattern peak broadening analysis is utilized to measure dislocation density local variations after LP which represent plastic work hardening effects. Local tensile properties are characterized by the digital image correlation technique with the corporation of the monotonic tensile test approach. Considerable increments in local material properties lead to the enhancement of overall joint tensile yield strength up to about 31% and ultimate tensile strength to 11% as a result of LP-induced compressive residual stresses, surface work hardening and joint tensile homogenization effects.

Classical fuzzy time series forecasts are comprised of three steps: fuzzification, identification of fuzzy relation, and defuzzification. In this paper, we propose a new approach and add an error learning step to improve forecasts. In the fuzzification step, a hybrid method, based on the fuzzy c-means clustering and the fuzzy Silhouette criterion, is employed to determine the optimal number of intervals, which avoids time-consuming iterations of the whole algorithm. In the defuzzification step, an optimization model is set up to explain the rule of defuzzification. In the model structure, an error term is assembled into the traditional model to express model error, which is predicted by linear fitting and abnormal errors processing. Learning of model errors and considering of data characteristics guarantee good interpretability and accuracy. The numerical results show that the proposed approach has superior forecast performance to existing methods.

The estimation of the minimum probability of a multinomial distribution is important for a variety of application areas. However, standard estimators such as the maximum likelihood estimator and the Laplace smoothing estimator fail to function reasonably in many situations as, for small sample sizes, these estimators are fully deterministic and completely ignore the data. Inspired by a smooth approximation of the minimum used in optimization theory, we introduce a new estimator, which takes advantage of the entire data set. We consider both the cases with a known and an unknown number of categories. We categorize the asymptotic distributions of the proposed estimator and conduct a small-scale simulation study to better understand its finite sample performance.

In this paper we study estimating ruin probability which is an important problem in insurance. Our work is developed upon the existing nonparametric estimation method for the ruin probability in the classical risk model, which employs the Fourier transform but requires smoothing on the density of the sizes of claims. We propose a nonparametric estimation approach which does not involve smoothing and thus is free of the bandwidth choice. Compared with the Fourier-transformation-based estimators, our estimators have simpler forms and thus are easier to calculate. We establish asymptotic distributions of our estimators, which allows us to consistently estimate the asymptotic variances of our estimators with the plug-in principle and enables interval estimates of the ruin probability.

A phase differential heterodyne interferometer for simultaneous measurement of straightness error and displacement is proposed. In this interferometer, a modified mobile sensor composed of a Wollaston prism and a semi-reflective plane mirror is adopted to obtain the straightness error and displacement information simultaneously. A phase differential measurement is utilized to obtain phase differential signals for straightness error and displacement measurement, respectively, by using phase retarder and polarizing beam-splitter. Based on the relationship of π phase difference between the nonlinear errors of phase differential signals, the periodic nonlinear error of measurement results can be compensated. Benefiting from this design, the proposed interferometer can not only obtain the straightness error and displacement simultaneously, but also reduce the nonlinearity of measurement and the influence of the measured object’s rotation. The optical configuration and measurement principle are described in detail. The influence of Wollaston prism’s roll error is also discussed. And three verification experiments are presented at last.

This study investigated the influence of multiple laser shock peening on microstructure, crystallographic texture, and pitting corrosion behavior of Aluminum-Lithium alloy 2060-T8 (in 3.5% NaCl) using EBSD, SEM and XPS techniques. Results show that microstructure and crystallographic texture were noticeably influenced by the peening passes. At single peening, plastic strain accommodation was homogenous, resulting in higher fraction of low Σ CSL boundaries, and significant crystallographic texture transformation from fibre (unpeened) into Cube {001}〈100〉 component (corresponding to dynamic recovery as plastic deformation mode) was induced. In contrast, repetitive peening (3 & 5 passes) induced heterogeneous plastic strain accommodation, developed random and low angle grain boundaries, and texture transformation from fibre to Goss {011}〈100〉, implying recrystallization as corresponding plastic deformation mode. As a result of dense atomic structured microstructures/textures, pitting corrosion after single peening was significantly lowered than that of multiple peening. Major reason for the improved corrosion behavior at single peening pass was the formation of dense and uniform α-Al2O3 type oxide film, which significantly lowered the materials dissolution. Whereas, multiple peening led to the formation of porous γ-Al2O3, θ-Al2O3 oxides and Cu-rich regions, which activated the deeper and wider pitting. Besides, the effect of precipitates (Al2CuLi, θ′ (Al2Cu) and β′ (Al3Zr)) on pitting corrosion is quantitatively examined.

In this paper we study spatial quantile regression estimation of multivariate threshold time series models. Bahadur’s representations for our estimators are established, which naturally lead to asymptotic normality of the estimators. Simulations and a real example are used to evaluate the performance of the proposed estimators.

We propose a high dimensional classification method that involves nonparametric feature augmentation. Knowing that marginal density ratios are the most powerful univariate classifiers, we use the ratio estimates to transform the original feature measurements. Subsequently, penalized logistic regression is invoked, taking as input the newly transformed or augmented features. This procedure trains models equipped with local complexity and global simplicity, thereby avoiding the curse of dimensionality while creating a flexible nonlinear decision boundary. The resulting method is called Feature Augmentation via Nonparametrics and Selection (FANS). We motivate FANS by generalizing the Naive Bayes model, writing the log ratio of joint densities as a linear combination of those of marginal densities. It is related to generalized additive models, but has better interpretability and computability. Risk bounds are developed for FANS. In numerical analysis, FANS is compared with competing methods, so as to provide a guideline on its best application domain. Real data analysis demonstrates that FANS performs very competitively on benchmark email spam and gene expression data sets. Moreover, FANS is implemented by an extremely fast algorithm through parallel computing.

Estimating ruin probability is an important problem in insurance. Zhang et al. (2014) proposed a novel nonparametric estimation method for the ruin probability in the classical risk model with unknown claim size distribution, based on the Fourier transform and the kernel density estimation. However, asymptotic distributions of their estimators are unknown, which hampers statistical inference for the ruin probability. The authors establish asymptotic normal distributions of the estimators with known and with unknown intensity. Since the standard deviations of estimators are hard to estimate, a bootstrap method is advanced to estimate them. This allows one to construct a confidence interval estimate of the ruin probability. Furthermore, a new method is proposed to fast calculate the estimates, and the numerical results are stable and free of the “curse of large initial surplus” problem. Simulations are conducted to demonstrate nice finite sample performance of the estimators. A real dataset from a car insurance company is analyzed for illustrating the use of the proposed methodology.

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.

We propose a new method to test the superior predictive ability (SPA) of a benchmark model against a large group of alternative models. The proposed test is useful for reducing potential data snooping bias. Unlike previous methods, we model the covariance matrix by factor models and develop a generalized likelihood ratio (GLR) test statistic for the above testing problem. The GLR test is also extended to a stepwise GLR (step-GLR) test in the spirit of the step-RC test of Romano and Wolf (Econometrica 73(4):1237–1282, 2005) and step-SPA test of Hsu et al. (J Empir Financ 17(3):471–484, 2010). The step-GLR test can identify the most contributed predictive models to the rejection of the null hypothesis. A Monte Carlo simulation study shows that the GLR test is much more powerful and less conservative than the SPA test of Hansen (J Bus Econ Stat 23(4):365–380, 2005). We also present an application to illustrate the use of the GLR test and make a comparison between our GLR and Hansen’s SPA tests.

The maximum likelihood estimator (MLE) of Gini-Simpson’s diversity index (GS) is widely used but suffers from large bias when the number of species is large or infinite. We propose a new estimator of the GS index and show its unbiasedness. Asymptotic normality of the proposed estimator is established when the number of species in the population is finite and known, finite but unknown, and infinite. Simulations demonstrate advantages of our estimator over the MLE, and a real example for the extinction of dinosaurs endorses the use of our approach. Mathematics Subject Classification (MSC) codes is 60E05, which refers to distributions: general theory.

Summary 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.

SUMMARY Vector time series data are widely found in practice. In this paper we propose a multivariate functional-coefficient regression model with heteroscedasticity for modeling such data. The local linear smoother is employed to estimate the unknown coefficient matrices. Asymptotic normality 10 of the proposed estimators is established, and bandwidth selection is considered. To deal with cointegration widely observed in financial markets, we propose an error-corrected multivariate functional-coefficient model. Simulations show that the proposed estimation procedures capture nonlinear structures of coefficients well. Analysis of United States interest rates illustrates the proposed methodology. 15

We propose a geoadditive model with spatial random effects to model the earthquake distribution in Mainland China. The error is modeled an infinite mixture of Gaussian distributions with a stochastic constraint that ensures inference on the quantiles of interest. The spatial random effects are used to capture individual area effects which allow for heterogeneity among regions. We run Bayesian quantile regression for the spatial trend of the geoadditive model under a flexible Bayesian framework. The proposed method not only allows for a full span of quantile-restricted error distributions, but also separates a large-scale geographical trend from local spatial correlation. This makes the Bayesian quantile regression feasible and flexible. Our method can be generalized to other applications that involve spatial correlation along irregular contours or in discontinuous spatial domains. Our results demonstrate the usefulness and effectiveness of the proposed methodology.

This paper studies nonparametric estimation of the regression function with surrogate outcome data under double-sampling designs, where a proxy response is observed for the full sample and the true response is observed on a validation set. A new estimation approach is proposed for estimating the regression function. The authors first estimate the regression function with a kernel smoother based on the validation subsample, and then improve the estimation by utilizing the information on the incomplete observations from the non-validation subsample and the surrogate of response from the full sample. Asymptotic normality of the proposed estimator is derived. The effectiveness of the proposed method is demonstrated via simulations.

A new method of statistical classification (discrimination) is proposed. The method is most effective for high dimension, low sample size data. It uses a robust mean difference as the direction vector and locates the classification boundary by minimizing the error rates. Asymptotic results for assessment and comparison to several popular methods are obtained by using a type of asymptotics of finite sample size and infinite dimensions. The value of the proposed approach is demonstrated by simulations. Real data examples are used to illustrate the performance of different classification methods.

This paper studies local M-estimation of the nonparametric components of additive models. A two-stage local M-estimation procedure is proposed for estimating the additive components and their derivatives. Under very mild conditions, the proposed estimators of each additive component and its derivative are jointly asymptotically normal and share the same asymptotic distributions as they would be if the other components were known. The established asymptotic results also hold for two particular local M-estimations: the local least squares and least absolute deviation estimations. However, for general two-stage local M-estimation with continuous and nonlinear ψ-functions, its implementation is time-consuming. To reduce the computational burden, one-step approximations to the two-stage local M-estimators are developed. The one-step estimators are shown to achieve the same efficiency as the fully iterative two-stage local M-estimators, which makes the two-stage local M-estimation more feasible in practice. The proposed estimators inherit the advantages and at the same time overcome the disadvantages of the local least-squares based smoothers. In addition, the practical implementation of the proposed estimation is considered in details. Simulations demonstrate the merits of the two-stage local M-estimation, and a real example illustrates the performance of the methodology.

Summary The paper studies estimation of partially linear hazard regression models with varying coefficients for multivariate survival data. A profile pseudo-partial-likelihood estimation method is proposed. The estimation of the parameters of the linear part is accomplished via maximization of the profile pseudo-partial-likelihood, whereas the varying-coefficient functions are considered as nuisance parameters that are profiled out of the likelihood. It is shown that the estimators of the parameters are root n consistent and the estimators of the non-parametric coefficient functions achieve optimal convergence rates. Asymptotic normality is obtained for the estimators of the finite parameters and varying-coefficient functions. Consistent estimators of the asymptotic variances are derived and empirically tested, which facilitate inference for the model. We prove that the varying-coefficient functions can be estimated as well as if the parametric components were known and the failure times within each subject were independent. Simulations are conducted to demonstrate the performance of the estimators proposed. A real data set is analysed to illustrate the methodology proposed.

The advance of technology facilitates the collection of statistical data. Flexible and refined statistical models are widely sought in a large array of statistical problems. The question arises frequently whether or not a family of parametric or nonparametric models fit adequately the given data. In this paper we give a selective overview on nonparametric inferences using generalized likelihood ratio (GLR) statistics. We introduce generalized likelihood ratio statistics to test various null hypotheses against nonparametric alternatives. The trade-off between the flexibility of alternative models and the power of the statistical tests is emphasized. Well-established Wilks’ phenomena are discussed for a variety of semi- and non-parametric models, which sheds light on other research using GLR tests. A number of open topics worthy of further study are given in a discussion section.

Semiparametric additive models (SAMs) are very useful in multivariate nonparametric regression. In this paper, the authors study nonparametric testing problems for the nonparametric components of SAMs. Using the backfitting algorithm and the local polynomial smoothing technique, they extend to SAMs the generalized likelihood ratio tests of Fan &Jiang (2005). The authors show that the proposed tests possess the Wilks-type property and that they can detect alternatives nearing the null hypothesis with a rate arbitrarily close to root-n while error distributions are unspecified. They report simulations which demonstrate the Wilks phenomenon and the powers of their tests. They illustrate the performance of their approach by simulation and using the Boston housing data set.

This article studies estimation of partially linear hazard regression models for multivariate survival data. A profile pseudo–partial likelihood estimation method is proposed under the marginal hazard model framework. The estimation on the parameters for the linear part is accomplished by maximization of a pseudo–partial likelihood profiled over the nonparametric part. This enables us to obtain -consistent estimators of the parametric component. Asymptotic normality is obtained for the estimates of both the linear and nonlinear parts. The new technical challenge is that the nonparametric component is indirectly estimated through its integrated derivative function from a local polynomial fit. An algorithm of fast implementation of our proposed method is presented. Consistent standard error estimates using sandwich-type ideas are also developed, which facilitates inferences for the model. It is shown that the nonparametric component can be estimated as well as if the parametric components were known and the...

Time- and state-domain methods are two common approaches to nonparametric prediction. Whereas the former uses data predominantly from recent history, the latter relies mainly on historical information. Combining these two pieces of valuable information is an interesting challenge in statistics. We surmount this problem by dynamically integrating information from both the time and state domains. The estimators from these two domains are optimally combined based on a data-driven weighting strategy, which provides a more efficient estimator of volatility. Asymptotic normality is separately established for the time domain, the state domain, and the integrated estimators. By comparing the efficiency of the estimators, we demonstrate that the proposed integrated estimator uniformly dominates the other two estimators. The proposed dynamic integration approach is also applicable to other estimation problems in time series. Extensive simulations are conducted to demonstrate that the newly proposed procedure outper...

We consider the additive hazard model when some of the true covariates are measured only on a randomly selected validation set whereas auxiliary covariates are observed for all study subjects. An updated pseudoscore estimation approach is proposed for the parameters of the additive hazard model. It allows one to fit the model with auxiliary covariates, while leaving the baseline hazard unspecified. Asymptotic properties of the proposed estimators are established, and consistent standard error estimators are developed. Simulations demonstrate that the asymptotic approximations of the proposed estimates are adequate for practical use. A real example is used to illustrate the performance of the proposed method. Copyright 2007, Oxford University Press.

Summary Autoregressive conditional heteroscedastic (ARCH) models and its extensions are widely used in modelling volatility in financial time series. One of the variants, the double-threshold autoregressive conditional heteroscedastic (DTARCH) model, has been proposed to model the conditional mean and the conditional variance that are piecewise linear. The DTARCH model is also useful for modelling conditional heteroscedasticity with nonlinear structures such as asymmetric cycles, jump resonance and amplitude-frequence dependence. Since asset returns often display heavy tails and outliers, it is worth studying robust DTARCH modelling without specific distribution assumption. This paper studies DTARCH structures for conditional scale instead of conditional variance. We examine L1-estimation of the DTARCH model and derive limiting distributions for the proposed estimators. A robust portmanteau statistic based on the L1-norm fit is constructed to test the model adequacy. This approach captures various nonlinear phenomena and stylized facts with desirable robustness. Simulations show that the L1-estimators are robust against innovation distributions and accurate for a moderate sample size, and the proposed test is not only robust against innovation distributions but also powerful in discriminating the delay parameters and ARCH models. It is noted that the quasi-likelihood modelling approach used in ARCH models is inappropriate to DTARCH models in the presence of outliers and heavy tail innovations.

Additive models with backfitting algorithms are popular multivariate nonparametric fitting techniques. However, the inferences of the models have not been very well developed, due partially to the complexity of the backfitting estimators. There are few tools available to answer some important and frequently asked questions, such as whether a specific additive component is significant or admits a certain parametric form. In an attempt to address these issues, we extend the generalized likelihood ratio (GLR) tests to additive models, using the backfitting estimator. We demonstrate that under the null models, the newly proposed GLR statistics follow asymptotically rescaled chi-squared distributions, with the scaling constants and the degrees of freedom independent of the nuisance parameters. This demonstrates that the Wilks phenomenon continues to hold under a variety of smoothing techniques and more relaxed models with unspecified error distributions. We further prove that the GLR tests are asymptotically o...

This paper studies spectral density estimation based on amplitude modulation including missing data as a specific case. A generalized periodogram is introduced and smoothed to give a consistent estimator of the spectral density by running local linear regression smoother. We explore the asymptotic properties of the proposed estimator and its application to time series data with periodic missing. A simple data-driven local bandwidth selection rule is proposed and an algorithm for computing the spectral density estimate is presented. The effectiveness of the proposed method is demonstrated using simulations. The application to outlier detection based on leave-one-out diagnostic is also considered. An illustrative example shows that the proposed diagnostic procedure succeeds in revealing outliers in time series without masking and smearing effects.

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.

Time-varying copula models have been shown to offer additional flexibility among multiple financial time series. In this paper we propose a new nonparametric time-varying mixture copula model, in which both weights and dependence parameters are deterministic functions of time. Asymptotic properties of the local constant estimators are established, and a revised expectation maximization (EM) algorithm is employed to reduce the computational burden. We use Monte Carlo simulation to examine the finite sample performance of the proposed estimators. In a financial example, we show that our proposed model outperforms the benchmark copula 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 L1-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 L1-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 © 2001 John Wiley & Sons, Ltd.

A robustified residual autocorrelation is defined based onL 1-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 usingL 1-norm fitting. Empirical results show thatL 1-norm estimators and the proposed portmanteau statistic are robust against outliers, error distributions, and accuracy for a given finite sample.

This paper provides a new methodology to test the superior predictive ability (SPA) of technical trading rules relative to the benchmark without potential data snooping bias. Unlike other previous methods, we explicitly approximate the covariance matrix through certain decomposition, which decreases the number of elements needed to be estimated. With the help of covariance matrix, we are able to exploit more information contained in the diagonal and off-diagonal terms and as a result, so that we improve the effectiveness of testing result. Due to the nuisance parameter in composite hypothesis, we choose the generalized likelihood ratio (GLR) test which is of uniform most power, to alleviate such problem and at the same time, to provide a pivotal distribution. Bootstrap procedure is employed in our simulation to obtain the power of the test. The result shows that the GLR test dominates the SPA test proposed by Hansen (2005) in terms of power and our GLR test is sensitive to the inclusion of superior models. Therefore, it increases the power faster than that of SPA test. The result also suggests that the GLR test is less conservative than SPA test.

High throughput genetic sequencing arrays with thousands of measurements per sample and a great amount of related censored clinical data have increased demanding need for better measurement specific model selection. In this paper we establish strong oracle properties of nonconcave penalized methods for nonpolynomial (NP) dimensional data with censoring in the framework of Cox's proportional hazards model. A class of folded-concave penalties are employed and both LASSO and SCAD are discussed specifically. We unveil the question under which dimensionality and correlation restrictions can an oracle estimator be constructed and grasped. It is demonstrated that nonconcave penalties lead to significant reduction of the "irrepresentable condition" needed for LASSO model selection consistency. The large deviation result for martingales, bearing interests of its own, is developed for characterizing the strong oracle property. Moreover, the nonconcave regularized estimator, is shown to achieve asymptotically the information bound of the oracle estimator. A coordinate-wise algorithm is developed for finding the grid of solution paths for penalized hazard regression problems, and its performance is evaluated on simulated and gene association study examples., Published in at http://dx.doi.org/10.1214/11-AOS911 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)