Nonconcave penalized likelihood with a diverging number of parameters

A class of variable selection procedures for parametric models via nonconcave penalized likelihood was proposed by Fan and Li to simultaneously estimate parameters and select important variables. They demonstrated that this class of procedures has an oracle property when the number of parameters is finite. However, in most model selection problems the number of parameters should be large and grow with the sample size. In this paper some asymptotic properties of the nonconcave penalized likelihood are established for situations in which the number of parameters tends to \infty as the sample size increases. Under regularity conditions we have established an oracle property and the asymptotic normality of the penalized likelihood estimators. Furthermore, the consistency of the sandwich formula of the covariance matrix is demonstrated. Nonconcave penalized likelihood ratio statistics are discussed, and their asymptotic distributions under the null hypothesis are obtained by imposing some mild conditions on the penalty functions

Preparation and field-induced electrical properties of perovskite relaxor ferroelectrics

(111)-oriented and random oriented Pb0.8Ba0.2ZrO3 (PBZ) perovskite relaxor ferroelectric thin films were fabricated on Pt(111)/TiOx/SiO2/Si substrate by sol-gel method. Nano-scaled antiferroelectric and ferroelectric two-phase coexisted in both (111)-oriented and random oriented PBZ thin film. High dielectric tunability (i = 75%, E = 560 kV/ cm ) and figure-of-merit (FOM ~ 236) at room temperature was obtained in (111)-oriented thin film. Meanwhile, giant electrocaloric effect (ECE) (AT = 45.3 K and AS = 46.9 JK-1kg-1 at 598 kVcm-1) at room temperature (290 K), rather than at its Curie temperature (408 K), was observed in random oriented Pb0.8Ba0.2ZrO3 (PBZ) thin film, which makes it a promising material for the application to cooling systems near room temperature. The giant ECE as well as high dielectric tunability are attributed to the coexistence of AFE and FE phases and field-induced nano-scaled AFE to FE phase transition