Bootstrap consistency for general semiparametric M-estimation

Consider $M$-estimation in a semiparametric model that is characterized by a Euclidean parameter of interest and an infinite-dimensional nuisance parameter. As a general purpose approach to statistical inferences, the bootstrap has found wide applications in semiparametric $M$-estimation and, because of its simplicity, provides an attractive alternative to the inference approach based on the asymptotic distribution theory. The purpose of this paper is to provide theoretical justifications for the use of bootstrap as a semiparametric inferential tool. We show that, under general conditions, the bootstrap is asymptotically consistent in estimating the distribution of the $M$-estimate of Euclidean parameter; that is, the bootstrap distribution asymptotically imitates the distribution of the $M$-estimate. We also show that the bootstrap confidence set has the asymptotically correct coverage probability. These general conclusions hold, in particular, when the nuisance parameter is not estimable at root-$n$ rate, and apply to a broad class of bootstrap methods with exchangeable bootstrap weights. This paper provides a first general theoretical study of the bootstrap in semiparametric models.Comment: Published in at http://dx.doi.org/10.1214/10-AOS809 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Numerical analysis and thermal fatigue life prediction of solder layer in a SiC-IGBT power module

Limited by the mechanical properties of materials, silicon (Si) carbide insulated gate bipolar transistor (IGBT) can no longer meet the requirements of high power and high frequency electronic devices. Silicon carbide (SiC) IGBT, represented by SiC MOSFET, combines the excellent performance of SiC materials and IGBT devices, and becomes an ideal device for high-frequency and high-temperature electronic devices. Even so, the thermal fatigue failure of SiC IGBT, which directly determines its application and promotion, is a problem worthy of attention. In this study, the thermal fatigue behavior of SiC-IGBT under cyclic temperature cycles was investigated by finite element method. The finite element thermomechanical model was established, and stress-strain distribution and creep characteristics of the SnAgCu solder layer were obtained. The thermal fatigue life of the solder was predicted by the creep, shear strain and energy model respectively, and the failure position and factor of failure were discussed