## 1 Introduction  
High-tech industry is the use of high technology for development and production, and it has become a key area in international economic and technological competition by virtue of its large R&D investment, high added value, good international market prospects, and far-reaching impacts on other industries, and its development plays an indispensable role in promoting the optimization and upgrading of the industrial structure [1]. Innovation has become a globally recognized important driving force, and the level of the high-tech industry is often regarded as one of the important indicators of the level of economic development. It is worth noting that not only limited to developed countries, emerging market countries have also increased investment in high-tech industry to enhance their own innovation capacity [2]. As a strategic leading industry in China, high-tech industry directly affects China's national scientific and technological competitiveness and industrial core competitiveness [3], and innovation activities are the key driving force for competitive advantage, so the assessment of the innovation efficiency of China's high-tech industry has attracted extensive attention. High-tech industries can be further subdivided into high-tech manufacturing and high-tech service industries [4]. According to the Statistical Classification Directory of High-Tech Industries (Manufacturing) issued by the National Bureau of Statistics of China in 2013, China's high-tech industries (manufacturing) are classified into six industries, namely,the pharmaceutical manufacturing industry; the aviation, spacecraft, and equipment manufacturing industry; the electronics and communication equipment manufacturing industry; the computer and office equipment manufacturing industry; medical instrumentation and instrumentation manufacturing; and information chemicals manufacturing. Therefore, this study attempts to investigate the efficiency of innovation activities in China's provincial high-tech manufacturing industries and to provide a corresponding basis for decision making. Currently, there are many assessment methods for the development of the high-tech industry. [PERSON] et al. explored the key factors of the ecological development of the high-tech industry based on hierarchical analysis [5]. [PERSON] and [PERSON] explored the influence relationship of the technological innovation efficiency of the high-tech industry through factor analysis and multiple-regression analysis [6]. [PERSON] used the improved CRITIC objective assignment method to assign weights to the indicators and graded the development level of high-tech industries in 31 provinces (cities and districts) of China by the non-integer rank-order sum ratio method WRSR [7]. [PERSON] and [PERSON] used the comprehensive index method to measure the high-quality comprehensive development index of high-tech industries in 30 provinces (municipalities and autonomous regions) in China [8]. [PERSON], [PERSON] et al. used the improved TOPSIS method to assess the provincial competitiveness of China's high-tech industries [9]. [PERSON] and [PERSON] measured the global industrial chain level of China's provincial high-tech industry by the entropy value method-TOPSIS method [10]. The most commonly used method to assess the innovation efficiency of high-tech industries is data envelopment analysis (DEA) [11; 12]. First of all, the traditional DEA model has the characteristic of a \"black box\", and some scholars believe that China's high-tech innovation activities should be divided into two processes: the R&D stage and the commercialization stage [13; 14]. On this basis, some scholars consider the initial inputs in the R&D stage, the additional inputs in the commercialization stage, and the shared inputs between the two stages [15; 16; 17]. Second, the traditional DEA model is still a static model. In order to solve the problem, [PERSON] et al.