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A simple yet easy to implement method is proposed to further improve the finite sample approximation of the recently developed central limit theorems for aggregates of envelopment estimators. Focusing on the simple mean efficiency, we propose using the bias-corrected individual efficiency estimate to improve the variance estimator. The extensive Monte-Carlo experiments confirm that, for relatively small sample sizes (≤ 100), with both low dimensions and especially for high dimensions, our new method combined with the data sharpening method generally provides better ‘coverage’ (of the true values by the estimated confidence intervals) than the previously developed approaches.

Supplementary Material 3

We expand the recently developed framework for the inference for aggregate efficiency, by extending the existing theory and providing guidelines for practitioners. In particular, we develop the central limit theorems (CLTs) for aggregate input-oriented efficiency, analogous to the output-oriented framework established by Simar and Zelenyuk (2018). To further improve the finite sample performance of the developed CLTs, we propose a simple yet easy to implement method through using the bias- corrected individual efficiency estimate to improve the variance estimator. The extensive Monte-Carlo experiments confirmed the developed CLTs for aggregate input- oriented efficiency and also confirmed the better performance of our proposed method in the finite sample sizes. Finally, we use two well-known empirical data sets to illustrate the differences between all the existing methods to facilitate the use by practitioners.

Seed orchards represent the link between forest breeding and conifer production forests, and their mating patterns determine the genetic quality of seed orchard crops to a large extent. We genotyped the parental clones and their open pollination offspring in the third-generation seed orchard of Chinese fir using microsatellite markers and observed the synchronization of florescence in the seed orchard to understand the genetic diversity and mating structure of the seed orchard population. Genetic coancestry among parental clones was detected in the third generation seed orchard of Chinese fir, and the genetic diversity of the open-pollinated offspring was slightly higher than that of the parental clones. The external pollen contamination rate ranged from 10.1% to 33.7%, 80% of the offspring were produced by 44% of the parental clones in the orchard, and no evidence of selfing was found. We found that 68.1% of the effective pollination occurred within 50 m, and 19.9% of the effective pollination occurred in the nearest neighbors. We also found that successful mating requires about 30% of florescence overlap between males and females, and there was a significant positive correlation between male reproductive energy and male parental contribution. Our results provide a valuable reference for the management and design of advanced generation seed orchards.

This study used three winter wheat (Triticum aestivum L.) genotypes (H6756, H311 and SP8581) to compare the effects of sampling time, callus induction media, differentiation media and rooting media on in vitro culture of young spikes in wheat. In all these three genotypes, the frequencies of green plantlet differentiation were high when their young spikes were cultured between the stages of protective glume primordium formation and pistil and stamen primordium formation, but low at other stages. The optimum medium for callus induction was Murashige and Skoog (MS) medium+2 mg/l 2,4-dichlorophenoxyacetic acid (2,4-D). The optimum green plantlet differentiation medium was MS medium. Some abnormal plantlets regenerated from calli. When these plantlets were transferred to another differentiation medium [MS+1.0 mg/l 1-naphthaleneacetic acid (NAA)+0.2 mg/l 6-benzylaminopurine (6-BA)], shoot formation and elongation were induced. This allowed 90.91% of them to develop into normal green plantlets. The optimum rooting medium was 1/2MS+0.2 mg/l 3-Indolylacetonitrile (IAA)+80 g/l sucrose. An efficient regeneration system for young spike culture of wheat was set up based on such methods. Using this wheat-regeneration system, young spikes and immature embryos of 17 genotypes of wheat were in vitro cultured to study and compare the callus induction frequencies and green plantlet differentiation frequencies. The results of two successive years showed that in 15 out of the 17 genotypes (88.24%) the green plantlet differentiation frequencies were higher than those of immature embryos by 6.2–65.1%. These results showed that the regeneration system established in this trial for young spike culture of wheat was effective.