A general theory of minimum aberration and its applications

Minimum aberration is an increasingly popular criterion for comparing and assessing fractional factorial designs, and few would question its importance and usefulness nowadays. In the past decade or so, a great deal of work has been done on minimum aberration and its various extensions. This paper develops a general theory of minimum aberration based on a sound statistical principle. Our theory provides a unified framework for minimum aberration and further extends the existing work in the area. More importantly, the theory offers a systematic method that enables experimenters to derive their own aberration criteria. Our general theory also brings together two seemingly separate research areas: one on minimum aberration designs and the other on designs with requirement sets. To facilitate the design construction, we develop a complementary design theory for quite a general class of aberration criteria. As an immediate application, we present some construction results on a weak version of this class of criteria.Comment: Published at http://dx.doi.org/10.1214/009053604000001228 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Atomic and magnetic structures of (CuCl)LaNb2_2O7_7 and (CuBr)LaNb2_2O7_7: Density functional calculations

The atomic and magnetic structures of (Cu$X$)LaNb$_2$O$_7$ ($X$=Cl and Br) are investigated using the density-functional calculations. Among several dozens of examined structures, an orthorhombic distorted $2\times 2$ structure, in which the displacement pattern of $X$ halogens resembles the model conjectured previously based on the empirical information is identified as the most stable one. The displacements of $X$ halogens, together with those of Cu ions, result in the formation of $X$-Cu-$X$-Cu-$X$ zigzag chains in the two materials. The nearest-neighbor interaction within the zigzag chains are determined to be antiferromagnetic (AFM) for (CuCl)LaNb$_2$O$_7$ but ferromagnetic (FM) for (CuBr)LaNb$_2$O$_7$. On the other hand, the first two neighboring interactions between the Cu cations from adjacent chains are found to be AFM and FM respectively for both compounds. The magnitudes of all these in-plane exchange couplings in (CuBr)LaNb$_2$O$_7$ are evaluated to be about three times those in (CuCl)LaNb$_2$O$_7$. In addition, a sizable AFM inter-plane interaction is found between the Cu ions separated by two NbO$_6$ octahedra. The present study strongly suggests the necessity to go beyond the square $J_1-J_2$ model in order to correctly account for the magnetic property of (Cu$X)$LaNb$_2$O$_7$.Comment: 24 pages, 7 figure

Some results on 2n−m2^{n-m} designs of resolution IV with (weak) minimum aberration

It is known that all resolution IV regular $2^{n-m}$ designs of run size $N=2^{n-m}$ where $5N/16<n<N/2$ must be projections of the maximal even design with $N/2$ factors and, therefore, are even designs. This paper derives a general and explicit relationship between the wordlength pattern of any even $2^{n-m}$ design and that of its complement in the maximal even design. Using these identities, we identify some (weak) minimum aberration $2^{n-m}$ designs of resolution IV and the structures of their complementary designs. Based on these results, several families of minimum aberration $2^{n-m}$ designs of resolution IV are constructed.Comment: Published in at http://dx.doi.org/10.1214/08-AOS670 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Optimal experimental designs for fMRI via circulant biased weighing designs

Functional magnetic resonance imaging (fMRI) technology is popularly used in many fields for studying how the brain reacts to mental stimuli. The identification of optimal fMRI experimental designs is crucial for rendering precise statistical inference on brain functions, but research on this topic is very lacking. We develop a general theory to guide the selection of fMRI designs for estimating a hemodynamic response function (HRF) that models the effect over time of the mental stimulus, and for studying the comparison of two HRFs. We provide a useful connection between fMRI designs and circulant biased weighing designs, establish the statistical optimality of some well-known fMRI designs and identify several new classes of fMRI designs. Construction methods of high-quality fMRI designs are also given.Comment: Published at http://dx.doi.org/10.1214/15-AOS1352 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Climate Change and Crop Yield Distribution: Some New Evidence From Panel Data Models

This study examines the impact of climate on the yields of seven major crops in Taiwan based on pooled panel data for 15 prefectures over the 1977-1996 period. Unit-root tests and maximum likelihood methods involving a panel data model are explored to obtain reliable estimates. The results suggest that climate has different impacts on different crops and a gradual increase in crop yield variation is expected as global warming prevails. Policy measures to counteract yield variability should therefore be carefully evaluated to protect farmers from exposure to these long-lasting and increasingly climate-related risks.Yield response, Climate change, Panel data, Unit-root test

Is Contract Farming More Profitable and Efficient Than Non-Contract Farming-A Survey Study of Rice Farms In Taiwan

Trade liberalization and globalization has modernized the food retail sector in Taiwan, affecting consumers, producers and trade patterns. These changes have placed significant pressures on farmers and processors including more stringent quality control and product varieties. The government has launched a rice production-marketing contract program in 2005 to assist rice farmers and the agro-business sector to work together as partners. The minimum scale for each contract is 50 hectares of adjacent rice paddies with 50 participants including rice farmers, seedling providers, millers and marketing agents. In order to evaluate the outcome of this program, a survey is conducted in the summer of 2005 after the first (spring) crop is harvested. Information of price and value of output and major variable and fixed inputs are collected along with characteristics of the farmers and farms. The survey results show that the average revenue of a contract farm is about 11 percent higher than an average non-contract farm. The per hectare cost of production in a contract farm is about 13 percent lower and as a result the average profit margin under contract is more than 50 percent above those without contract. A swtiching regression profit frontier model is adopted to further investigate their efficiency performance. The result indicates that an average contract farms is 20 percent more efficient than an average non-contract farm in a comparable operating environment. The result also suggests that although contract farming has potential to improve the profit of smallholders, it is not a sufficient condition for such improvement.Land Economics/Use,