On the construction of trend free constant block sum PBIB designs

References

• Bansal, N., and D. K. Garg. 2022. Construction and existence of constant block sum PBIB designs. Communications in Statistics - Theory and Methods 51 (7):2231–41. doi: 10.1080/03610926.2020.1772308.
   Web of Science ®Google Scholar
• Bansal, N., D. K. Garg, and R. Khattree. 2023. Some results on the existence or nonexistence of constant block-sum triangular and other related designs. Journal of Statistical Theory and Practice 17 (1):1. doi: 10.1007/s42519-022-00301-8.
   Web of Science ®Google Scholar
• Bhowmik, A. 2013. Experimental designs involving treatments exhibiting interference effects. Unpublished Ph.D. Thesis., IARI, New Delhi. https://krishikosh.egranth.ac.in/handle/1/65165.
   Google Scholar
• Bhowmik, A., E. Varghese, S. Jaggi, and S. K. Yadav. 2018. Designs for animal experiments under two-way blocking structure in the presence of systematic trend. Indian Journal of Animal Sciences 88 (1):121–4.
   Web of Science ®Google Scholar
• Bhowmik, A., R. K. Gupta, S. Jaggi, E. Varghese, M. Harun, C. Varghese, and A. Datta. 2023. On the construction of trend resistant PBIB designs. Communications in Statistics - Simulation and Computation 52 (9):4052–64. doi: 10.1080/03610918.2021.1951763.
   Web of Science ®Google Scholar
• Bhowmik, A., S. Jaggi, C. Varghese, and E. Varghese. 2014. Trend free block designs balanced for interference effects from neighbouring experimental units. Journal of Combinatorics, Information and System Sciences 39 (1 and 2):117–33.
   Google Scholar
• Bhowmik, A., S. Jaggi, C. Varghese, and E. Varghese. 2015. Trend free second order neighbor balanced block designs. Journal of the Indian Statistical Association 53 (1 and 2):63–78.
   Google Scholar
• Bhowmik, A., S. Jaggi, E. Varghese, and S. K. Yadav. 2017. Trend free designs under two-way elimination of Heterogenity. Rashi 2 (1):34–8.
   Google Scholar
• Bose, R. C., and D. M. Mesner. 1959. On linear associative algebras corresponding to association schemes of partially balanced designs. The Annals of Mathematical Statistics 30 (1):21–38. doi: 10.1214/aoms/1177706356.
   Google Scholar
• Bose, R., and K. Nair. 1939. Partially balanced incomplete block designs. Sankhyā: The Indian Journal of Statistics 4 (3):337–72.
   Google Scholar
• Bradley, R. A., and C. M. Yeh. 1980. Trend-free block designs: Theory. Annals of Statistics 8:883–93.
   Web of Science ®Google Scholar
• Connor, W. S., and W. H. Clatworthy. 1954. Some Theorems for Partially Balanced Designs. The Annals of Mathematical Statistics 25 (1):100–12. doi: 10.1214/aoms/1177728849.
   Google Scholar
• Das, M. N. 1960. Circular designs. Journal of the Indian Society of Agricultural Statistics 12:45–56.
   Google Scholar
• Dey, A. 1986. Theory of block designs, 1st ed. New York: John Wiley and Sons.
   Google Scholar
• Dhall, S. P. 1986. Some studies on robustness of designs. Unpublished Ph. D. Thesis., IARI, New Delhi.
   Google Scholar
• Fisher, R. A., and F. Yates. 1957. Statistical tables for biological, agricultural and medical research, 5th ed. Edinburgh: Oliver and Boyd.
   Google Scholar
• Gupta, S. 2021. Constant block-sum two-associate class group divisible designs. Statistics and Applications 19 (1):141–8.
   Web of Science ®Google Scholar
• Jacroux, M., D. Majumdar, and K. R. Shah. 1995. Efficient block designs in the presence of trends. Statistica Sinica 5:605–15.
   Web of Science ®Google Scholar
• Jacroux, M., D. Majumdar, and K. R. Shah. 1997. On the determination and construction of optimal block designs in the presence of linear trend. Journal of the American Statistical Association 92 (437):375–82. doi: 10.2307/2291483.
   Web of Science ®Google Scholar
• Khattree, R. 2019a. A note on the nonexistence of the constant block-sum balanced incomplete block designs. Communications in Statistics - Theory and Methods 48 (20):5165–8. doi: 10.1080/03610926.2018.1508715.
   Web of Science ®Google Scholar
• Khattree, R. 2019b. The Parshavnath Yantram yields a Constant-Sum partially balanced incomplete block design. Communications in Statistics - Theory and Methods 48 (4):841–9. doi: 10.1080/03610926.2017.1417439.
   Web of Science ®Google Scholar
• Khattree, R. 2020. On construction of constant block-sum partially balanced incomplete block designs. Communications in Statistics - Theory and Methods 49 (11):2585–606. doi: 10.1080/03610926.2019.1576895.
   Web of Science ®Google Scholar
• Khattree, R. 2022. On construction of equireplicated constant block-sum designs. Communications in Statistics - Theory and Methods 51 (13):4434–50. doi: 10.1080/03610926.2020.1814816.
   Web of Science ®Google Scholar
• Lal, K., R. Prasad, and V. K. Gupta. 2007. Trend-free nested balanced incomplete block designs and designs for diallel cross experiments. Calcutta Statistical Association Bulletin 59 (3-4):203–21. doi: 10.1177/0008068320070306.
   Google Scholar
• Lin, W. C., and J. Stufken. 1999. On finding trend-free block designs. Journal of Statistical Planning and Inference 78 (1-2):57–70.
   Web of Science ®Google Scholar
• Majumdar, D., and R. J. Martin. 2002. Finding optimal designs in the presence of trends. Journal of Statistical Planning and Inference 106 (1–2):17790. doi: 10.1016/S0378-3758(02)00211-2.
   Google Scholar
• Saha, G. M., A. Dey, and A. C. Kulshreshtha. 1974. Circular designs – further results. Journal of the Indian Society of Agricultural Statistics 26:87–92.
   Google Scholar
• Sarkar, K. A., A. Bhowmik, S. Jaggi, E. Varghese, and C. Varghese. 2017. Trend resistant neighbour balanced bipartite block designs. Journal of the Indian Society of Agricultural Statistics 71 (1):53–1.
   Google Scholar
• Sharma, V. K., C. Varghese, and S. Jaggi. 2010. Tetrahedral and cubical association schemes with related PBIB (3) designs. Model Assisted Statistics and Applications 5 (2):93–9. doi: 10.3233/MAS-2010-0146.
   Google Scholar
• Stufken, J. 1988. On the existence of linear trend free block designs. Communications in Statistics - Theory and Methods 17 (11):3857–63. doi: 10.1080/03610928808829840.
   Web of Science ®Google Scholar
• Yeh, C. M., and R. A. Bradley. 1983. Trend-free block designs: Existence and construction results. Communications in Statistics - Theory and Methods 12 (1):1–24. doi: 10.1080/03610928308828438.
   Web of Science ®Google Scholar
• Yeh, C.-M., R. A. Bradley, and W. I. Notz. 1985. Nearly trend-free designs. Journal of the American Statistical Association 80 (392):985–92. doi: 10.1080/01621459.1985.10478214.
   Web of Science ®Google Scholar