Date of Submission


Date of Award


Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name

Computer Science


Theoretical Statistics and Mathematics Unit (TSMU-Kolkata)


Sinha, Bikas Kumar (TSMU-Kolkata; ISI)

Abstract (Summary of the Work)

la. General Dbaervations and Literature ReviewExperimentation playe an easential role in moet of the atatistioal investigations carried out for drawing inferences about certain unknown parametera of interest. If the eituation allowe for only one experiment to be executed out of a number of available alternative experiments, the experimenter ehould sim at perfoming the one which le optimum in This ie how the problem of ohooeing the beet experiment some sense. comes up.To judge the relative performances of various statistical exf mente, Blackwell (1951, 1953) and Blackwell and Girahiok (1954) introduced the concopt of sufficient experiments . However, in the ontext of ign settinge fitting into the usual Analysie of Varience (ANDVA) models,ie not etraightforward to eettle the question of exietence or nan-exiet of aufficient experimental design in ganeral terms, even though, in some simple aettinge (such as oneway ANOVA) the non-axistence of a auffioient experiment ie readily ascertained. In such si tuatione, therefore, the choice of optimum experiments is guided by specifio optimality oriterion which evolvee from different consideratione depending on the particuler probleme of intereat.The early work of Smith (1918) introduced a formal definition of deeign optimality in the study of reeponee aurface funotion. The inaugural peper in the literature on op timality of block designe ie due to Wal 143). In this paper, he posed a very important optimality criterion and establishec optimality of a different kind of the Latin S quare Deaigne (LSD e). (vide also Nandi (1950) in this context). But it was not until 1958, when the theory wan given a preciso snd syetomatio formulation. Con- fining to the oless of oonnected block designa Klefer (1958) aoneidored the general problom of eatimating e full aot of orthonormal oontrasta D = PE, whereP is n-lxn lower submatrix of an nxn arthogonal matrix o having the first row as (1/√n,1/√n,...,1/√n). He gave preoise definitions and investigated the interrelaticna of a numbor of atandard optimelity oriterie, namaly A-, D-, E-, L-, M- optimality ariterie for judging the performences of the least squere eetimates of the orthonermel contrasta in D. So fer as the non-randomized deeigne ero gonoerned, hie fundemental result ostablishee such optimality of Balanced Incompleto Block Oaeigne (BIBD a) in one way elimination of heterogeneity set-up end thet of the Latin Square Designs (LSD e) and Youden Square Doeigne (YSD e)in two way olimination of heterogencity aet-up, whenever such designe exist. At the same time, again for astimating a full aat of orthonormel treatment contraste, Mote (1958) independently proved the E-optimality of BIBD s among binery designe and Kehirsagar (1958) proved the A- and D- optimality of .BIBD s and YSD s also among binery deeigna. Contemporarily, Roy (1958) came up with the following findinge with respect to A-optimality criterion: For estimeting all alementary treatment oontreaste, in the clese of proper, incomplote blook deeigns, a most efficient deeign, whenever it exists, is necesearily a BIBD. All these results pertain to the optimity of symmetrical deeigns.


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