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Contributions To The Neyman-Scott And Mixture Problem., Joydeep Bhanja Dr.
Contributions To The Neyman-Scott And Mixture Problem., Joydeep Bhanja Dr.
Doctoral Theses
Neyman and Scott (1948) were the first to point out that the method of maximum likelihood fails to provide elfficient estimates when the number of parameters grows with the sample size n. Consider the following examples introduced by them:Ezample 1.1 Let { Xi } be a sequence of independent random vectors in I", components Xij of Xi being independent normal with mean u, and variance o2 Ilere o2 is the parameter of interest. It is casy to sce that the maxinum likelihood estimate for o2 is not even consistent. It is also known (see Lindsay (1980), Pfanzagl (1982), van der …
The Mazur Intersection Property In Banach Spaces And Related Topics., Pradipta Bandyopadhyaya Dr.
The Mazur Intersection Property In Banach Spaces And Related Topics., Pradipta Bandyopadhyaya Dr.
Doctoral Theses
In the first part of this chapter we explain in general terms the main theme of this thesis and provide a chapter wise summary of its principal results. The second part recapitulates some of the known notions and results used in the subsequent chapters. The numbers given in parentheses correspond to those in the list of references on page 70.S. Mazur (40] was the first to consider the following smoothness property in normed linear spaces, called the Mazur Intersection Property (MIP), or, more briefly, the Property (1):Every closed bounded convex set is the intersection of closed balls containing it.He showed …