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On The Asymptotic Theory Of Quantiles And L-Statistics., Kesar Singh Dr.
On The Asymptotic Theory Of Quantiles And L-Statistics., Kesar Singh Dr.
Doctoral Theses
Let {Xi} be a sequence of r.v.s. nth stage we At the define e.d.f. as Fn (x) = (# Xi, ≤ x :≤ i ≤ n)/n and the ttn sample quantile as Qnt = inf {x : Fn (x) ≥ t} for t > 0 and = en(0+) for t=0. Most of the techniques of studying the process Qnt: 0 ≤ t≤ 1} consist of relating {Qnt} with some suitable linear statistics. The following are some of the commonly used methods for studying quantiles :(i) The Direct Methods In The Independent Case. Here, one can actually find the exact dis tribution …
Theory Of Estimation In Algebraic And Analytic Exponential Families With Applications To Variance Components Models., Krishnan Unni Dr.
Theory Of Estimation In Algebraic And Analytic Exponential Families With Applications To Variance Components Models., Krishnan Unni Dr.
Doctoral Theses
There are many important statistical problems of the following kind. The family of probability measures O is parametrized by a vector parame ter n varying in a q-dimen- sional domain. P can be represented as an exponential family of probability distributions with k canonical para- me ters where k is greater than q. The canonical parameters do not vary in a domain in R, but are restricted by polyno- mial or analytic equations. They vary on a curved surface defined by the polynomial or analytic equations within the natural parame ter space of the exponential family. The present work is …