Pranab Kumar Sen's Theory and Applications of Sequential Nonparametrics PDF

By Pranab Kumar Sen

ISBN-10: 0898710510

ISBN-13: 9780898710519

P. ok. Sen is without doubt one of the pioneering researchers in nonparametric statistic. the subject of sequential research is getting progressively more realization because of advances in workforce sequential tools and adaptive designs. although you hardly see a nonparametric method of the matter. it is a great monograph to introduce you to the subject. if you'd like entire information Sen has a full-length booklet at the topic additionally.

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Extra info for Theory and Applications of Sequential Nonparametrics (CBMS-NSF Regional Conference Series in Applied Mathematics)

Sample text

Therefore, the details are omitted. 5 are based on the minimal assumptions on the underlying distributions. Cox (1972) has introduced a quasinonparametric model where the hazard functions for a given set of covariates are proportional to a basic (unknown) hazard function and these proportionality factors are sole functions of these covariates (of specified forms involving unknown (regression) parameters). For this reason, these are termed proportional hazard models (PHM). For such a PHM, Cox (1972), (1975) has justified (rather heuristically) the adaptability of the partial likelihood approach and proposed the usual scores statistics relating to these partial likelihood functions for the formulation of suitable test statistics.

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2. 3. 4. 5. The last section deals with some general remarks on all these sequential procedures. 2. Asymptotically minimum risk sequential point estimation. v. f. F (belonging to a family &), and let 9 = 9(F) be a parameter of interest. Based on a sample X , , . . , Xn)) be an estimator of 6, and consider the loss incurred due to estimating 6 by Tn as where g(-) is a suitable nondecreasing and nonnegative function on R + (= [0, oo)) with g(0) = 0 and c denotes the cost per unit sample. At this stage, we 45 46 CHAPTER 4 assume that there exists a positive integer rc0 (<«>), such that pn(F) = EFg(\Tn -6\) exists for every n ^ n0 and pn(F) is \i in n with limn^

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Theory and Applications of Sequential Nonparametrics (CBMS-NSF Regional Conference Series in Applied Mathematics) by Pranab Kumar Sen

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