Sankhyā : The Indian Journal of Statistics
1998, Volume 60, Series B, Pt. 2, pp. 378-379
Inferential Problems in Survey Sampling by Parimal Mukhopadhyay,
New Age International Publishers, 242 pp. (1996)
This book is a ‘review of the overall development’ of the theory of survey
sampling based on the fixed population and the superpopulation approaches.
It is divided into 11 chapters. In the first chapter (17 pp.) a model for fixed
population is introduced which is fundamental for discussions in chapters 2 and
3 on varying probability without replacement designs (55 pp.) and on inference
problems under this set up respectively (26 pp.). Chapter 4 considers the BrewerRoyall prediction theoretic approach (16 pp.) followed by the robustness of
model-dependent optimal strategies based on this approach in chapter 5 (17
pp.). Randomization due to both sampling designs and superpopulation models
is combined to construct predictors in the next chapter (11 pp.) while chapters 7
(16 pp.) and 8 (12 pp.) discuss certain assymptotic properties of these strategies
and their robustness. In chapter 9 (10 pp.) sampling designs within a class of
optimal designs which make certain conventional predictors robust and nearoptimal are developed. Next the concepts of ‘φ - optimality’ and related criteria
borrowed from the theory of optimum designs are introduced in chapter 10 (14
pp.). For researchers in the theory of sampling as well as experimental designs
this chapter will be found very useful. Chapter 11 deals with the important
practical problem of variance estimation under different super population models
(12 pp.). Three pages of explanation of general notations used in the book, a
list of abbreviations used for the names of journals and about 350 references
are given at the end of the book. An author-index and a subject index are also
appended.
As mentioned in the preface, there was an attempt to arange the main results
systematically along with short proofs, examples, remarks and notes. It is hoped
that the book will be helpful to scholars who choose to pursue research in this
field. Chapter 11 on variance estimation will be useful for the practitioners as
well, but they may not benefit much from Chapter 2 which condenses 40 years
of research into 55 pages.
The book serves as a good reference text for teachers giving an advancedlevel course in survey sampling theory and for research scholars. However, there
are many trivial misprints and omissions which are sometimes confusing and
disturbing to the readers. To mention a few - the style used for alternative
phrases in square brackets [
] is confusing [ not confusing ] when they appear
0
on p.11
[ do not appear ] with multiplication brackets; The estimator (ii) Ȳˆ
pps
could as well be mentioned in Chapter 3 on p.78; The symbol v for V is confusing
379
on pp. 12 and 13. The same symbol is used for ‘proportionality’ and ‘infinity’
(pp. 147-150). As mentioned earlier, corrections such as tr0 for t0r (p.14), α for a
in denominator of (2.2.6), ‘varieties’ for ‘variates’ (p.35), 1977 for 1971 (p.106)
etc. are too many. In this age of electronic media one would expect thoroughly
‘proof-read’ and ‘spell-checked’ material. In the preface, one has to supply the
missing word ‘considers’ after chapter 6, on page 1, the word ‘way’ after ‘long’,
the word ‘of’ in the subtitle of section 2.4.1 and so on.
In the references, several names of authors are wrongly spelled; for example,
some of these authors are : Asok, Dalenius, Kempthorne, Korwar, Mukerjee,
Srivenkataramana etc.
The book is priced at Rs. 450/- which is quite reasonable for a research
fellow/lecturer in Indian universities. A corrected and thoroughly proof-read
version probably with an expanded chapter 2 and chapter 10 enhances the usefulness of this good reference book.
Indian Statistical Institute, Calcutta
T.J. Rao