Professor C.R. Rao Interview

I am aware that you received your M.A. in Mathematics

from Andhra University in India, your M.A. in Statistics

from Calcutta University and your Ph.D. from Cambridge

University. Could you tell us when did your interest in

Statistics originally start? Have any family members, even

distant ones, followed your statistical interests?

I received the M.A. degree in Mathematics from Andhra

University in 1940 and, after six months of frustration of

applying for jobs and not getting any response, I joined the

Indian Statistical Institute (ISI) in 1941 to undergo what was

called a one-year training course in statistics to improve my

prospects of getting a job. The course was elementary, but it

gave me an opportunity to start doing research in

collaboration with K.R. Nair, one of the mathematicians

recruited by P.C. Mahalanobis, the founder of the ISI, as

that was the best way of learning statistics in the absence of

books and advanced courses in statistics at the universities

at that time. When I was half way through the training

program at the ISI, Calcutta University started a Master’s

course in Statistics, which I took and earned an M.A. degree

in Statistics by the end of 1943, with a first class, first rank

and record number of marks, which remains unbeaten till

today. Mahalanobis offered me the job of Technical

Apprentice at the ISI on Rs. 75 a month in 1943, which was

the beginning of my career as a statistician.

During the period 1941-46, I published 33 research papers;

one of which published in 1945 is the most quoted one in

literature and generated the technical terms, Cramer-Rao

Inequality, Rao-Blackwell Theorem, Fisher-Rao metric and

Rao distance in statistical inference. Another paper

published in 1946 contained a combinatorial arrangement

called orthogonal arrays, which is widely used in industrial

experimentation to design new products. Mahalanobis

doubled my salary to Rs. 150 per month. This encouraged

me to pursue my career as a statistician! In 1946, I got an

offer from Cambridge University, UK, to do statistical

analysis on some skeletal measurements, based on

methods developed in India. I was glad to accept the offer

considering it as transfer of technology from an

underdeveloped country to an advanced country. I arrived in

Cambridge in the fall of 1946 and started working at the

University’s Museum of Archeology and Ethnology as a

Research Fellow on £20 a month and also received

admission in King’s College (of which I am now one of the

11 Life Fellows) and registered myself as a research scholar

under the supervision of R.A. Fisher for a Ph.D. degree. I

completed the project by the middle of 1948 and also wrote

a thesis for my Ph.D. degree that was approved by the

examiners. I returned to India in the fall of 1948 to continue

my research work at the ISI.

Mahalanobis doubled my salary to Rs. 300 a month,

perhaps as a reward for my additional qualification of a

Ph.D. degree from Cambridge University and a few

additional papers I published during my stay in Cambridge.

The stage was set for me to continue to work at the ISI for

the next 32 years until I took mandatory retirement at the

age of 60.

I chose to study statistics out of necessity to improve my job

prospects and found it an interesting area to pursue as a

career.

I started to learn statistics at a time when it was a new field

that provided job opportunities. But now, several new fields

have opened up, especially in information technology, with

better job opportunities. None of my family members, even

distant ones, chose statistics as a career.

Who were the three people who influenced your career the

most, and why?

The three people who had an early influence on my career

in statistics are P.C. Mahalanobis, R.A. Fisher and R.C.

Bose. Mahalanobis encouraged me to pursue research in

statistics and put me in a responsible position at the ISI as

the Head of the Research and Training School for the

development of statistical education and research in India.

R.A. Fisher was a frequent visitor to the ISI and he was an

inspiring guide when I was working at Cambridge. R.C.

Bose made remarkable contributions to combinatorial

mathematics, the most famous of which is disproof of

Euler’s Conjecture on the nonexistence of orthogonal Latin

squares of certain orders, and my work on orthogonal arrays

was inspired by his contributions.

Of all your accomplishments, and there are countless,

which one in particular are you most proud of achieving?

I have some intellectual satisfaction for the esteem I earned

from the peers in my profession, who introduced some

technical terms in statistical inference, attaching my name to

them. The most widely quoted term in the literature on

statistics, engineering and lately in quantum physics is the

Cramer-Rao inequality. Perhaps, my greater contribution is

the encouragement and guidance I provided to my Ph.D.

students (fifty to date), some of whom have made

outstanding contributions to statistics and who, in turn,

produced about 300 Ph.D.’s (according to the information on

the genealogy website). This is a matter of great pride for

me.

I understand that you have received numerous honorary

degrees from universities and institutions around the

world. How do you feel about all that you have achieved so

far?

Up to date, I have 29 honorary degrees from universities in

17 countries. This statistic may or may not be meaningful,

but what I value most is my Sc.D. degree from Cambridge

University which, I am told, is based on a peer evaluation of

published research work and its contribution to natural

knowledge.

If you were to start up a statistics department at a new

university, what advice would you give to the new

Department Head?

Statistics is not a discipline like physics, chemistry or biology

where we study a subject to solve problems in the same

subject. We study statistics with the main aim of solving

problems in other disciplines. So, the teaching of statistics

must be different from that of other disciplines. Of course,

curriculum of a statistics course should include the

established statistical methods in common use, and also

selected areas of mathematics and probability necessary to

develop new statistical methodology. But emphasis should

be given to the application of various tools using real data

for demonstration.

The statistics department should also take the responsibility

of developing special courses in statistics for students

studying other subjects like psychology, sociology, biology,

etc., with greater emphasis on applications than on theory.

Finally, I would encourage the statistics department to run

consultation services to help research workers in other

departments in designing experiments, collecting necessary

data and drawing inferences. The consulting division of the

department would also be useful in providing hands-on

experience for students taking regular courses in statistics.

Can you identify any gaps in statistical methodology that

are most deserving of the profession’s attention? What

new statistical challenges are awaiting you in the

forthcoming years?

The methods of statistical analysis are changing with the

advent of computers, availability of large data sets and

refined measurement techniques. Model based techniques

developed for analyzing small data sets using hand driven

computers are being replaced by algorithmic and computer

intensive methods without model assumptions. A new brand

of statistics is coming up in the name of data mining. There

are different schools of statisticians postulating different

approaches to statistical inference and it is not unusual for

different statisticians working on the same data arriving at

different conclusions. It is not so much the gaps in statistical

methodology that we have to worry about. Judging from the

current trends of drop in the demand for courses in

statistical theory, static or diminishing number of members

of statistical societies and assumed advantage of each

subject matter department developing its own courses in

statistics with special applications to the concerned subject,

there is an apprehension that autonomous university

statistics departments may cease to exist. There are some

serious discussions among statisticians concerning

development of statistics in the 21st century. We have to

think of the future of statistics as a separate discipline with a

well-defined philosophy and methodology, and the role of

autonomous statistics departments in educating statisticians

and developing research in statistics.

One of the problems that many universities (and the

International Statistical Institute) are currently faced with is

the decreasing number of young students. What can you

say to anyone who is considering a career in the statistical

profession? What would your advice be to young academic

statisticians today?

Because of availability of attractive jobs in the emerging

areas of information science and technology, young

students are attracted to courses in computer and

information sciences to qualify themselves for the new jobs.

Perhaps, courses in statistics with specialization in some

field of application would be more attractive to young

students rather than a course confined to what is known as

mathematical statistics dealing with rigorous derivations of

statistical results using mathematical and probability

theorems.

I believe there is more to be done by way of research in

developing a coherent and practically oriented theory for

statistics. I would encourage some academically bent

students to pursue a research career in the foundations of

statistics.

You have held professorships and taught in different

countries such as India and the United States of America.

Were there differences in the academic philosophy in the

institutions you attended that you found to be significant?

The courses in statistics offered at the Indian universities

are somewhat rigid. All students have to take a prescribed

set of courses covering theoretical and applied statistics.

The syllabus followed in all the Indian universities are more

or less the same. In the USA, the students can exercise

their choices depending on their interests. However, in the

USA there is greater emphasis on mathematical statistics,

whereas some areas of statistics like design of experiments

and sample surveys are not covered in many universities. In

India, courses seem to be well-balanced between theory

and practice. But the academic philosophy is the same,

since the courses are taught using the same set of text

books.

How many ISI Sessions have you attended? Do you have

any suggestions as to how the ISI Session concept can be

improved? As an ISI Honorary member, what new roles do

you think that the ISI can play in the international statistical

community in the future?

I have attended quite a number of ISI Sessions. I am glad to

find that the scientific program of these Sessions is

becoming more and more broad based to meet the

increasing demand for statistical methodology and statistical

thinking in diverse areas of human endeavor.

The programs of the special Sections of the ISI, the

Bernoulli Society, International Associations for Official

Statistics, Education, Statistical Computing and Survey

Statisticians, are also well-balanced and reflect the modern

trends of theoretical research and applications in these

areas. There is probably a need to create special sections in

other areas such as bio-informatics (including mathematical

genetics) and environmental statistics, where there is much

activity all over the world.

You have published a large volume of work. Have you ever

stepped back and tried to identify the genesis of the

creative process in yourself? For example, some people

find that they are more creative in certain environments, or

at certain times in the day. Are there any “common

denominators” in your own creative process?

When I was working in India during the period 1941-1978,

there were only a few people to consult or collaborate with

in research work. About 76% of my published papers are

authored by me and 19% with one joint author and 5% with

more than one joint author. The source of problems on

which I worked arose from the applied work I was involved

in or questions raised or not fully answered by authors in

statistical journals. Under these circumstances, there is

plenty of scope for doing creative work. You have to think

for yourself. My 1945 paper, where the Cramer-Rao

Inequality is derived, actually arose out of a question put to

me by a student when I was teaching estimation theory.

There is no particular time or environment conducive to do

research work. I generally do research work in the early

hours of the morning, a habit which was forced on me by my

mother who used to wake me up from my bed at 4AM in the

morning, light up the lamp and made me study. Some

researchers prefer to work late in the night and wake up late

in the morning. I do have some experience of going to bed

thinking of some difficult problem and finding an easy way of

arriving at a solution on getting up in the morning. Perhaps

the brain keeps working even if you are not in a fully

conscious state!

When I moved to the USA, where statistics and

mathematics departments have a large number of faculty

members and visitors, I found opportunities for collaborative

work. About 80% of my published papers, while working in

the USA during 1979-2004, are jointly with others and 20%

by me, which is a reverse of the corresponding figures in

India. The average number of papers published per year

increased by 3. It is difficult to evaluate the difference in

quality of my papers published while working in India and

the USA. Einstein has said: “Creative work depends more

on one’s imagination rather than on other inputs through

discussion with others, knowledge from published works,

and particular work environments.”

Of the twelve books and hundreds of research papers you

have (co-) authored, which one(s) was (were) the most

challenging/satisfying? Which do you find to be your most

defining work?

It is difficult to answer this question as every piece of work,

a research paper or book, needs some imagination and

hard work, and is never completed to the author’s

satisfaction. Usually, the author is not aware how important

his work is until he comes to know how well it is received.

Some of my books and papers are mathematically oriented

and written for advanced students. The most challenging

and satisfying book I have written is Statistics and Truth:

Putting Chance to Work (published by the World Scientific

Press, Singapore and translated into 6 languages), which is

not a traditional book summarizing available knowledge, but

discusses philosophical and practical aspects of knowledge

and the role of statistics in acquiring knowledge on which we

can act upon. Two of my papers, which generated some

technical terms with my name attached and are reproduced

in the book on Breakthroughs in Statistics (1890-1990), will

probably be part of statistical literature for some time.

There are a number of theorems credited with your work

and name. Which one did you find to have the most

interesting process prior to becoming a theorem?

I have already mentioned four of my papers published

during 1945-1949 provided some technical terms named

after me. There are a few other papers published after 1949

that also generated technical terms bearing my name. Some

results catch the attention of the researchers immediately

after publication, a few others take time and many go

unnoticed and unreferred to by other writers. My result on

the lower bound to the variance of an unbiased estimator

published in 1945 was named as Cramer-Rao Inequality by

Neyman and Scott in 1948. It is a simple result obtained by

using the Cauchy-Schwarz Inequality and it generated

considerable research. It is frequently quoted in papers on

statistics, engineering and has begun to appear in papers

on quantum physics. I introduced a new asymptotic test

criterion called the Score Test in a paper published in 1948.

It took almost 40 years for it to be recognized as a useful

criterion and find a place in text books as Rao’s Score Test.

I mention these two as they are the most quoted results. My

paper on orthogonal arrays developed during 1945-1949, on

which there is a full-length book, led to considerable

research in combinatorial mathematics and applications in

industry, coding theory and experimental designs.

Another result of mine is generalized inverse of a matrix

introduced in 1965, which has been accepted as a useful

contribution in the discussion of linear models and

multivariate distributions with a singular dispersion matrix. In

my 1945 paper, I introduced differential geometric methods

in statistical inference which led to the keywords, Rao

Metric, Rao Distance, Rao Measure and Cramer-Rao

Functional, and which is a topic of current research in

statistics. In my recent reseach, I introduced the concept of

quadratic entropy and cross entropy, which are finding

applications in statistical inference and some areas of

physics.

I learned that there was only a limited amount of literature

available on statistical theory and practice when you were

a student of statistics, in particular, Sir R.A. Fisher’s

Statistical Methods for Research Workers. How greatly has

R.A. Fisher influenced you and your work? Are there any

other individuals you feel have done the same?

As I mentioned before, R.A. Fisher is the statistician who

influenced my work in statistics. Long before I met him, I

learnt all my statistics from his book, Statistical Methods for

Research Workers. I think it is a classic that served as a

guide to research workers over a long period of time;

especially, to those working in biology, where the

assumption of normality of measurements holds at least

approximately, and the number of observations is limited.

There are, however, some controversial issues, which are

inevitable when someone is creating a new branch of

knowledge. He was involved in bitter controversies over

some of them. However, the three methodological problems,

specification, estimation and testing of hypotheses

enunciated by him as relevant to statistical analysis of data,

constitute the framework for all statistical theory and

research.

If you could relive any part of your career, which part would

it be? If you would prefer to omit any part of your career,

which part would it be? If you were to start again and

choose a profession other than statistics, what would you

want to be?

If I could relive any part of my career, it would be my stay in

India, the country to which I belong, where I had the

opportunity to guide students in new areas of research.

The choice of one’s profession, however, depends much on

what is attractive in terms of job satisfaction and

remunerative to meet the needs of the family. Statistics

provided such opportunities when I completed my university

education. Under the present circumstances, I might have

chosen some areas of information science and technology,

which offers greater challenges.

You will be eighty-five this September. What plans do you

have to mark this special occasion?

There are several unfinished tasks. I only hope that I will be

able to complete some. The Government of Andhra Pradesh

(one of the states in India) has announced plans to develop

an Institute for basic research. They have named the

Institute as C.R. Rao Advanced Institute for Mathematics,

Statistics and Computer Science, the three basic sciences

that have a fundamental role in the improvement of natural

knowledge. Perhaps, I will spend some time in developing

this Institute