亚木普迪‧拉达克利西纳‧劳Calyampudi Radhakrishna Rao

亚木普迪‧拉达克利西纳‧劳的父母是C Daraiswamy Naidu（1879-1940），一名警察督察，和A Laxmikanthamma。他是父母十个孩子中的第八个，其中两个在婴儿期死亡。我们应该解释，名字亚木普迪‧拉达克利西纳‧劳是他名字的一部分——事实上，他家里所有的男孩都叫亚木普迪‧拉达克利西纳‧劳。他的另一个名字亚木普迪‧拉达克利西纳‧劳来自神Krishna（他是父母孩子中的第八个，因此，习俗是以Krishna命名第八个孩子）。只有家里的男孩接受学校教育，这是当时的传统，但这因家庭频繁搬迁而相当中断，因为他们的父亲被从一个地方调到另一个地方。亚木普迪‧拉达克利西纳‧劳 亚木普迪‧拉达克利西纳‧劳在Gudur完成了前两年的学业，接下来两年在Nuzvid，然后6年级和7年级在Nandigama，这些都是Andhra Pradesh州的城镇。在这些年里，CR，我们将在本传记中这样称呼亚木普迪‧拉达克利西纳‧劳，很少见到他的父亲，他完全沉浸在工作中，但他的母亲是一个主要的影响[11]：-

……在我年轻的时候，[我的母亲]每天早上四点叫醒我，为我点亮油灯，让我在清晨安静的时刻学习，那时头脑清醒。

1931年，CR的父亲退休，全家定居在Andhra Pradesh海岸的Visakhapatnam。家庭选择这个城市是因为那里为孩子们提供了优秀的教育设施。CR在那里学习了十年，先是在高中，然后在A V N 夫人学院的 intermediate 学习数学、物理和化学，之后进入安得拉大学。在 intermediate college，他在两年中都赢得了Chandrasekara Iyer奖学金。1935年的学校杂志发表了他的照片，标题是：-

亚木普迪‧拉达克利西纳‧劳今年赢得了Chandrasekara奖学金。他在整个学校生涯中获得了最令人垂涎的奖项，这是独一无二的荣誉。

CR在采访[5]中谈到了他父亲的影响：-

我11岁时，不用纸笔就能做复杂的算术题。父亲欣赏我对数学的兴趣和我在学校的良好表现，他认为我最终应该获得数学学位，并继续做研究以获得博士学位。他给我看了一本名为⟦E1⟧的书，这是一位数学家为他的女儿⟦N1⟧解决而设置的问题集。他让我每天在书中做5到10道题。我喜欢解决这些问题，这进一步激发了我追求数学的兴趣。因此，我进入数学领域源于我从父亲那里得到的鼓励和我自己对解决数学问题的兴趣。

他于1940年从安得拉大学获得数学一等荣誉硕士学位。他申请了安得拉大学的研究奖学金，但他的申请因在截止日期后收到而被拒绝。在这个阶段，在家人的鼓励下，他决定参加竞争激烈的印度公务员考试，但由于只有二十岁，他必须等待十八个月才能被允许参加考试。他申请了陆军测量单位数学家的职位，以填补参加公务员考试之前的时间。他被叫到加尔各答面试，但未能获得这份工作。然而，这对CR来说是一个转折点，因为他在面试前住在南印度酒店，在那里他遇到了一位正在印度统计学院接受统计学培训的年轻人。CR在安得拉大学攻读硕士学位时曾上过一门probability课程，但他从未听说过印度统计学院。这位年轻人带CR参观了学院，当时学院位于总统学院物理系。这似乎既提供了一份工作，也提供了一个测试他是否喜欢研究的机会，因此CR申请了为期一年的统计学培训课程。

此时家庭陷入了一些经济困难，因为CR的父亲在前一年去世了。然而，他的一个兄弟和母亲设法资助他在研究所度过了一年。培训课程相当令人失望，由对统计理论了解甚少的人教授。然而，研究所有所长马哈拉诺比斯，以及其他顶级研究人员，如K Raghavan Nair、Samarendra Nath Roy和钱德拉·鲍斯。CR开始与Nair进行研究，他们发表了一篇联合论文Confounded designs for asymmetrical factorial experiments（1941）。在接下来的一年里，他发表了六篇论文，其中四篇是与Nair的联合发表，例如A general class of quasi-factorial designs leading to confounded designs for factorial experiments和A note on partially balanced incomplete block designs。

他在印度统计学院接受培训几个月后，加尔各答大学宣布设立新的统计学硕士学位。该大学的讲师正是印度统计学院的统计学家，他师从K Raghavan Nair、Samarendra Nath Roy和钱德拉·鲍斯学习课程。1943年，他以一等成绩和金牌获得该学位。他的学位论文是四个领域的重要工作：实验设计、线性模型、多元分析和概率分布的特征。这些成为他整个职业生涯持续研究的主题。除了统计学研究，CR开始与钱德拉·鲍斯研究组合问题，与萨尔瓦达曼·邱拉研究数论问题。

CR于1943年11月开始被任命为印度统计学院的技术学徒，几个月后，在1944年6月，他还在加尔各答大学担任兼职讲师。到1946年底，他已经发表了三十多篇论文[5]：-

我继续研究组合数学，涉及实验设计，并写了许多论文，其中一些与钱德拉·鲍斯和S D 邱拉合作。我发展了一种最小二乘的一般理论，不对伴随变量做任何假设。我找到了一种检验多变量分析中指定变量集冗余性的方法。

CR在此期间获得的最重要结果现在被称为哈拉尔德·克拉梅尔-亚木普迪‧拉达克利西纳‧劳不等式，它给出了参数无偏估计的方差界限。它出现在他的论文Information and accuracy attainable in the estimation of statistical parameters（1945年）中。这篇论文的重要性可以从它在S Kotz和N Johnson（编），Breakthroughs in Statistics: 1889-1990（Springer Verlag，纽约，柏林，1991年）中重新发表这一事实看出。1946年8月，CR登上了从加尔各答驶往英国的船。他获得了在剑桥人类学博物馆从事统计工作的职位，并且还在剑桥大学注册为研究生。他在剑桥大学国王学院的博士研究由罗纳德·费希尔指导。CR每天在人类学博物馆工作，每天晚上他花几个小时在罗纳德·费希尔的遗传学实验室里绘制数千只活鼠的染色体图谱。在剑桥期间，CR写了他的有影响力的论文Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation，该论文于1948年发表在《剑桥哲学学会会刊》上。他于1948年因他的学位论文Statistical Problems of Biological Classification获得博士学位，该论文由约翰·威沙特审查。

他于8月回到加尔各答，回到印度统计学院的职位。到达后不久，1948年9月9日，他与Smt Bhargavi结婚，一个他从小就认识的女孩；他们有一个女儿Tejaswini和一个儿子Veerendra。CR返回时被任命为监督统计师，但印度政府向学院提供的大笔拨款使学院得以建立研究和培训学校，并任命教授、助理教授和其他学术级别。比CR资深的钱德拉·鲍斯和A Bhattacharya大约在这时离开了学院。S N Roy被任命为教授，CR被任命为助理教授。然而，Roy在任命后不久就去了美国，CR于1949年7月成为教授，年仅28岁。1959年，学院被授权授予自己的学位，并开始了自己的本科课程。由于人手不足，CR发现自己做了相当多的本科教学，但发现这是一种有益的经历。1964年，他成为研究和培训学校的主任，然后在1972年被任命为印度统计学院的主任兼秘书。1976年，他被命名为贾瓦哈拉尔·尼赫鲁教授。

现在让我们看看CR出版的一些极具影响力的书籍。第一本是Advanced statistical methods in biometric research（1952年），他在剑桥攻读博士学位时开始写这本书。他在序言中陈述的目标是：-

……介绍若干统计方法，同时兼顾两类读者的需求：一类是对所采用的某一特定方法的基础提出质疑的学生，另一类是寻求处理其数据之现成办法的实际工作者。

他的下一本书Linear statistical inference and its applications（1965）数学性更强，是为大学数学统计课程而编写的。他于1970年出版了Computers and the Future of Human Society，次年与Sujit Kumar Mitra合著出版了Generalized inverse of matrices and its applications。R J Plemmons解释说，他们：

……对奇异矩阵、以及一般矩形矩阵在复数域上的可逆性概念，给出了一种统一的处理。……这些内容应当能成为一门为期一学期的矩阵代数或数理统计课程的好教材。

随后又出版了其他著作，如与A 韦尼阿明·卡甘合著的Characterization Problems of Mathematical Statistics（俄文版1972年，英文译本1973年）以及尤里·弗拉基米罗维奇·林尼克。

1979年，CR在达到六十岁强制退休年龄之前离开了印度统计学院，前往美国，被任命为匹兹堡大学的大学教授。1988年，他搬到匹兹堡的宾夕法尼亚州立大学，被命名为Eberly家族统计学教授。退休后，他成为Emeritus Eberly教授。

他移居美国后出版的书籍包括：（与J Kleffe）Estimation of variance components and applications（1988），Statistics and truth. Putting chance to work（1989），（与D N Shanbhag）Choquet-Deny type functional equations with applications to stochastic models（1994），（与H Toutenburg）Linear models. Least squares and alternatives（1995），以及（与M B 亚木普迪‧拉达克利西纳‧劳）Matrix algebra and its applications to statistics and econometrics（1998）。

亚木普迪‧拉达克利西纳‧劳获得的荣誉之多，根本无法一一列举。以下选列若干，以见他在全世界所受到的崇高敬重。首先列出他获得的部分奖项与荣誉：科学与工业研究理事会颁发的S S Bhatnagar奖（1963年）、Royal Statistical Society的Guy银质奖章（1965年）、1968年由印度政府授予Padma Bhushan称号、1969年获印度国家科学院的Megnadh Saha奖章、1979年获Bose研究所的Jagdish Chandra Bose金质奖章、1984年获Andhra Pradesh科学院银盘奖、1988年《印度时报》将亚木普迪‧拉达克利西纳‧劳列为有史以来印度十大科学家之一、1989年获美国统计协会的塞缪尔·S·威尔克斯纪念奖：

因对多元统计理论及其在生物计量学问题中应用的重大贡献；因作为国家和国际组织的顾问而在世界范围内开展的活动；因长期作为教师、编辑、作者和学术机构创建者而尽职尽责；以及因他对统计思想在不同科学学科中应用所产生的巨大影响，他在四十余年的职业生涯中体现了塞缪尔·S·威尔克斯的精神与理想。

其他奖项包括：印度科学大会颁发的马哈拉诺比斯诞辰百年金奖（1996年），American Statistical Association颁发的杰出成就奖章（1997年）：-

……因对方法、问题、概念及环境统计应用的发展作出杰出贡献……

印度政府颁发的莲花装勋章（2001年），国家科学奖章（2002年），由乔治·W·布什总统于6月12日在白宫举行的仪式上颁发：-

……因其对统计理论基础和多元统计方法论及其应用的开拓性贡献，丰富了物理、生物、数学、经济和工程科学……

Indian National Science Academy的拉马努金奖章（2003年），国际统计学会的国际马哈拉诺比斯奖（2003年），以及皇家统计学会的金质Guy奖章（2011年）：-

在皇家统计学会115年的历史中，他是第34位获奖者。他是首位获得该奖项的亚洲人、首位非欧洲人和首位非美国人。

他先后当选为伦敦皇家学会（1967年）、National Academy of Sciences, USA（1995年）、American Academy of Arts and Science、Indian National Science Academy、Lithuanian Academy of Sciences以及第三世界科学院院士。他还被授予国际统计学会荣誉会员（1983年）、国际生物统计学会荣誉会员（1986年）、Royal Statistical Society（1969年）、Finnish Statistical Society（1990年）、葡萄牙统计学会、组合学与应用研究所和世界创新基金会的荣誉会员。

他获得了来自六大洲十八个国家的大学授予的三十三个荣誉学位，包括：印度安得拉大学（1967年），苏联列宁格勒大学（1970年），印度德里大学（1973年），希腊雅典大学（1976年），印度海得拉巴奥斯马尼亚大学（1977年），美国哥伦布俄亥俄州立大学（1979年），秘鲁埃隆·拉格斯·利马国立圣马科斯大学（1982年），菲律宾马尼拉大学（1983年），芬兰坦佩雷大学（1985年），印度印度统计研究所（1989年），瑞士纳沙泰尔大学（1989年），美国科林斯堡约翰·柯林斯科罗拉多州立大学（1990年），印度海得拉巴大学（1991年），波兰波兹南农业大学（1991年），斯洛伐克布拉迪斯拉发斯洛伐克科学院（1994年），西班牙巴塞罗那大学（1995年），德国慕尼黑大学（1995年），印度蒂鲁帕蒂斯里文卡特斯瓦拉大学（1996年），加拿大圭尔夫大学（1996年），印度加尔各答大学（2003年），南非比勒陀利亚大学（2004年），美国金斯顿罗德岛大学（2007年），以及印度卡基纳达贾瓦哈拉尔·尼赫鲁技术大学（2011年）。

亚木普迪‧拉达克利西纳‧劳于1991年荣获《数量经济学杂志》为其出版的专刊。前言中给予了如下赞誉：-

亚木普迪‧拉达克利西纳‧劳是一位非常杰出的科学家，也是我们时代极为卓越的统计学家。他对统计理论与应用的贡献广为人知，他的许多以他名字命名的成果被纳入世界各地统计学本科和硕士课程的教学大纲。他是一位鼓舞人心的教师，指导了众多学生在统计学各个领域的研究工作。他早期的工作极大地影响了过去四十年统计研究的进程。本期专刊的目的之一是表彰亚木普迪‧拉达克利西纳‧劳本人对计量经济学的贡献，并肯定他在印度计量经济学研究发展中的重要作用。

亚木普迪‧拉达克利西纳‧劳曾担任五个统计学会的主席：印度计量经济学会（1971-1976年）；国际生物统计学会（1973-1975年）；数理统计学会（1976-1977年）；国际统计学会（1977-1979年），以及跨学科数学论坛（1982-1984年）。

最后我们记录，CR有许多爱好，如园艺、摄影、烹饪和印度古典舞蹈。在加尔各答，他晚上与教职员工和学生一起踢足球和打羽毛球。在美国，他的放松方式是散步。

Calyampudi Radhakrishna Rao's parents were C Daraiswamy Naidu (1879-1940), a police inspector, and A Laxmikanthamma. He was the eighth of his parents' ten children, two of whom died as infants. We should explain that the name Rao is part of his given name - in fact all the male children in his family were named Rao. His other given name Radhakrishna comes from the god Krishna (who was the eighth of his parents children and, for that reason, the custom was to name the eighth child after Krishna). Only the boys in the family were given a school education, as was the tradition at the time, but this was rather disrupted by frequent moves that the family made as their father was transferred from one place to another. Calyampudi Radhakrishna completed his first two years schooling in Gudur, his next two in Nuzvid, and then grades 6 and 7 in Nandigama, all towns in the state of Andhra Pradesh. During these years CR, as we will call Calyampudi Radhakrishna Rao throughout this biography, saw little of his father who was totally absorbed in his work but his mother was a major influence [11]:-

... in my younger days, [my mother] woke me up every day at four in the morning and lit the oil lamp for me to study in the quiet hours of the morning when the mind is fresh.

In 1931 CR's father retired and the family settled down in Visakhapatnam, on the coast of Andhra Pradesh. The family chose this city because of the excellent educational facilities that were available there for their children. CR studied there for ten years, first at high school, then mathematics, physics, and chemistry at the intermediate Mrs A V N College before attending Andhra University. At the intermediate college he won the Chandrasekara Iyer Scholarship in each of his two years. The School Magazine for 1935 published his picture with the caption:-

C Radhakrishna Rao who has won the Chandrasekara Scholarship this year. He has had the unique distinction of knocking off the most coveted prizes throughout his school career.

CR spoke in the interview [5] about the influence of his father:-

When I was 11, I could do complicated arithmetical problems without paper and pencil. My father appreciated my interest in mathematics and my good performance in school, and he thought that I should eventually get a degree in mathematics and proceed to do research to get a doctorate degree. He presented me with a book called 'Problems for Leelavathi', a collection of problems set by a mathematician for his daughter Leelavathi to solve. He asked me to work out 5 to 10 problems in the book every day. I enjoyed solving these problems, which aroused further interest in me to pursue mathematics. Thus, my entry into mathematics resulted from the encouragement I received from my father and my own interest in solving mathematical problems.

He graduated M.A. with First Class Honours in Mathematics from Andhra University in 1940. He applied for a research scholarship from Andhra University but his application was rejected on the grounds that it had been received after the deadline. At this stage, encouraged by his family, he decided to sit the competitive Indian Civil Service examinations but, being only twenty years old, he had to wait eighteen months before being allowed to take the examinations. He applied for job as a mathematician in an army survey unit to fill out the time before taking the Civil Service examinations. He was called to Calcutta for an interview but failed to get the job. However, this was a turning point for CR, for he stayed in the South Indian Hotel before his interview and there he met a young man who was being trained in statistics at the Indian Statistical Institute. CR had taken a course on probability while studying for his Master's degree at Andhra University but he had never heard of the Indian Statistical Institute. The young man took CR to visit the Institute, at that time located in the Physics Department of Presidency College. It seemed to provide both a job and a chance to test whether he would like research so CR applied for the one-year training course in statistics.

The family were in some financial difficulties by this time since CR's father had died in the previous year. However, one of his brothers and his mother managed to finance him through the year at the Institute. The training course was rather a disappointment, taught by people with little understanding of statistical theory. However, there was the head of the Institute P C Mahalanobis, as well as other top researchers working at the Institute such as K Raghavan Nair, Samarendra Nath Roy and Raj Chandra Bose. CR began undertaking research with Nair and they published a joint paper Confounded designs for asymmetrical factorial experiments (1941). In the following year he published six papers, four of them joint publications with Nair, for example A general class of quasi-factorial designs leading to confounded designs for factorial experiments and A note on partially balanced incomplete block designs.

A few months after he began training at the Indian Statistical Institute, Calcutta University announced a new Master's degree in statistics. Lecturers at the University were the same statisticians working at the Institute and he took courses from K Raghavan Nair, Samarendra Nath Roy and Raj Chandra Bose. He was awarded the degree in 1943 with First Class and the gold medal. His thesis was a major piece of work in four areas: the design of experiments, linear models, multivariate analysis, and the characterization of probability distributions. These would be the topics he continued to study throughout his career. As well as research in statistics, CR began to look at combinatorial problems with R C Bose and number theory problems with Sarvadaman Chowla.

CR was appointed as a Technical Apprentice at the Indian Statistical Institute beginning in November 1943 and, a few months later, in June 1944, he also worked as a part-time lecturer at Calcutta University. By the end of 1946 he had over thirty papers in print [5]:-

I continued my research on combinatorics with reference to design of experiments and wrote a number of papers, some jointly with R C Bose and S D Chowla. I developed a general theory of least squares without any assumptions on the concomitant variables. I found a test for redundancy of a specified set of variables in multivariate analysis.

The most significant result CR obtained during this period is now called the Cramér-Rao inequality and gives a bound for the variance of an unbiased estimate of a parameter. It appears in his paper Information and accuracy attainable in the estimation of statistical parameters (1945). The significance of this paper can be seen from the fact that it was republished in S Kotz and N Johnson (eds.), Breakthroughs in Statistics: 1889-1990 (Springer Verlag, New York, Berlin, 1991). In August 1946 CR boarded a ship sailing from Calcutta to England. He had been offered a position undertaking statistical work at the Anthropological Museum in Cambridge and he also registered as a research student at Cambridge University. His Ph.D. studies at King's College, Cambridge, were supervised by R A Fisher. CR worked at the Anthropological Museum every day and every evening he spent a few hours in Fisher's genetics laboratory mapping the chromosomes of thousands of live mice. While at Cambridge CR wrote his influential paper Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation which was published in the Proceedings of the Cambridge Philosophical Society in 1948. He was awarded his doctorate in 1948 for his thesis Statistical Problems of Biological Classification which was examined by John Wishart.

He returned to Calcutta in August to his post at the Indian Statistical Institute. Soon after arriving, on 9 September 1948, he married Smt Bhargavi, a girl he had known from childhood; they had a daughter Tejaswini and a son Veerendra. CR was appointed as a Superintending Statistician on his return but a major grant to the Institute from the Indian government allowed the Institute to set up a Research and Training School and appoint professors, assistant professors and other academic grades. Those senior to CR, R C Bose and A Bhattacharya, left the Institute around this time. S N Roy was appointed to a professorship and CR to an assistant professorship. However, Roy left for the United States soon after his appointment and CR became a professor in July 1949 at the young age of 28. The Institute was given authority to award its own degrees in 1959 and started up its own undergraduate programme. Being understaffed CR found himself doing quite a bit of undergraduate teaching but found that a rewarding experience. In 1964 he became the director of the Research and Training School, and then in 1972 he was appointed Director-Secretary of the Indian Statistical Institute. He was named Jawaharlal Nehru Professor in 1976.

Let us now look at some of the highly influential books CR has published. The first was Advanced statistical methods in biometric research (1952) which he began writing while working for his doctorate at Cambridge. His aim, stated in the Preface, is:-

... to present a number of statistical techniques, keeping in view the requirements of both the student who questions the basis of a particular method employed and the practical worker who seeks a recipe for the reduction of his data.

His next book Linear statistical inference and its applications (1965) was more mathematical, and designed to be used for mathematical statistics courses in universities. He published Computers and the Future of Human Society in 1970, and in the following year, jointly with Sujit Kumar Mitra, he published Generalized inverse of matrices and its applications. R J Plemmons explains that they:-

... present a general unified treatment of the concept of inversability of singular, and in general rectangular, matrices over the complex field. ... the material should make a good text for a one term course in matrix algebra or mathematical statistics.

Further books followed such as Characterization Problems of Mathematical Statistics (Russian edition 1972, English translation 1973) with A Kagan and Yu V Linnik.

In 1979 CR left the Indian Statistical Institute, just before reaching the mandatory retirement age of sixty, and went to the United States where he was appointed to a University Professorship at the University of Pittsburgh. In 1988 he moved to Pennsylvania State University in Pittsburgh where he was named Eberly Family Professor in Statistics. After retiring he became Emeritus Eberly Professor.

Books he published after moving to the United States include: (with J Kleffe) Estimation of variance components and applications (1988), Statistics and truth. Putting chance to work (1989), (with D N Shanbhag) Choquet-Deny type functional equations with applications to stochastic models (1994), (with H Toutenburg) Linear models. Least squares and alternatives (1995), and (with M B Rao) Matrix algebra and its applications to statistics and econometrics (1998).

C R Rao has received so many honours that it would be quite impossible to list them all. Here is a selection to give an impression of the high esteem that he is held in throughout the world. First we list some of the prizes and awards he has received: the S S Bhatnagar Prize of Council of Scientific and Industrial Research (1963), the Guy Medal in Silver of the Royal Statistical Society (1965), awarded the title of Padma Bhushan by the Indian Government (1968), received the Megnadh Saha Medal of the Indian National Science Academy (1969), the Jagdish Chandra Bose Gold Medal of the Bose Institute (1979), the Silver Plate of the Andhra Pradesh Academy of Sciences (1984), The Times of India listed Rao as one of the top 10 Indian scientists of all time (1988), awarded the Samuel S Wilks Memorial Award of the American Statistical Association (1989):-

For major contributions to the theory of multivariate statistics and applications of that theory to problems of biometry; for world wide activities as advisor to national and international organizations; for long time conscientious as a teacher, editor, author and founder of academic institutions; and for the great influence he has had on the applications of statistical thinking in different scientific disciplines, embodying over a career of more than 40 years the spirit and ideals of Samuel S Wilks.

Other awards include: the Mahalanobis Birth Centenary Gold Medal by the Indian Science Congress (1996), the Distinguished Achievement Medal from the American Statistical Association (1997):-

... for outstanding contributions to the development of methods, issues, concepts, and applications of environmental statistics ...

the Padma Vibhushan by the Government of India (2001), the National Medal of Science (2002), presented by President George W Bush on 12 June at a ceremony in the White House:-

... for his pioneering contributions to the foundations of statistical theory and multivariate statistical methodology and their applications, enriching the physical biological, mathematical, economic and engineering sciences ...

the Srinivasa Ramanujan Medal of the Indian National Science Academy (2003), the International Mahalanobis Prize of the International Statistical Institute (2003), and the Guy Medal in Gold of the Royal Statistical Society (2011):-

In the 115-year history of Royal Statistical Society, he is the 34th recipient of the award. He is the first Asian, first non-European and first non-American to receive the award.

He has been elected to the Royal Society of London (1967), the National Academy of Sciences, USA (1995), the American Academy of Arts and Science, the Indian National Science Academy, the Lithuanian Academy of Sciences, and the Third World Academy of Sciences. He was made an Honorary Member of the International Statistical Institute (1983), the International Biometric Society (1986), the Royal Statistical Society (1969), the Finnish Statistical Society (1990), the Portuguese Statistical Society, the Institute of Combinatorics and Applications, and the World Innovation Foundation.

He has been awarded thirty-three honorary degrees by universities in eighteen countries, in six continents, including: Andhra University, India (1967), Leningrad University, USSR (1970), Delhi University, India (1973), University of Athens, Greece (1976), Osmania University, Hyderabad, India (1977), Ohio State University, Columbus, USA (1979), Universidad Nacional de San Marcos, Lima, Peru (1982), University of the Philippines, Manila (1983), University of Tampere, Finland (1985), Indian Statistical Institute, India (1989), Université de Neuchâtel, Switzerland (1989), Colorado State University, Fort Collins, USA (1990), University of Hyderabad, India (1991), Agricultural University of Poznań, Poland (1991), Slovak Academy of Sciences, Bratislava, Slovakia (1994), University of Barcelona, Spain (1995), University of Munich, Germany (1995), Sri Venkateswara University, Tirupati, India (1996), University of Guelph, Canada (1996), University of Calcutta, India (2003), University of Pretoria, South Africa (2004), University of Rhode Island, Kingston, USA (2007), and Jawaharlal Nehru Technological University, Kakinada, India (2011).

The Journal of Quantitative Economics published a special issue in Rao's honour in 1991. The preface gives the following tribute:-

Dr Rao is a very distinguished scientist and a highly eminent statistician of our time. His contributions to statistical theory and applications are well known, and many of his results, which bear his name, are included in the curriculum of courses in statistics at bachelor's and master's level all over the world. He is an inspiring teacher and has guided the research work of numerous students in all areas of statistics. His early work had greatly influenced the course of statistical research during the last four decades. One of the purposes of this special issue is to recognize Dr Rao's own contributions to econometrics and acknowledge his major role in the development of econometric research in India.

C R Rao has served as president of five statistical societies: the Indian Econometric Society (1971-1976); the International Biometric Society (1973-1975); the Institute of Mathematical Statistics (1976-1977); the International Statistical Institute (1977-1979), and the Forum for Interdisciplinary Mathematics (1982-1984).

Finally we record that CR has many hobbies such as gardening, photography, cooking, and Indian classical dance. In Calcutta he played soccer and badminton with staff and students in the evenings. In the United Sates his relaxation is walking.