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\noindent{\bf Robert Charles GEARY}\\
b. 11 April 1896 - d. 8 February 1983
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\noindent{\bf Summary.} Geary contributed to areas of statistical theory,
including normality tests, stochastic ratios and time series analysis,
whilst working in Dublin as an official statistician and writing
influentially on topics in that field, such as national income
accounting and price deflation.
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Robert (Roy) Charles Geary was born in Dublin, Ireland,
the eldest child in a family of two sons and two daughters. His
father was a statistician in the General Registrar's Office in
Dublin and an enthusiast for statistics.  Roy's childhood was a
happy one.  He proceeded to University College, Dublin in 1913 to
study mathematics.  He gained all possible prizes and honours as a
student and won a Travelling Studentship to the Sorbonne in 1919.
He studied mathematics there for two years under Lebesgue,
Goursat, Borel, Cartan and Langevin and with Hadamard at the
College de France.  He returned to Dublin in 1921 where he gained
some teaching experience and continued to study and research in
mathematics.

This was the time of the Anglo-Irish War which was to lead to the
foundation of the Irish State in 1922.  Roy wished to contribute to
the fledgling state and so, at the beginning of 1923, he turned
down the offer of a university position in Southampton in favour of
a post as Statistician in the Statistics Branch of the Ministry of
Industry and Commerce in Dublin.  He was to remain a government
statistician until 1957, becoming Director of the newly estalished
Irish Central Statistics office in 1949.  He spent 1957-1960 in New
York as Chief of the National Accounts Branch, Statistical Office,
United Nations and then returned to Ireland to head the newly
established Economic research Institute (ERI) in Dublin (see
Kennedy, 1993).  He remained with the Institute (later to become
the Economics and Social Research Institute) for the rest of his
life - as Director until 1966 and as Consultant thereafter until
his sudden death.

Roy thus began work in 1923 publishing his first paper in 1925.
Statistics was then in the midst of a great formative period to be
dominated by Fisher (q.v.) who by 1925 had published his {\it Statistical
Methods for Research Workers} and who was to be the abiding
influence on Roy.  But the immediate task in Ireland was the
building up of the National Statistical Service and Roy, while
initially junior, of course, was to be the key figure in this.

Over his subsequent civil service career, he played the major role
in many aspects of national statistics including the provision of
greatly varied data.  He provided at different times several sets
of detailed population projections, a matter of great national
importance, thereby debunking alarmist views, widely held in the
1940's and early 1950's, that Ireland's unusual demographic
characteristics and high emigration propensity would lead to great
shrinkage of population.  He played the major role in the
development of Ireland's national accounts and in many other
statistics including various price and quantity index numbers.  He
also played an important role in official statistics at the
international level, being one of the founding members of the
Conference of European Statisticians.

Despite his arduous duties in the government statistical service,
Roy was a prolific publisher in academic journals.  This continued
while he directed the E(S)RI, and indeed, to his death.  Of his
some 120 publications, more than half were written after his
sixty-fifth birthday.  Most are theoretical, and of these the most
important were written between 1930 and 1956.

In a series of articles describing different elements of his life
and work, Spencer (1976, 1983, 1993, 1997), I have separated
his work into different streams.  Apart from his work as government
statistician (see Linehan, 1997), he wrote extensively and
influentially on (a) ratios of random variables, (b) testing for
normality and robustness, (c) estimating relationships between
variables, where the variables are measured with error.  A flavour
of some of this work follows.

In {\it Journal of the Royal Statistical Society (JRSS)} 1930, 
he considered the ratio of two correlated normal
variates and, under the assumption that the denominator was
unlikely to be negative, established the density of the ratio.  In
{\it Biometrika} 1944, he generalised a 1937 theorem of Cram\'er on the
distribution of the ratio of independent variates where the
denominator is non-negative with finite man to the case of
dependence.

In {\it Biometrika} 1935, 1947, he suggested the ratio of the mean
deviation to the standard deviation (the Geary Ratio) as a test for
normality.  In 1938 he published with his colleague E.S. Pearson, a
{\it Biometrika} brochure, "Tests for Normality".  In {\it JRSS}
1936 and in his
1947 {\it Biometrika} paper, he considered the robustness of $t$
and $F$
tests in situations where the underlying distributions were not
normal, showing, for example, that with $t$ tests the main trouble
arises with asymmetric parent populations.  Thus, positive skewness
of the parent population would lead to left tail rejection of the
null hypothesis too often.

His early work on estimation was based heavily on cumulant theory
and is much less cited than his famous 1949 {\it Econometrica} paper
which has been described as the definitive paper on instrumental
variable estimation for the errors in variables model and which has
led to Geary being described, with Reiersol, as the founder of the
Instrumental Variables method of estimation of relationships.

He showed in his 1936 {\it JRSS} paper on robustness that independence of
mean and variance imply normality, not just the well known reverse.
In a 1942 {\it JRSS} paper he showed that maximum likelihood minimises
that generalised variance and in a 1944 {\it Biometrika} paper, he
established some relationship between Pitman's (q.v.) closeness and
efficiency.  In 1954 {\it Incorporated Statistician}, he introduced his
contiguity ratio, a statistic designed to measure whether the data
for adjoining spatial regions are more similar than for regions not
adjoining.  This is perhaps his most cited paper - cited not only
in geography, but, in fields as diverse as agriculture,
archaeology, biology, ecology, epidemiology, genealogy, genetics,
human and veterinary medicine, sociology.

In almost all of his work, Roy's life in practical statistics is
evident.  How to forecast, how to estimate relationships, how to
test hypotheses when data is poorly measured and when underlying
assumptions are not strictly valid?  These are for him the
questions, with theory to be judged by how well it performs in
practice and with mathematical statistics having its raison d'etre
always in application.

This emphasis on application, while influenced no doubt by his life
as a working government statistician, stemmed from his highly
developed social conscience.  This conscience was there from the
beginning, exemplified perhaps by his decision to help with the
practical side of things at the formative state of the new Irish
State, but it probably increased as time passed.  He saw the
existence of a government statistical service as of enormous value
in the stabilising of public opinion.  Good data, he believed, had
a vital role in narrowing the differences between parties.  He
constantly, as a civil servant, sought to improve the relevance,
timeliness and accuracy of the official data and welcomed queries
and indeed vists from outsiders.  He believed that an independent
statistics office was one of the principle guarantees of civil
liberties and was proud to say that in his experience, the
independence of Irish statistics had never seriously been
challenged by the politicians.

He tirelessly advocated the necessity of quantification in research
and was strongly critical of theory without measurement in the
social sciences.  He was particularly critical of economics,
perhaps because he knew it best of the social sciences - indeed, he
contributed to it, for example, in regard to international
comparisons of real income (Neary, 1997) - and perhaps
because he thought it had, in principle, a lot to offer.

As a government statistician, much of his applied work must have
been unpublished.  he did, however, publish a great deal of applied
work including applications as example in his theory papers.  Thus,
his 1930 {\it JRSS} paper on ratios contained an application to Irish
data on mortality from tuberculosis, a topic in which he had a
continuing interest.  When he took over the Directorship of the new
ERI in 1960, his owrk became more obviously applied in response to
the need for relevant policy advice.  For the remaining
twenty-three years of his life, he increasingly turned to applied
economics and social science.  His personal prestige was crucial in
the establishment of the Institute and its reputation as a reliable
source of independent policy advice.

Roy received many honours in his life including Honorary
Fellowships of the Royal Statistical Society and American
Statistical Association.  He was Acting President of the
International Statistical Institute in 1957, was an influential
Chairman of Council of the International Association for Research
in Income and Wealth, 1961-1967 and was a Member of council,
Econometric Society, 1962-1964.  With all his success, he remained
a man of great courtesy and charm and with a strong sense of
humour.  He had wide life-long interests, including his family,
classical music, the theatre, sport, especially soccer, and
politics.  He abhorred conflict, whether labour-management conflict
or physical violence, perhaps especially that in Ireland.  His
greatest legacy must lie in his mathematical statistics, the great
bulk of which exemplifies the practical importance of good theory.
But his contribution to the orderly development of Irish society
through his work as government statistician and producer and
analyst of data was also significant, though to an extent that is
harder to measure.
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\begin{thebibliography}{3}
\bibitem{1}  Conniffe, D. (Ed.) (1997). Roy Geary, 1896-1983; Irish
Statistician. Centenary Lecture by John E. Spencer and Associated
Papers. Oak Tree Press and ESRI, Dublin (8 Chapters, xvii + 209pp).

\bibitem{2}  Kennedy, K.A. (1993). R.C. Geary and the ESRI,
{\it Economic and Social Review}, {\bf 24}, 225-245

\bibitem{3}  Linehan, T.P. (1997). Geary and Official Statistics.
Chapter 5, 137-151, in Cunniffe (1997).

\bibitem{4}  Neary, J.P. (1997). R.C. Geary's Contributions to
Economic Theory. Chapter 3, 93-118, in Cunniffe (1997).

\bibitem{5}  Spencer, J.E. (1976). The Scientific Work of Robert Charles Geary,
{\it Economic and Social Review}, {\bf 7}, 233-247.

\bibitem{6}  Spencer, J.E. (1983). Robert Charles Geary, {\it Econometrica},
{\bf 51}, 1599-1601.

\bibitem{7}  Spencer, J.E. (1993). Aspects of the Life and Personality of
R.C. Geary, {\it Economic and Social Review}, {\bf 24}, 215-224.

\bibitem{8}  Spencer, J.E. (1997). R.C. Geary: His Life and Work and 
Geary's Curriculum Vitae and Publication List. Chapters 1 and 2, 3-78
and 79-90 resp. in Conniffe (1997).
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\hfill{J.E. Spencer}

\end{thebibliography}

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