in a number of works in mathematical statistics carried out in Tashkent. When choosing theirsubject <strong>and</strong> the problems to be solved, Romanovsky strictly followed the Anglo-Americ<strong>and</strong>irection. At the same time we must point out that a considerable part of investigations inmathematical statistics that was performed in Tashkent was concerned with concreteapplications, <strong>and</strong> made wide use of those methods for their accomplishment which weredeveloped by the Chebyshev school, – although certainly adapted for the solution ofstatistical problems. […]…the specific nature of the socialist production in our country, as distinct from productionbased on private property in the capitalist nations, in some of which statistical research iswidely enough used, is not yet sufficiently taken account of in{our}investigations of theapplications of mathematical statistics, especially to industry. A number of our works both inthis direction <strong>and</strong> in other fields mostly flow into the common channel of foreigninvestigations.These circumstances dem<strong>and</strong> a serious ideological <strong>and</strong> methodological reconstruction inmathematical statistics. The issue already raised by Kolmogorov (1938, p. 176) ten yearsago, now becomes especially topical. He wrote then: “The development <strong>and</strong> reappraisal ofthe general concepts of mathematical statistics, which are now studied abroad under greatinfluence of the idealistic philosophy, remain a matter for the future”. However, recentinvestigations of methodological issues of mathematical statistics pay considerably moreattention to formal rigorous determination of its scope rather than to the extremely important,in the sense of ideology <strong>and</strong> subject, topic on the essence of its problems <strong>and</strong> on how shouldconcrete phenomena be statistically examined.8e. Resolution of the Second All-Union Conference on Mathematical <strong>Statistics</strong>27 September – 4 October 1948, Tashkent . , 1948(Second All-Union Conference on Mathematical <strong>Statistics</strong>. Tashkent, 1948). Tashkent, 1948,pp. 331 – 317The Five-Year Plan of reconstruction <strong>and</strong> further development of the national economy ofthe Soviet Union raises before Soviet science fundamentally new problems formulated byComrade Stalin in his slogan addressed to Soviet scientists, – “to overtake <strong>and</strong> surpass theachievements of the science abroad”. The Great Patriotic War{1941 – 1945}put forward forthe statisticians the topical issues concerning the theory of the precision of machinery,rejection of defective articles <strong>and</strong> inspection of the quality of mass products, etc. After thewar, the part played by statistics in a number of branches of the national economy increasedstill more. The role of statistics in the development of the main directions of natural sciencesis also great.Some statisticians took up idealistic positions, supported the Weismann direction inbiology <strong>and</strong> developed abstract patterns of formal genetics cut off from reality. This,however, does not at all discredit statistics itself as being a most important tool ofinvestigation in biology <strong>and</strong> other sciences. The Conference resolutely condemns the speechof V.S. Nemchinov, made at the session of the Lenin All-Union Agricultural Academy, forhis attempt statistically to “justify” the reactionary Weismann theories 7 . Objectively,Academician Nemchinov adhered to the Machian Anglo-American school which endowsstatistics with the role of arbiter situated over the other sciences, a role for which it is notsuited.The latest decisions of the Central Committee of the All-Union Communist Party(Bolsheviks) concerning ideological issues raised the problem of rooting out the survivals ofcapitalism from people’s minds, which, among the Soviet intellectuals, are expressed byservility <strong>and</strong> kow-towing to foreign ideas, by lack of a proper struggle for the priority of the
Russian, <strong>and</strong> especially of the Soviet science. Together with the past discussions on issues ofphilosophy, literature, music, <strong>and</strong>, finally, biology, these decisions directly indicate that it isnecessary to revise the contents of statistics from the viewpoint of the struggle againstbourgeois ideology as well as for attaining closer proximity between theoreticalinvestigations <strong>and</strong> the problems of socialist practice.Among statisticians, the passion for the theories of foreign, <strong>and</strong> especially English <strong>and</strong>American scientists, is still great. Along with these theories, often uncritically grasped, aWeltanschauung alien to Soviet scientists, <strong>and</strong> in particular the Machian concepts of theAnglo-American statistical school of Pearson, Fisher <strong>and</strong> others, had sometimes beenintroduced. Even during this Conference attempts had been made to force through theMachian Weltanschauung disguising it by loud revolutionary phrases (Brodovitsky,Zakharov).The Conference accepts with satisfaction the statement of a most eminent Sovietstatistician, the Full Member of the Uzbek Academy of Sciences, Professor Romanovsky,who confessed to having made ideological mistakes in some of his early works. TheConference considers it necessary to list the following essential shortcomings in the work ofSoviet statisticians.1. The existence of a gap between theory <strong>and</strong> practice resulting in that some serioustheoretical findings were not carried out onto practical application.2. The lack of prominent monographs generalizing numerous theoretical achievements ofSoviet statistics <strong>and</strong> harmoniously explicating the concepts of Soviet statistics 8 .3. The methods of bourgeois statistics were not always critically interpreted; sometimesthey had been propag<strong>and</strong>ized <strong>and</strong> applied.4. The teaching of the theory of probability <strong>and</strong> mathematical statistics, in spite of theirever increasing significance for studying most important issues in natural sciences,technology <strong>and</strong> economics, is either altogether lacking in the appropriate academicinstitutions or carried out insufficiently <strong>and</strong> sometimes on a low level. In particular, utterlyinsufficient attention is given to the training of specialists in mathematical statistics in theuniversities <strong>and</strong> the teaching of the elements of statistics is not at all introduced intechnological academic institutions.5. The publication of a special statistical periodical has yet not begun 9 which greatlyhampers the intercourse <strong>and</strong> the exchange of experience between theoreticians <strong>and</strong>practitioners.6. The existing educational literature <strong>and</strong> monographs on statistics <strong>and</strong> probability theoryare meager, their quality is sometimes unsatisfactory <strong>and</strong> they are insufficiently connectedwith concrete applications.In mathematical statistics, the Conference considers research in the following directionsas most topical.1. A construction of a consistent system of mathematical statistics embracing all of itsnewest ramifications <strong>and</strong> based on the principles of the Marxist dialectical method.2. A further development of the theory of estimation of parameters <strong>and</strong> of checkinghypotheses. In particulara) The development of such a theory for series of dependent observations.b) The development of methods for an unfixed number of observations (of the type ofsequential analysis).3. The development of statistical methods of inspection of manufacture <strong>and</strong> of finishedarticles; <strong>and</strong> in particular of methods not assuming a stationary condition of manufacturing.4. Construction of a rational methodology of designing <strong>and</strong> treating field experiments <strong>and</strong>agricultural forecasts.5. The further development of statistical methods of investigation in geophysics; inparticular, in synoptic meteorology.
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of All Countries and to the Entire
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(Coll. Works), vol. 4. N.p., 1964,
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individuals of the third class, the
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From the theoretical point of view
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Second case: Each crossing can repr
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On the other hand, for four classes
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f i = i S + i , i = 1, 2, 3, 4, (
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f 1 = C 1 P(f 1 ; …; f n+1 ), C 1
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ut in this case f = 2 , f 1 = 2 ,
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I also note the essential differenc
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A 1 23n1 + 1 A 1 A 1 … A 11A 2 A
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coefficient of 2 in the right side
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h(A r h - c h A r 0 ) = - A r0we tr
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Notes1. Our formulas obviously pres
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Bernstein’s standpoint regarding
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Corollary 1.8. A true proposition c
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It is important to indicate that al
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ut for the simultaneous realization
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devoid of quadratic divisors and re
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propositions (B i and C j ) can be
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A ~ A 1 and B = B 1 , we will have
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included in a given totality as equ
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For unconnected totalities we would
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proposition given that a second one
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On the other hand, let x be a parti
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totality is perfect, but that the j
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In this case, all the finite or inf
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probabilities p 1 , p 2 , … respe
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where x is determined by the inequa
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totality of the second type (§3.1.
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- Page 71 and 72: 10. (§2.1.5). Such two proposition
- Page 73 and 74: F(x + h) - F(x) = Mh, therefore F(x
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- Page 79 and 80: |(x 1 ; t 0 ; t 1 ) - 1 t0tf(t)dt|
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- Page 113 and 114: second, it is not based on assumpti
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- Page 121 and 122: Uspekhi Matematich. Nauk, vol. 10,
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- Page 141 and 142: considered as the limiting case of
- Page 143 and 144: and, inversely,] = m ...1 2 N[ ch h
- Page 145 and 146: µ 2 2 = m 2 2 - 2m 2 m 1 2 + m 1 4
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- Page 149 and 150: the thus obtained relations as pert
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ϕ′1(x)1E(a|x 1 ; x 2 ; …; x n
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Theorem 3. If the prior density 3
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P( ≤ ≤ |, 1 , 2 , …, s )
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6. A Sensible Choice of Confidence
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0 = A 0 n, = B2, = B2, 0 = C 0 n
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Note also that (95),(96), (83),(85)
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Γ(n / 2)Γ [( n −1) / 2]k = (1/2
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f (x 1 , x 2 , …, x n ) = 1 if x
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and the probability of achieving no
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E = kEµ. (14)In many particular ca
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a = np, b = np 2 = a 2 /n, = a/nand
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with number (2k - 2), we commit an
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(67)which is suitable even without
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" = 1/[1 - e - ], = - ln [1 - (1/
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Such structures are entirely approp
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11. As a result of its historical d
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exaggeration towards a total denial