THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

Data Mining - Concepts and Techniques.

The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the definitions and indicates how the theory will yield solutions to problems arising outside it. Chapter 1 sets out the basic general theorems, which are then specialized in Chapter 2 to the space C[0, l ] of continuous functions on the unit interval and in Chapter 3 to the space D [0, 1 ] of functions with discontinuities of the first kind. The results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables. " The book develops and expands on Donsker's 1951 and 1952 papers on the invariance principle and empirical distributions. The basic random variables remain real-valued although, of course, measures on C[0, l ] and D[0, l ] are vitally used. Within this framework, there are various possibilities for a different and apparently better treatment of the material. More of the general theory of weak convergence of probabilities on separable metric spaces would be useful. Metrizability of the convergence is not brought up until late in the Appendix. The close relation of the Prokhorov metric and a metric for convergence in probability is (hence) not mentioned (see V. Strassen, Ann. Math. Statist. 36 (1965), 423-439; the reviewer, ibid. 39 (1968), 1563-1572). This relation would illuminate and organize such results as Theorems 4.1, 4.2 and 4.4 which give isolated, ad hoc connections between weak convergence of measures and nearness in probability. In the middle of p. 16, it should be noted that C*(S) consists of signed measures which need only be finitely additive if 5 is not compact. On p. 239, where the author twice speaks of separable subsets having nonmeasurable cardinal, he means "discrete" rather than "separable." Theorem 1.4 is Ulam's theorem that a Borel probability on a complete separable metric space is tight. Theorem 1 of Appendix 3 weakens completeness to topological completeness. After mentioning that probabilities on the rationals are tight, the author says it is an

Convergence of probability measures

Stable non-Gaussian random processes , by G. Samorodnitsky and M. S. Taqqu. Pp. 632. £49.50. 1994. ISBN 0-412-05171-0 (Chapman and Hall).

저작근 근전도에 관한 정상교합자와 ii급 부정교합자의 비교 연구

http://www.jiyeliang.net/Cms_Data/Contents/SXU_JYL/Folders/JournalPapers/~contents/68F2VTUJUT9PLKVM/MGRS_a%20mulit-granulation%20rough%20set.pdf

MGRS: A multi-granulation rough set

http://www.yuhuaqian.net/Cms_Data/Contents/SXU_YHQ/Folders/JournalPapers/~contents/KD22X6U6AUY584JT/Positive%20approximation-an%20accelerator%20for%20attribute%20reduction%20in%20rough%20set%20theory.pdf

Positive approximation: An accelerator for attribute reduction in rough set theory

This technical note addresses the stability problem of delayed positive switched linear systems whose subsystems are all positive. Both discrete-time systems and continuous-time systems are studied. In our analysis, the delays in systems can be unbounded. Under certain conditions, several stability results are established by constructing a sequence of functions that are positive, monotonically decreasing, and convergent to zero as time tends to infinity (additionally continuous for continuous-time systems). It turns out that these functions can serve as an upper bound of the systems' trajectories starting from a particular region. Finally, a numerical example is presented to illustrate the obtained results.

Stability Analysis of Positive Switched Linear Systems With Delays

The original rough-set model is primarily concerned with the approximations of sets described by a single equivalence relation on a given universe. With granular computing point of view, the classical rough-set theory is based on a single granulation. This correspondence paper first extends the rough-set model based on a tolerance relation to an incomplete rough-set model based on multigranulations, where set approximations are defined through using multiple tolerance relations on the universe. Then, several elementary measures are proposed for this rough-set framework, and a concept of approximation reduct is introduced to characterize the smallest attribute subset that preserves the lower approximation and upper approximation of all decision classes in this rough-set model. Finally, several key algorithms are designed for finding an approximation reduct.

/pdf/incomplete-multigranulation-rough-set-2qux49ftzc.pdf

Incomplete Multigranulation Rough Set

Based on the complement behavior of information gain, a new definition of information entropy is proposed along with its justification in rough set theory. Some properties of this definition imply those of Shannon's entropy. Based on the new information entropy, conditional entropy and mutual information are then introduced and applied to knowledge bases. The new information entropy is proved to also be a fuzzy entropy.

/pdf/a-new-method-for-measuring-uncertainty-and-fuzziness-in-u0x7zczti9.pdf

Chuangyin Dang

Papers

MGRS: A multi-granulation rough set

Positive approximation: An accelerator for attribute reduction in rough set theory

Stability Analysis of Positive Switched Linear Systems With Delays

Incomplete Multigranulation Rough Set

A new method for measuring uncertainty and fuzziness in rough set theory