Inférence par les martingales pour des processus ponctuels à compensateur discontinu

L'auteur introduit un modèle d'intensité mutltiplicative généralisé pour les processus ponctuels à compensateur discontinu. Il en étudie l'inférence par les martingales et obtient un résultat de normalité asymptotique. Il applique ces résultats à l'estimateur de Nelson‐Aalen du taux de panne cumulé dans le cas de données de durée de vie censuées et de loi non nécessairement continues.     

Estimation of the mean utilizing prior information

Katti [1] et Mehta et Srinivasan [2] ont considérés le probléme d'estimer la moyenne μ d'une population quand de l'information a priori sur μ est disponible. Dans [1], la supposition est que cette information a priori est sous forme d'un “estimé deviné”. Un estimateur à deux degres de deux échantillons est présenté. Quand à [2], un estimateur “shrinkage” basé sur un seul échantillon et une “valeur à priori” est considéré. En suivant les techniques présentées dans ces deux articles, nous suggérons des estimateurs du paramètre quand les données viennent d'une population Binomiale ou Poisson.     

A geometric optimally of Cox's partial likelihood

The paper proves geometric optimality of Cox's partial likelihood score functions via estimating functions. As an illustration, Cox's proportional-hazards model is considered. Les auteurs démontrent l'optimalité g?ométrique des fonctions scores de vraisemblance partielle de Cox au moyen des fonctions d'estimation. Le modéle des risques proportionnels de Cox permet d'illustrer leur résultat.     

Miscellany and Notices

Abstract

Trade of United States: The History of Trade between the United Kingdom and the United States. By Sydney J. Chapman. London. Swan, Sonnenschein & Co. 1899. Reviewed by Worthington C. Ford.

Natality: Sur les variations du taux de natalité et sur l'âge moyen des époux, suivant les conditions économiques. By Enrico Raseri. Bulletin de l'Institut International de Statistique. Vol. xi; 149. Reviewed by C.-E. A. Winslow.

Natality: La natalité selon le degré d'aisance. By Jacques Bertillon. Bulletin de 1'Institut International de Statistique. Vol. xi; 163. Reviewed by C.-E. A. Winslow.

Study of Charity Statistics: The Labor Bulletin of Massachusetts (October, 1899. No. 12) contains a very valuable “Study of Charity Statistics” (pp. 119-155).

Notes on Vital Statistics: Les naissances et les décès suivant les heures de la journée. By Enrico Raseri. Bulletin de l'Institut International de Statistique. Vol. xi; 144. Reviewed by C.-E. A. Winslow.

State Publications: State Publications: a Provisional List of the Official Publications of the Several States of the United States from their Organization. Compiled under the editorial direction of R. R. Bowker, Part I: New England States. New York. Office of the Publishers' Weekly. 1899. Pp. 99.

Notes: Report of the Director of the Twelfth Census to the Secretary of the Interior. 1899. Washington. Pp, 5.

Notes: Report to the Legislature of New York by the Joint Committee on Taxation. January 15, 1900. Pp. 19. Tables 6.     

Modified inference function for margins for the bivariate clayton copula-based SUN Tobit Model

This paper extends the analysis of the bivariate Seemingly Unrelated Regression (SUN) Tobit model by modeling its nonlinear dependence structure through the Clayton copula. The ability to capture/model the lower tail dependence of the SUN Tobit model where some data are censored (generally, left-censored at zero) is an useful feature of the Clayton copula. We propose a modified version of the (classical) Inference Function for Margins (IFS) method by Joe and XP [H. Joe and J.J. XP, The estimation method of inference functions for margins for multivariate models, Tech. Rep. 166, Department of Statistics, University of British Columbia, 1996], which we refer to as Modified Inference Function for Margins (MIFF) method, to obtain the (point) estimates of the marginal and Clayton copula parameters. More specifically, we employ the (frequenting) data augmentation technique at the second stage of the IFS method (the first stage of the MIFF method is equivalent to the first stage of the IFS method) to generate the censored observations and then estimate the Clayton copula parameter. This process (data augmentation and copula parameter estimation) is repeated until convergence. Such modification at the second stage of the usual estimation method is justified in order to obtain continuous marginal distributions, which ensures the uniqueness of the resulting Clayton copula, as stated by Solar's [A. Solar, Fonctions de répartition à n dimensions et leurs marges, Publ. de l'Institut de Statistique de l'Université de Paris 8 (1959), pp. 229–231] theorem; and also to provide an unbiased estimate of the association parameter (the IFS method provides a biased estimate of the Clayton copula parameter in the presence of censored observations in both margins). Since the usual asymptotic approach, that is the computation of the asymptotic covariance matrix of the parameter estimates, is troublesome in this case, we also propose the use of resampling procedures (bootstrap methods, such as standard normal and percentile, by Efron and Tibshirani [B. Efron and R.J. Tibshirani, An Introduction to the Bootstrap, Chapman & Hall, New York, 1993] to obtain confidence intervals for the model parameters.     

Reviews and Notices

Abstract

Statistics in Hungary: Geschichte und Organization der amtlichen Statistik in Ungarn. By Gustav Bokor. Pp. v, 291. Budapesth. Pester Buchdruckerei Active Gesellschaft, 1896.

Bertillon's Treatise: Cours élementaire de statistique conforme au programme arrêtépar le Gonseil Supérieur de Statistique pour l'examen d'admission dans diverses administrations publiques. By Dr. Jacques Bertillon, Chef des Travaux Statistiques of Paris, France. Three parts. Pp. 599. Paris, 1895.

Muhleman's Monetary System: Monetary Systems of the World. By Maurice L. Muhleman. Revised edition. New York, 1897. Pp. 239.

Notes: Financial Reform Almanac for 1897. London. Pp. 316.

Notes: Eighth Annual Report by the Chief Labor Correspondent on Trade Unions, 1894–95. London, 1896. Pp. xxix, 515.

Notes: Third Annual Report of the Labour Department of the Board of Trade, 1895–96, with Abstract of Labour Statistics. London, 1896. Pp. xxviii, 200.

Report of the Secretary of the American Statistical Association. Reviewed by Davis R. Dewey.     

Estimation for seasonal fractional ARIMA with stable innovations via the empirical characteristic function method

Seasonal fractional ARIMA (ARFISMA) model with infinite variance innovations is used in the analysis of seasonal long-memory time series with large fluctuations (heavy-tailed distributions). Two methods, which are the empirical characteristic function (ECF) procedure developed by Knight and Yu [The empirical characteristic function in time series estimation. Econometric Theory. 2002;18:691–721] and the Two-Step method (TSM) are proposed to estimate the parameters of stable ARFISMA model. The ECF method estimates simultaneously all the parameters, while the TSM considers in the first step the Markov Chains Monte Carlo–Whittle approach introduced by Ndongo et al. [Estimation of long-memory parameters for seasonal fractional ARIMA with stable innovations. Stat Methodol. 2010;7:141–151], combined with the maximum likelihood estimation method developed by Alvarez and Olivares [Méthodes d'estimation pour des lois stables avec des applications en finance. Journal de la Société Française de Statistique. 2005;1(4):23–54] in the second step. Monte Carlo simulations are also used to evaluate the finite sample performance of these estimation techniques.     

On a minimum distance estimate of the period in functional autoregressive processes

We consider a continuous time random process with functional autoregressive representation. We state statistical results on a mean functional estimator determining a minimum distance estimator of the period giving consistency and a limit law stated in Mourid and Benyelles [13 Mourid, T. and Benyelles, W. 2002. Estimation de la p ériode de la représentation autorégressive d'un processus à temps continu. : 89–101. Annales de l'I.S.U.P, Volume XXXXVI-Fascicule 1–2 [Google Scholar]]. Then we discuss their performance on numerical simulations and on real data analyzing the cycle of a climatic phenomena.     

Mixture Representation of the Maximum Entropy Density Through Archimedean Copulas

In this article, we obtain a mixture representation of the maximum entropy density introduced by Rodrigues (2004 Rodrigues , J. ( 2004 ). An entropy model for dependent variables . Commun. Statist. Theor. Meth. 4 ( 33 ): 979 – 990 . [Google Scholar]) via Laplace approximation. This representation suggests, as in Sklar (1959 Sklar , A. ( 1959 ). Fonctions de répartition à ndimensions et marges . Publications de l 'Université de Paris 8 : 229 – 231 . [Google Scholar]), a dependence structure through Archimedean copulas independently of the specified marginal distributions. This result can be used as a natural Bayesian and non Bayesian procedure to estimate the dependence function and the marginal, separately.     

On Large Deviations of Sums of Independent Random Variables

Extensions of some limit theorems are proved for tail probabilities of sums of independent identically distributed random variables satisfying the one-sided or two-sided Cramér's condition. The large deviation x-region under consideration is broader than in the classical Cramér's theorem, and the estimate of the remainder is uniform with respect to x. The corresponding asymptotic expansion with arbitrarily many summands is also obtained.     

Reviews and Notices

Abstract

Suicide in the European Armies. Reviewed by Fred P. Emery.

Movement of Population in France For 1890. Reviewed by G. N. Calkins.

Statistical Year-Books and Annuals: Die Bevolkerung der Erde. VIII By H. Wagner and A. Supan. Justus Perthus. Gotha, 1891. Pp. x, 271.

Statistical Year-Books and Annuals: Statistical Abstract of the United States, 1890. Published by the Bureau of Statistics, Department of the Treasury. Washington, 1891. Pp. 346.

Statistical Year-Books and Annuals: The Statistical Year-Book of Canada for 1890. Published by the Department of Agriculture. Compiled by Sydney C. D. Roper. Ottawa, 1891. Pp. 628.

Statistical Year-Books and Annuals: Statistical Tables for British India. 15th issue. Compiled in the Statistical Branch of the Finance and Commerce Department. Cal-cutta, 1891. Pp. 176.

Statistical Year-Books and Annuals: Oesterreichisches Statistisches Handbuch. Ninth Year, 1890. Published by the K. K. Statistischen Central-Commission. Vienna, 1891. Pp.282.

Statistical Year-Books and Annuals: Annuaire Statistique de la Belgique. 21st issue, 1890. Brussels, 1890. Pp. 357. Published by the Ministére de l'Intérieur.

Statistical Year-Books and Annuals: Statistisk Arsbok för Finland. Issued by the Statistiska Central-byran. 12th issue, 1891. Helsingfors. Pp. 166.

Statistical Year-Books and Annuals: Statistish: Aarbog for Kongeriget Norge. 10th issue, 1890. Christiana, 1890. Pp. 161.

Statistical Year-Books and Annuals: Annuaire Statistique de la Suisse. Published by Le Bureau de Statistique du Départment Fédéral de l'Intérieur. First year, 1891. Berne. Pp. xiv, 265; two maps.

Statistical Year-Books and Annuals: Résumé Statistique de l' Empire du Japan. No. V. Tokio, 1891. Pp. 159; map and chart.

Statistical Year-Books and Annuals: Annual Statistical Report of the American Iron and Steel Association for 1890. By James M. Swank. Secretary. Philadelphia, 1891. Pp.80.

Statistical Year-Books and Annuals: American Electrical Directory for 1890–91. Published by the Star Iron Tower Co. Fort Wayne, Ind. Pp. 593.

Statistical Year-Books and Annuals: The Financial Reform Almanac, 1891. London. Pp, 200.

Statistical Year-Books and Annuals: Low's Hand-Book to the Charities of London, 55th year, 1891. London. Sampson Low, Marston & Co. Pp. 296.

Statistics Of German Cities: Statistisches Jahrbuch deutscher Städte. By Dr. M. Neefe, Direktor des Statistischen Amtes der Stadt Breslau. First issue. Breslau, 1890. Reviewed by Roland P. Falkner.

French Statistical Album. Reviewed by William Z. Ripley.

Preliminary Report of the Census of the United Kingdom.     

Reviews and Notices

Abstract

Hoffman's Statistical Study of the Negro: Race Traits and Tendencies of the American Negro, by Frederick L. Hoffman, Publications of the American Economic Association, Vol. XI, Nos. 1, 2, and 3, August, 1896. Reviewed by Miles Menander Dawson.

Infant Mortality in Prussia: Kindersterblichkeit sozialer Bevölkerungsgruppen insbesondere im preussischen Staate und seiner Provinzen, In Beiträge zur, Geschichte der Bevölkerung in Deutschland seit dem Anfange dieses Jahrhunderts. Reviewed by By Dr. Seutemann. Tübingen, 1894. Reviewed by Gary N. Calkins.

Inebriety and Suicide: Trunksucht und Selbstmord und deren gegenseitige Beziehungennebst einem statistischen Anhang und 2 Karten. By Dr. F. Prinzing. Leipzig, 1895. Reviewed by A. T. Hosmer.

Notes on Vital Statistics: Statistics of the Colony of New Zealand for the Year 1894, with Abstracts of the Agricultural Statistics of February, 1895, and Statistics of Local Governing Bodies for the Year Ended March 31, 1895. Compiled in the Regietrar-General's Office from Official Records. Wellington, 1895. Pp. xiv, 469. Reviewed by Cressy L. Wilbur.

Notes on Vital Statistics: Cape of Good Hope. Reports on the Public Health for the Year 1894, including the Report of the Acting Medical Officer of Health for the (Colony, together with Reports of District Surgeons, Medical Officers, Medical Inspectors, and Local Authorities. Cape Town, 1895. Pp. cxxxviii, 242.

Notes on Vital Statistics: Mariages, Naissances et Décès en Suisse de 1871 à 1890. Publiépar le Bureau de Statistique du Département Fédéral de l'Intériéur. Berne, 1895.

Notes on Vital Statistics: Annual Report of the Central Sanitary Bureau Attached to the Home Department of the Imperial Japanese Government, for the Twenty-fifth Year of Meiji (1892). Tōkyō, 1895.

Notes on Vital Statistics: Jahresbericht über die Verwaltung des Medicinalwesens die Kranken-Anstalten, und die öffentlichen Gesundheitsverhaltnisse der Stadt Frankfurt a. M. xxxviii. 1894. Frankfurt a. M., 1895.

Notes on Vital Statistics: Anuario Demogréfico de la Republica Oriental del Uruguay. Año 1894. Director, L. C. Bollo. Montevideo, 1895.

Notes on Vital Statistics: Annual Summary of Births, Deaths, and Causes of Death in London and other Large Towns, 1894. London, 1895. Pp, lxxxvi.

Middle-Class Expenditure: Some Statistics of Middle-Class Expenditure. Edward Grubb, M.A. The Economic Review, Vol. VI, No.3. Pp.358–370.

Sociological Statistics of New York City: The Federation of Churches and Christian Workers in New York City. First Sociological Canvass. Supervised and Tabulated by Rev. Walter Laidlaw, Secretary. Pp. 112. Reviewed by Harry D. Hunt.

Notes: Eighth Report on the Custody and Condition of the Public Records of Parishes, Towns, and Counties of Massachusetts. Robert T. Swan, Commissioner. Boston, 1896. Pp. 42.

Notes: Sixty-Sixth Annual Report of the Inspectors of the State Penitentiary for the Eastern District of Pennsylvania. Philadelphia, 1895. Pp.143.

Notes: Twenty-Third Annual Report of the State Charities Aid Association of New York. December 1, 1895. New York, 1895. Pp. 138.

Notes: Ninth Annual Report of the General Superintendent of Prisons in Massachusetts Concerning Prison Labor. December, 1895. Pp.63.

Notes: Report of the Attorney-General of Massachusett, for tne Year Ending January l5, 1896. Boston, 1896.

Notes: Third Annual Report of the Bureau of Agriculture, Labor, and Industry of Montana for the Year Ended November 30, 1896. Helena, 1896. Pp. 405.     

Reviews and Notices

Abstract

Employment of Women in England: Report by Miss Collet on the Statistics of Employment of Women and Girls. Labor Department, Board of Trade. London, 1894. Reviewed by M. K. Conynton.

Taxation in Paris: The Tax Paid by a Parisian Family. Report by L. Beaurin-Gressier, Journal de la Société de Statistique de Paris, October, 1895. Reviewed by Wm. Herbert King.

Taxation in Illinois: Eighth Biennial Report of the Bureau of Labor Statistics of Illinois. Subject: Taxation. By the Commission, George A. Schilling, Secretary. Springfield, III. 1895. Pp. 490. Reviewed by Miles Menander Dawson.

Canada Assurance: Canada Life Assurance Company. Mortality Experience, 1847 to 1893. Published by the Company, Hamilton, Ontario. Reviewed by Miles Menander Dawson.

Vital Statistics: Mouvement de la Population de la Suisse pendant l'Annee 1893. Berne, 1895.

Vital Statistics: Breslauer Statistik. Im Auftrage des Magistrats der königl. Haupt- und Residenzstadt Breslau. Herausgegeben vom statistischen Amt der Stadt Breslau. Bd. 16, Erstes Heft. Breslau, 1895.

Charity Statistics: Armenstatik. Compiled by H. Silbergleit, Superintendent of the Bureau of Statistics for the City of Magdeburg. Magdeburg, 1895. Pp.29. Reviewed by M. K. Conynton.

Thirteenth Biennial Report of Public Oharities of Illinois. Springfield, 1894. Pp. 127.

Criminal Statistics: Annual Report of the Department of Police and Excise, Brooklyn, N. Y., for 1894. Pp. 137.

Railways in United States: Seventh Annual Report of the Statistics of Railways of the United States for the Year Ending June 30, 1894. Prepared by the Statistician to the Interstate Commerce Commission. Washington, 1895. Pp. 102; diagrams 9.

Notes: Catechism for Social Observation; a Manual of Social Phenomena. By C. R. Henderson. Boston: D. C. Heath. 1894. Pp. 58.

Notes: Katalog der Bibliothek des Statistischen Amtes der Stadt Dresden. Second Edition. October 15, 1894. Dresden. Pp, 119.

Notes: Memoir of Henry Wheatland, M.D. By William P. Upham. Re-printed from the proceedings of the Massachusetts Historical Society. 1895. Pp.27.

Notes: The Rain and Snowfall of the Province of Ontario. By Hugh V. Payne. Meteorological Service. Dominion of Canada. Ontario. Pp. 16 and chart.

Notes: Seventh Report of the Custody and Condition of the Public Records of Parishes, Towns, and Counties. By Robert T. Swan, Commissioner. Public Document. Boston, 1895. Pp, 39.

Notes: Garland's Banks, Bankers, and Banking: A Financial Directory of Canada. Second edition. Ottawa, 1895. Pp.515.

Notes: Report of the Chief Labor Correspondent on the Strikes and Lockouts of 1893. Board of Trade, Labor Department, Great Britain. London, 1895.

Notes: Forty-First Annual Report of the City Comptroller of Philadelphia for 1894. Pp. 221.

Notes: Twenty-Fifth Annual Report of the Board of Directors of City Trusts, Philadelphia, for 1894. Pp. 191.

Notes: Renseigmements statistiques sur le mouvement dans les asiles publics d'aliénés de la Suisse et dans les principaux e'tablissements privés. No. 99. Pp.76. Berne, 1894.     

Tail asymptotic of Weibull-type risks

With motivation from Arendarczyk and De¸bicki [Asymptotics of supremum distribution of a Gaussian process over a Weibullian time. Bernoulli. 2011;17:194–210], in this paper we derive the tail asymptotics of the product of two dependent Weibull-type risks, which is of interest in various statistical and applied probability problems. Our results extend some recent findings of Schlueter and Fischer [The weak tail dependence coefficient of the elliptical generalized hyperbolic distribution. Extremes. 2012;15:159–174] and Bose et al. [Product of exponentials and spectral radius of random k circulants. Annales de l'Institut Henri Poincare Probabilites et Statistiques. 2012;48:424–443].     

Approximate exchangeability and de Finetti priors in 2022

This is a review paper, beginning with de Finetti's work on partial exchangeability, continuing with his approach to approximate exchangeability, and then his (surprising) approach to assigning informative priors in nonstandard situations. Recent progress on Markov chain Monte Carlo methods for drawing conclusions is supplemented by a review of work by Gerencsér and Ottolini on getting honest bounds for rates of convergence. The paper concludes with a speculative approach to combining classical asymptotics with Monte Carlo. This promises real speed-ups and makes a nice example of how theory and computation can interact.     

A bias-reduced estimator for the mean of a heavy-tailed distribution with an infinite second moment

We use bias-reduced estimators of high quantiles of heavy-tailed distributions, to introduce a new estimator for the mean in the case of infinite second moment. The asymptotic normality of the proposed estimator is established and checked in a simulation study, by four of the most popular goodness-of-fit tests. The accuracy of the resulting confidence intervals is evaluated as well. We also investigate the finite sample behavior and compare our estimator with some versions of Peng's estimator of the mean (namely those based on Hill, t-Hill and Huisman et al. extreme value index estimators). Moreover, we discuss the robustness of the tail index estimators used in this paper. Finally, our estimation procedure is applied to the well-known Danish fire insurance claims data set, to provide confidence bounds for the means of weekly and monthly maximum losses over a period of 10 years.     

Looking for max-semistability: A new test for the extreme value condition

To test the extreme value condition, Cramér-Von Mises type tests were recently proposed by Drees et al. (2006) and Dietrich et al. (2002). Hüsler and Li (2006) presented a simulation study on the behavior of these tests and verified that they are not robust for models in the domain of attraction of a max-semistable distribution function. In this work we develop a test statistic that distinguishes quite well distribution functions which belong to a max-stable domain of attraction from those in a max-semistable one. The limit law is deduced and the results from a numerical simulation study are presented.     

A note on scheffé's method of deriving confidence sets for directions and ratios of normals

Scheffé (1970) introduced a method for deriving confidence sets for directions and ratios of normals. The procedure requires use of an approximation and Scheffé provided evidence that the method performs well for cases in which the variances of the random deviates are known. This paper extends Scheffé's numerical integrations to the case of unknown variances. Our results indicate that Scheffé's method works well when variances are unknown     

A Generalized Time-Dependent Conditional Linear Model with Left-Truncated and Right-Censored Data

Consider the model φ(S(y | X)) = β(y) ^T X, where φ is a known link function, S(· | X) is the survival function of a response Y given a covariate X = (1, X, X ²,…, X ^p ), and β(y) is an unknown vector of time-dependent regression coefficients. The response Y is subject to left truncation and right censoring. We assume that given X, Y is independent of (C, T) where C and T are censoring and truncation variables with P(C ≥ T) = 1. In this article, with some modification of the assumptions in Lemmas 5 and 6 of Iglesias-Pérez and González-Manteiga (1999 Iglesias-Pérez , C. J. , González-Manteiga , W. G. ( 1999 ). Strong representation of a generalized product-limit estimator for truncated and censored data with some application . J. Nonparametric Statist. 10 : 213 – 244 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), we present an almost sure representation for the generalized product-limit estimator (GPL) of S(y | X). Based on the GPL and the approach of Teodorescu et al. (2010 Teodorescu , B. , Keilegom , I. V. , Cao , R. ( 2010 ). Generalized time-dependent conditional linear models under left truncation and right censoring . Ann. Instit. Statist. Math. 62 : 465 – 485 .[Crossref], [Web of Science ®] , [Google Scholar]), a least squares estimator of β(y) is obtained and a bootstrap procedure is proposed to choose the optimum bandwidth.     

Reviews and Notices

Abstract

Vital Statistics: Medizinal-statistiche Mittheilungen aus dem kaiserlichen Gesund-heitsamte. Berlin, 1897. Reviewed by H. J. Gerling.

Vital Statistics: Report Relating to the Registration of Births, Marriages, and Deaths in the Province of Ontario for 1896. Toronto, 1897, pp. 36, ccxviii.

Vital Statistics: Twenty-eighth Annual Report Relating to the Registry and Return of Births, Marriages, and Deaths in Michigan for the Year 1894. Lansing, 1897. Pp. 338, 33.

Vital Statistics: Forty-third Report Relating to the Registry and Return of Births, Marriages and Deaths, and of Divorce in Rhode Island for 1895. Prepared by Gardner P. Swarts, M.D., Providence, R. I. 1897. Pp. vi, 291.

Vital Statistics: Sixth Biennial Report of the North Carolina Board of Health, 1895–96. Winston, 1897. Pp. 212.

Vital Statistics: This subject is also dealt with in the Tulane University publications, No.2, on the Social and Physical Conditions of Negroes in Cities. Tulane, 1897, pp. 72, 14.

Physical and Mental Condition of School Children in London: Report on the scientific study of the mental and physical condition of childhood. With particular reference to children of defective constitution; and with recommendation as to education and training. London: Published by the Committee, Parker Museum, Margaret Street, W., 1895. Pp. 117.

Physical and Mental Condition of School Children in Switzerland: Résultats du dénombrement des enfants faibles d'esprit en âge de fréquenter l'école, y compris ceux qui sont atteints d'infirmités physiques ou, qui sont négligés et moralement abandonnés, enquête qui a eu lieu en Suisse au mois de mars, 1897. Part I. Berne, 1897. Pp. xxx, 91.

German Income Tax Statistics: Die mittleren Klassen der Einkomminsteuer in einigen deutschen Grosstädten in der Jahren 1880–1895. By Dr. Wilhelm Böhmert. In Jahrbuch für Gesetzgebung, Verwaltung und Volkswirtschaft. Leipzig, 1896. Reviewed by H. D. Hunt.

Municipal Electric Lighting: Twelfth Annual Report of the Board of Gas and Electric Light Commissioners of the Commonwealth of Massachusetts, June, 1897. Boston, 1897. Pp. 182, clvi.

Notes: Statistical Report of the Colony of the Cape of Good Hope for the year 1896. Cape Town, May, 1897. Pp. xv, 359.

Notes: Report of the Results of a Census of the Colony of New Zealand, taken for the night of the 12th of July, 1896. Wellington, New Zealand, 1897. Pp, 163.

Notes: Mitteilungen des Bernischen statistischen Bureaus. Year 1897, No. 2. Berne, 1897. Pp. 73–193.

Notes: Fourth Annual Report of Changes in Wages and Hours of Labor in the United Kingdom for 1896. London, 1897. Pp. lxxxi, 273.

Notes: Synoptical Index of the Reports of the Statistician. United States Department of Agriculture, 1893–1894. By George F. Thompson. Washington, 1897. Pp. 258.

Notes: The Manual of American Water Works. 1897. Edited by M. N. Baker, Associate Editor of Engineering News. Engineering News Publishing Co., New York, 1897. Pp. 611, cxiv

Insanity in England.