Approximation spline de la prevision d'un processus fonctionnel autorégressif d'ordre 1

ABSTRACT We present a method to approximate and forecast, on an entire interval, a continuous-time process. For this purpose, we use the modelization of ARH(l) processes, defined by Bosq (1991). We deal with the practical problem of the discretization of the observed trajectories and approximate them by means of spline functions. We show by simulations that for well-chosen smoothing parameters, good prediction can be obtained in comparison with the “predictable” part of the process. Finally, we apply this model to forecast road traffic and compare it with a SARIMA model.     

LOCAL LINEAR FORECASTS USING CUBIC SMOOTHING SPLINES

This paper shows how cubic smoothing splines fitted to univariate time series data can be used to obtain local linear forecasts. The approach is based on a stochastic state‐space model which allows the use of likelihoods for estimating the smoothing parameter, and which enables easy construction of prediction intervals. The paper shows that the model is a special case of an ARIMA(0, 2, 2) model; it provides a simple upper bound for the smoothing parameter to ensure an invertible model; and it demonstrates that the spline model is not a special case of Holt's local linear trend method. The paper compares the spline forecasts with Holt's forecasts and those obtained from the full ARIMA(0, 2, 2) model, showing that the restricted parameter space does not impair forecast performance. The advantage of this approach over a full ARIMA(0, 2, 2) model is that it gives a smooth trend estimate as well as a linear forecast function.     

Heterogeneity,school-effects and the North/South achievement gap in Italian secondary education: evidence from a three-level mixed model

With the aim of assessing the extent of the differences in the context of Italian educational system, the paper applies multilevel modeling to a new administrative dataset, containing detailed information for more than 500,000 students at grade 6 in the year 2011/2012, provided by the Italian Institute for the Evaluation of Educational System. Data are grouped by classes, schools and geographical areas. Different models for each area are fitted, in order to properly address the heteroscedasticity of the phenomenon. The results show that it is possible to estimate statistically significant “school effects”, i.e., the positive/negative association of attending a specific school and the student’s test score, after a case-mix adjustment. Therefore, the paper’s most important message is that school effects are different in terms of magnitude and types in the three geographical macro areas (Northern, Central and Southern Italy) and are dependent on specific students’ and schools’ characteristics.     

Preface

The appearance of this issue will mark almost two years since its inception by the late Editor, Professor Don B. Owen. Professor Malay Ghosh suggested a special issue on Pitman's Measure of Closeness (PMC) to Professor Owen in autumn of 1989. After a thorough review process the issue was finalized in June 1991. It is with remorse that we publish this special issue in memory of Professor Owen.

The completion of the issue coincided with a special conference, “Pitman's Measure of Cfoseness: Celebrating a Decade of Renaissance,” held on June 15, 1991 at the University of Texas at San Antonio (UTSA). The papers in this special issue, except those of Professor Kubokawa and Drs. Bertuzzi and Gandolfi, were presented and discussed. The conference participants included C.R. Rao (Pennsylvania State University), Colin Blyth (Queen's University), and H.T. David (Iowa State University). Further, P.K. Sen (University of North Carolina) and Malay Ghosh (University of Florida) gave keynote addresses that respectively set the themes for the morning and afternoon sessions.

The conference banquet held in the Regent's Room at the University of Texas at San Antonio, featured stimulating addresses by C.R. Rao and Colin Blyth on some of the major controversies of PMC such as intransitiveness and Berkson's conjecture. We are grateful to the University of Texas at San Antonio for making this conference a reality. In particular, we thank Professor Shair Ahmad, Director of the Division of Mathematics, Computer Science, and Statistics at UTSA for funding travel expenses not only for the invited speakers but also for many of the younger researchers. We also acknowledge University President Samuel Kirkpatrick who made the KIVA room available for the technical sessions and the Regent's Room for the Banquet. We also acknowledge the financial support of Bell Helicopter Textron, Inc. as a cosponsor of the conference.     

Bivariate multilevel models for the analysis of mathematics and reading pupils' achievements

The purpose of this paper is to identify a relationship between pupils' mathematics and reading test scores and the characteristics of students themselves, stratifying for classes, schools and geographical areas. The data set of interest contains detailed information about more than 500,000 students at the first year of junior secondary school in the year 2012/2013, provided by the Italian Institute for the Evaluation of Educational System. The innovation of this work is in the use of multivariate multilevel models, in which the outcome is bivariate: reading and mathematics achievement. Using the bivariate outcome enables researchers to analyze the correlations between achievement levels in the two fields and to predict statistically significant school and class effects after adjusting for pupil's characteristics. The statistical model employed here explicates account for the potential covariance between the two topics, and at the same time it allows the school effect to vary among them. The results show that while for most cases the direction of school's effect is coherent for reading and mathematics (i.e. positive/negative), there are cases where internal school factors lead to different performances in the two fields.     

Testing the adequacy of a linear model VIA critical smoothing

An important problem for fitting local linear regression is the choice of the smoothing parameter. As the smoothing parameter becomes large, the estimator tends to a straight line, which is the least squares fit in the ordinary linear regression setting. This property may be used to assess the adequacy of a simple linear model. Motivated by Silverman's (1981) work in kernel density estimation, a suitable test statistic is the critical smoothing parameter where the estimate changes from nonlinear to linear, while linearity or non- linearity requires a more precise judgment. We define the critical smoothing parameter through the approximate F-tests by Hastie and Tibshirani (1990). To assess the significance, the “wild bootstrap” procedure is used to replicate the data and the proportion of bootstrap samples which give a nonlinear estimate when using the critical bandwidth is obtained as the p-value. Simulation results show that the critical smoothing test is useful in detecting a wide range of alternatives.     

A Survey of the Teaching of Statistics in M.B.A. Programs

A survey of business schools was conducted to obtain information about the current state of the teaching of business statistics to students enrolled in M.B.A. degree programs. The survey was undertaken for and presented at a June 1986 conference on “Making Statistics More Effective in Schools of Business,” held at the University of Chicago's Graduate School of Business. Information was elicited concerning both the required statistics sequence and elective statistics courses for M.B.A. students, as well as computer usage in these courses. This article summarizes the information obtained from the survey.     

Pena's statistic for the Liu regression

In fitting regression model, one or more observations may have substantial effects on estimators. These unusual observations are precisely detected by a new diagnostic measure, Pena's statistic. In this article, we introduce a type of Pena's statistic for each point in Liu regression. Using the forecast change property, we simplify the Pena's statistic in a numerical sense. It is found that the simplified Pena's statistic behaves quite well as far as detection of influential observations is concerned. We express Pena's statistic in terms of the Liu leverages and residuals. The normality of this statistic is also discussed and it is demonstrated that it can identify a subset of high Liu leverage outliers. For numerical evaluation, simulated studies are given and a real data set has been analysed for illustration.     

Dynamic financial distress prediction based on Kalman filtering

In models for predicting financial distress, ranging from traditional statistical models to artificial intelligence models, scholars have primarily paid attention to improving predictive accuracy as well as the progressivism and intellectualization of the prognostic methods. However, the extant models use static or short-term data rather than time-series data to draw inferences on future financial distress. If financial distress occurs at the end of a progressive process, then omitting time series of historical financial ratios from the analysis ignores the cumulative effect of previous financial ratios on the current consequences. This study incorporated the cumulative characteristics of financial distress by using the characteristics of a state space model that is able to perform long-term forecasts to dynamically predict an enterprise's financial distress. Kalman filtering is used to estimate the model parameters. Thus, the model constructed in this paper is a dynamic financial prediction model that has the benefit of forecasting over the long term. Additionally, current data are used to forecast the future annual financial position and to judge whether the establishment will be in financial distress.     

On Galton's Change From “Reversion” to “Regression”

Galton's first work on regression probably led him to think of it as a unidirectional, genetic process, which he called “reversion.” A subsequent experiment on family heights made him realize that the phenomenon was symmetric and nongenetic. Galton then abandoned “reversion” in favor of “regression.” Final confirmation was provided through Dickson's mathematical analysis and Galton's examination of height data on brothers.     

The empirical Bayes estimators of the parameter of the Poisson distribution with a conjugate gamma prior under Stein's loss function

For the hierarchical Poisson and gamma model, we calculate the Bayes posterior estimator of the parameter of the Poisson distribution under Stein's loss function which penalizes gross overestimation and gross underestimation equally and the corresponding Posterior Expected Stein's Loss (PESL). We also obtain the Bayes posterior estimator of the parameter under the squared error loss and the corresponding PESL. Moreover, we obtain the empirical Bayes estimators of the parameter of the Poisson distribution with a conjugate gamma prior by two methods. In numerical simulations, we have illustrated: The two inequalities of the Bayes posterior estimators and the PESLs; the moment estimators and the Maximum Likelihood Estimators (MLEs) are consistent estimators of the hyperparameters; the goodness-of-fit of the model to the simulated data. The numerical results indicate that the MLEs are better than the moment estimators when estimating the hyperparameters. Finally, we exploit the attendance data on 314 high school juniors from two urban high schools to illustrate our theoretical studies.     

中国短期资本外流规模再估算及其影响因素分析

通过比较资本外流的三种核算口径，本文将间接法与权益差额调整法相结合，对我国1982-2016年资本外流的规模进行估计。结果显示，2008年全球金融危机以来，我国资本外流规模逐年增加且近年呈增速递增趋势。通过构建非限制性VAR模型，本文进一步对导致资本外流的结构性与周期性“推动”及“拉动”因素进行分析，经验结果显示，2008年全球金融危机爆发至2013年美联储货币周期转向以前，导致我国资本外流的主要因素为人民币贬值预期与我国经济周期性调整等国内“推动”因素。2014年以来，我国资本外流进一步加剧主要受美国经济复苏步伐加快以及我国房地产市场调整等国内外“拉动”与“推动”因素共同作用。其中，外部“拉动”因素是主要诱因。在资本加速流出背景下，我国金融开放步伐应渐进审慎。     

On robustness of the Shiryaev–Roberts change-point detection procedure under parameter misspecification in the post-change distribution

The gist of the quickest change-point detection problem is to detect the presence of a change in the statistical behavior of a series of sequentially made observations, and do so in an optimal detection-speed-versus-“false-positive”-risk manner. When optimality is understood either in the generalized Bayesian sense or as defined in Shiryaev's multi-cyclic setup, the so-called Shiryaev–Roberts (SR) detection procedure is known to be the “best one can do”, provided, however, that the observations’ pre- and post-change distributions are both fully specified. We consider a more realistic setup, viz. one where the post-change distribution is assumed known only up to a parameter, so that the latter may be misspecified. The question of interest is the sensitivity (or robustness) of the otherwise “best” SR procedure with respect to a possible misspecification of the post-change distribution parameter. To answer this question, we provide a case study where, in a specific Gaussian scenario, we allow the SR procedure to be “out of tune” in the way of the post-change distribution parameter, and numerically assess the effect of the “mistuning” on Shiryaev's (multi-cyclic) Stationary Average Detection Delay delivered by the SR procedure. The comprehensive quantitative robustness characterization of the SR procedure obtained in the study can be used to develop the respective theory as well as to provide a rational for practical design of the SR procedure. The overall qualitative conclusion of the study is an expected one: the SR procedure is less (more) robust for less (more) contrast changes and for lower (higher) levels of the false alarm risk.     

Statistical monitoring of a web server for error rates: a bivariate time-series copula-based modeling approach

The monitoring of web servers through statistical frameworks is of utmost important in order to verify possible suspicious anomalies in network traffic or misuse actions that compromise integrity, confidentiality, and availability of information. In this paper, by considering the Plackett copula function, we propose a bivariate beta-autoregressive moving average time-series model for proportion data over time, which is the case for variables present in web server monitoring such as error rates. To illustrate the proposed methodology, we monitor a Brazilian web server's rate of connection synchronization and rejection errors in a web system, with error logging rate in the past 10?min. In essence, the entire methodology may be generalized to any number of time-series of error rates.     

Electronic Resources Workflow: Design,Analysis and Technologies for an Overdue Solution

During the summer of 2013, a joint team involving Duke University Libraries and IBM spent three months configuring IBM Business Process Manager to improve electronic resources workflows in the Libraries’ Technical Services department. The resulting workflow showcases the application's ability to transform the management of online databases. This article will provide an overview of the “before” and “after” database workflow, with a demo of the new system and its integration points with other tools.     

Statistical learning theory for fitting multimodal distribution to rainfall data: an application

The promising methodology of the “Statistical Learning Theory” for the estimation of multimodal distribution is thoroughly studied. The “tail” is estimated through Hill's, UH and moment methods. The threshold value is determined by nonparametric bootstrap and the minimum mean square error criterion. Further, the “body” is estimated by the nonparametric structural risk minimization method of the empirical distribution function under the regression set-up. As an illustration, rainfall data for the meteorological subdivision of Orissa, India during the period 1871–2006 are used. It is shown that Hill's method has performed the best for tail density. Finally, the combined estimated “body” and “tail” of the multimodal distribution is shown to capture the multimodality present in the data.     

Fitting of self-exciting threshold autoregressive moving average nonlinear time-series model through genetic algorithm and development of out-of-sample forecasts

Self-exciting threshold autoregressive moving average (SETARMA) nonlinear time-series model is considered here. Sufficient conditions for invertibility and stationarity are derived. Parameter estimation algorithm is developed by employing real-coded genetic algorithm stochastic optimization procedure. A significant feature of the work done is that optimal out-of-sample forecasts up to three-step ahead and their forecast error variances are derived analytically. Relevant computer programs are written in statistical analysis system (SAS) and C. As an illustration, annual mackerel catch time-series data are considered. Forecast performance of the fitted model for hold-out data is evaluated by using Naive and Monte Carlo approaches. It is found that optimal out-of-sample forecast values are quite close to actual values and estimated variances are quite close to theoretical values. Superiority of the SETARMA model over the SETAR model for equal predictive ability through Diebold–Mariano test is also established.     

Statistical analysis of firm interdependence using duration data—parametric approach

A pioneer first enters the market as the monopolist and later experiences the competition when a similar product is brought to the market by the competitor. In 2012, Wang and Xie suggested to decompose the pioneer survival to “monopoly” and “competition” durations and estimate the two survivals of the pioneer individually with the competitor's survival via regression analysis. In their article, several regression analyses were performed to study the effect of order entry to the pioneer and the later entrant in different market status. Using the same datasets from their study, our main interest is to investigate the interdependent relationship between two competitive firms and study whether the market pioneer and the later entrant can benefit from the competition. The major contribution of this article is that the interdependence between two competitive firms is explicitly expressed and three survival durations can be estimated in one model. The proposed method relates the survival times of two competitive firms to pioneer's monopoly time and some observable covariates via proportional hazard model, and incorporates frailty variables to capture the interdependence in the competition. This article demonstrates a new method that formulates the interdependence between competitive firms and shows data analyses in the industries of newspapers and high technology.     

The Training of Statisticians

Harold Hotelling, Chairman of the Committee on the Teaching of Statistics* * Members of the Committee: Harold Hotelling, (Chairman), Professor of Mathematical Statistics and Associate Director, Institute of Statistics, University of North Carolina; Dr. W. Edwards Deming, Division of Statistical Standards, Bureau of the Budget, Washington, D. C.; Dr. Walter Bartky, Dean of Arts and Sciences. University of Chicago; Dr. Milton Friedman Associate Professor of Statistics, School of Business, University of Chicago; Dr. Paul G. Hoel, Associate Professor of Mathematics, University of California, Los Angeles. of the Institute of Mathematical Statistics, has prepared this brief-summary of the Committee's report to the Board of Directors of IMS. Professor Hotelling will discuss the subject more fully in “Symposium on Probability and Statistics” to be published by the University of California Press. The Committee's report will be published in full in “The Annals of Mathematical Statistics”.

     

Bootstrapping stochastic regression models under homoskedasticity: wild bootstrap vs. pairs bootstrap

We investigate by simulation how the wild bootstrap and pairs bootstrap perform in t and F tests of regression parameters in the stochastic regression model, where explanatory variables are stochastic and not given and there exists no heteroskedasticity. The wild bootstrap procedure due to Davidson and Flachaire [The wild bootstrap, tamed at last, Working paper, IER#1000, Queen's University, 2001] with restricted residuals works best but its dominance is not strong compared to the result of Flachaire [Bootstrapping heteroskedastic regression models: wild bootstrap vs. pairs bootstrap, Comput. Statist. Data Anal. 49 (2005), pp. 361–376] in the fixed regression model where explanatory variables are fixed and there exists heteroskedasticity.