Estimation of nonlinear errors-in-variables models: an approximate solution

We propose an easy to derive and simple to compute approximate least squares or maximum likelihood estimator for nonlinear errors-in-variables models that does not require the knowledge of the conditional density of the latent variables given the observables. Specific examples and Monte Carlo studies demonstrate that the bias of this approximate estimator is small even when the magnitude of the variance of measurement errors to the variance of measured covariates is large. Cheng Hsiao and Qing Wang's work was supported in part by National Science Foundation grant SeS91-22481 and SBR94-09540. Liqun Wang gratefully acknowledges the financial support from Swiss National Science Foundation. We wish to thank Professor H. Schneeweiss and a referee for helpful comments and suggestions.     

Perturbation by multiplicative noise and the Simulation Extrapolation method

While most of the literature on measurement error focuses on additive measurement error, we consider in this paper the multiplicative case. We apply the Simulation Extrapolation method (SIMEX)—a procedure which was originally proposed by Cook and Stefanski (J. Am. Stat. Assoc. 89:1314–1328, 1994) in order to correct the bias due to additive measurement error—to the case where data are perturbed by multiplicative noise and present several approaches to account for multiplicative noise in the SIMEX procedure. Furthermore, we analyze how well these approaches reduce the bias caused by multiplicative perturbation. Using a binary probit model, we produce Monte Carlo evidence on how the reduction of data quality can be minimized. For helpful comments, we would like to thank Helmut Küchenhoff, Winfried Pohlmeier, and Gerd Ronning. Sandra Nolte gratefully acknowledges financial support by the DFG. Elena Biewen and Martin Rosemann gratefully acknowledge the financial support by the Federal Ministry of Education and Research (BMBF). The usual disclaimer applies.     

Fundamentals and asset price dynamics

The relation between fundamentals and asset returns is analyzed by means of Markov-switching regression models with time-varying transition probabilities. By referring to the Italian Stock Exchange over the 1973-2002 period, we find that (i) returns switch between a zero-expected return/low volatility state and a high expected return/high volatility state; (ii) states are persistent and hence state changes can be forecast to some extent; (iii) the probability of state changes can be explained in terms of changes in the fundamentals; (iv) fundamentals do not have a direct impact on the expected returns but they only affect the transition probability matrix. Overall, our results show that a non-linear relation between market price changes and market fundamentals can be caught within the framework of (Markov) switching regession models.A previous draft of the paper was presented at the XL Scientific Meeting of The Italian Statistical Society, Firenze, April 2000. We would like to thank Maurizio Vichi (the editor) and several anonymous referees for important suggestions. A special thank to Lorenzo Sevini for valuable research assistance. Partial financial support by Italian M.I.U.R. grants is gratefully acknowledged.     

Tabulating weighted sup-norm functionals used in change-point analysis

We introduce a number of weighted partial sum processes of which certain sup-norm functionals may be used, for example, to detect changes in the mean of independent observations. Their limiting distributions are derived mathematically, simulated and then tabulated. With this information, a detailed numerical investigation of the power of these functionals is carried out.* ^*Research mainly done while at Carleton University, partially supported by an NSERC Canada Grant of Miklós Csörg? at Carleton University, Ottawa. Also supported by the Austrian Science Foundation (FWF) under grant SFB#010 (‘Adaptive Information Systems and Modelling in Economics and Management Science’) while at Technische Universität Wien. ? ^?Research partially supported by an NSERC Canada Grant of Miklós Csörg? at Carleton University, Ottawa.      

Hedonic price indices for the Paris housing market

Summary: In this paper, we calculate a transaction–based price index for apartments in Paris (France). The heterogeneous character of real estate is taken into account using an hedonic model. The functional form is specified using a general Box–Cox function. The data basis covers 84 686 transactions of the housing market in 1990:01–1999:12, which is one of the largest samples ever used in comparable studies. Low correlations of the price index with stock and bond indices (first differences) indicate diversification benefits from the inclusion of real estate in a mixed asset portfolio.*This paper has been developed at the Research Program Real Estate Finance at Goethe-University of Frankfurt/Main (Germany). We gratefully acknowledge iii Internationales Immobilien Institut, IVG Holding AG and Stiftung Rheinische Hypothekenbank for their financial support. For further information, see www.real-estate-finance.de. We thank the participants of the 8th Conference of the European Real Estate Society (ERES), the International Conference of the American Real Estate and Urban Economics Association (AREUEA), the 10th Global Finance Conference 2003 and the anonymous referees for helpful comments, which improved the paper substantially.     

Preisindikatoren für Wohnimmobilien in Deutschland

Zusammenfassung: Vermögenspreise im Allgemeinen und Immobilienpreise im Besonderen gewannen in den zurückliegenden Jahren mehr und mehr an Bedeutung. Während sie in den späten 80er Jahren (nach dem Börsencrash im Herbst 1987) und im vergangenen Jahrzehnt vornehmlich unter dem Schlagwort asset-price inflation/deflation betrachtet wurden, stehen neuerdings die Tragfähigkeit und Bestandsfestigkeit der Finanzsysteme im Vordergrund. In den Ausführungen geht es vor allem um die Frage, warum, seit wann und aufgrund welcher Grunddaten die Deutsche Bundesbank auf diesem Gebiet der Preisstatistik tätig geworden ist. Dabei wird nicht nur auf das hohe Maß an Unsicherheit in den vorgelegten Angaben hingewiesen, sondern auch der Second–Best–Charakter der Berechnungen hervorgehoben.

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Summary: Asset prices in general and property prices in particular have gained increasing importance in recent years. Whereas in the late 1980s (after the stock market crash in autumn 1987) and in the last decade these prices mainly came under the heading of asset-price inflation/deflation, the focus has recently shifted to sustainable and viable financial systems. The notes primarily explain why the Bundesbank is involved in this area of price statistics, when this involvement began and what underlying data the Bundesbank uses. At the same time, they not only indicate the large degree of uncertainty in the reported data but also highlight the second-best nature of the calculations.

*Vortrag anlässlich der 9. Konferenz Messen der Teuerung am 17./18. Juni 2004 in Marburg. Der Verfasser gibt seine persönliche Auffassung wieder, die nicht unbedingt mit derjenigen der Deutschen Bundesbank übereinstimmen muss.     

影响中国农村劳动力省际迁移动因的实证分析——基于新劳动力迁移理论

利用2005年中国1%人口抽样调查数据中的农村劳动力省际迁移数据,结合新劳动力迁移经济理论,对logit模型进行了扩展,加入了农村信贷市场、农业生产性固定资产、农业受灾比例和老年抚养比,考察它们对省际迁移的影响。结果显示：农村信贷市场越不完善、农业生产性固定资产原值越高、农业受灾比例越大和老年人抚养比越高的地区,农村劳动力外迁的比例也就越大。因此,在中国农村金融和保险市场不完善的前提下,农村劳动力迁移是农民分散农业风险和稳定家庭收入的一种有效方式。     

Tail index estimation in small smaples Simulation results for independent and ARCH-type financial return models

Estimation of the tail index of stationary, fat-tailed return distributions is non-trivial since the well-known Hill estimator is optimal only under iid draws from an exact Pareto model. We provide a small sample simulation study of recently suggested adaptive estimators under ARCH-type dependence. The Hill estimator’s performance is found to be dominated by a ratio estimator. Dependence increases estimation error which can remain substantial even in larger data sets. As small sample bias is related to the magnitude of the tail index, recent standard applications may have overestimated (underestimated) the risk of assets with low (high) degrees of fat-tailedness. This paper is a shortened version of the Berkeley Research Program in Finance Working Paper RPF-295. Thanks are to the Center for Mathematical Sciences at Munich University of Technology for generously providing access to computer facilities and to participants at the IAFE 2001 Budapest, OR 2002 Klagenfurt, EIR 2002 London, DGF 2002 Cologne, FBI 2002 Karlsruhe conferences and the 2001 Wallis Workshop for helpful comments. Two anonymous referees provided helpful suggestions in streamlining the material. Niklas Wagner acknowledges a Maple program by Klaus Kiefersbeck and financial support by Deutsche Forschungsgemeinschaft (DFG).     

A Note on Estimation of Parameters for Branching Processes with Immigration

It is proved that under certain conditions the conditional least-squares estimator of the offspring mean for a sequence of nearly critical Ji?ina processes with immigration is consistent but not asymptotically normal and the conditional least-squares estimator of the immigration mean is not consistent. These results differ from the existing results in the case where the initial values are zero (see Ispány et al., 2005 Ispány , M. , Pap , G. , Zuijlen , M. V. ( 2005 ). Fluctuation limit of branching processes with immigration and estimation of the means . Adv. Appl. Probab. 37 : 523 – 538 . [Google Scholar]).     

Using quantile regression for duration analysis

Summary Quantile regression methods are emerging as a popular technique in econometrics and biometrics for exploring the distribution of duration data. This paper discusses quantile regression for duration analysis allowing for a flexible specification of the functional relationship and of the error distribution. Censored quantile regression addresses the issue of right censoring of the response variable which is common in duration analysis. We compare quantile regression to standard duration models. Quantile regression does not impose a proportional effect of the covariates on the hazard over the duration time. However, the method cannot take account of time-varying covariates and it has not been extended so far to allow for unobserved heterogeneity and competing risks. We also discuss how hazard rates can be estimated using quantile regression methods. This paper benefitted from the helpful comments by an anonymous referee. Due to space constraints, we had to omit the details of the empirical application. These can be found in the long version of this paper, Fitzenberger and Wilke (2005). We gratefully acknowledge financial support by the German Research Foundation (DFG) through the research project ‘Microeconometric modelling of unemployment durations under consideration of the macroeconomic situation’. Thanks are due to Xuan Zhang for excellent research assistance. All errors are our sole responsibility.     

A general algorithm fob,univariate and multivariate goodness of pit tests based on graphical representation

This paper presents a general algorithm tor assessing the distributional assumptions. Empirical distributions of the corresponding test statistics are obtained and examples are given to illustrate various applications of the proposed test. By using the squared radii and angles, it is shown that the problem of assessing multivariate normality can be reduced to that of testing for a univariate distribution. A limited comparison is made to investigate the power of the proposed test. This work was supported in part by the National Science Foundation under Grant NO.G88135. Support from the Computer Applications ami Software Engineering (CASE) Center of Syracuse University is also gratefully acknowledged     

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”.

     

Weighted log-normal kernel density estimation

ABSTRACT

The log-normal (LN) kernel estimator of a density with support [0, ∞) was discussed by Jin and Kawczak (2003 Jin, X., Kawczak, J. (2003). Birnbaum–Saunders and lognormal kernel estimators for modelling durations in high frequency financial data. Ann. Econ. Finance 4:103–124. [Google Scholar]). The contribution of this paper is to suggest a new class of LN kernel estimators using the idea of weighted distribution. The asymptotic properties of the new class of estimators are studied. Also, numerical studies based on both simulated and real data set are presented.     

Adaptive importance sampling in general mixture classes

In this paper, we propose an adaptive algorithm that iteratively updates both the weights and component parameters of a mixture importance sampling density so as to optimise the performance of importance sampling, as measured by an entropy criterion. The method, called M-PMC, is shown to be applicable to a wide class of importance sampling densities, which includes in particular mixtures of multivariate Student t distributions. The performance of the proposed scheme is studied on both artificial and real examples, highlighting in particular the benefit of a novel Rao-Blackwellisation device which can be easily incorporated in the updating scheme. This work has been supported by the Agence Nationale de la Recherche (ANR) through the 2006–2008 project ’ . Both last authors are grateful to the participants to the BIRS meeting on “Bioinformatics, Genetics and Stochastic Computation: Bridging the Gap”, Banff, for their comments on an earlier version of this paper. The last author also acknowledges an helpful discussion with Geoff McLachlan. The authors wish to thank both referees for their encouraging comments.     

The German Administrative Record Census – An object identification problem

Summary: The next German census will be an Administrative Record Census. Data from several administrative registers about persons will be merged. Object identification has to be applied, since no unique identification number exists in the registers. We present a two–step procedure. We briefly discuss questions like correctness and completeness of the Administrative Record Census. Then we focus on the object identification problem, that can be perceived as a special classification problem. Pairs of records are to be classified as matched or not matched. To achieve computational efficiency a preselection technique of pairs is applied. Our approach is illustrated with a database containing a large set of consumer addresses.*This work was partially supported by the Berlin–Brandenburg Graduate School in Distributed Information Systems (DFG grant no. GRK 316). The authors thank Michael Fürnrohr for previewing the paper. We would like to thank also for the helpful comments of an anonymous reviewer.     

Erste Ergebnisse faktischer Anonymisierung wirtschaftsstatistischer Einzeldaten

Summary: This paper presents first results of the project Factual anonymization of business microdata. The project aims at creating and providing scientific–use files of business data. For this, appropriate anonymization strategies and methods are created. The anonymization procedures are judged by whether they can guarantee the factual anonymity of company and operating data without limiting their potential value for statistical analysis. As an example the survey of German cost structure in the processing industry is considered. Here, both the impact of different anonymization methods on the potential use of the data as well as their effect on the re–identification risk is examined.

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Zusammenfassung: Mit diesem Beitrag werden erste Ergebnisse des Projektes Faktische Anonymisierung wirtschaftsstatistischer Einzeldaten vorgestellt. Ziel des Projektes ist es, die Grundlagen für die Erstellung von Scientific–use–files im Bereich der Unternehmens– und Betriebsdaten zu legen. Hierzu werden entsprechende Anonymisierungsverfahren und –strategien entwickelt. Die Anonymisierungsverfahren müssen danach beurteilt werden, ob sie die faktische Anonymität von Unternehmens– und Betriebsdaten sicherstellen können, ohne das Analysepotenzial über Gebühr einzuschränken. Am Beispiel der Kostenstrukturerhebung im Verarbeitenden Gewerbe werden erste Ergebnisse vorgestellt. Dabei wird sowohl untersucht, wie sich verschiedene Anonymisierungsmaßnahmen auf das Analysepotenzial der Daten auswirken, als auch welche Effekte sie auf das Re–Identifikationsrisiko haben.

     

VIX指数对股票市场间联动性影响的实证研究

近期金融危机频繁发生,国际金融市场之间的动态联动性成为一个重要的研究课题。以往学者大都直接研究金融市场间的相关性,而忽略了外生金融变量对金融市场间相关性的影响。本文将对上述问题进行研究,借鉴Silvennoinen和Terasvirta(2015) STCC模型的思想,假定Copula参数受外生变量的影响,建立时变动态Copula模型——ST-VCopula模型,并基于该模型探究市场波动率（VIX指数）对股票市场之间相关性的影响,进而对几个国家的股票指数数据进行了实证分析。实证结果表明VIX指数对股票市场间联动性产生了显著的影响。VIX指数的获取简单便捷且更为直观,为市场间动态联动性的研究提供了另一种途径,可以为投资者在进行分散投资等金融活动时提供一定的指导和建议。     

Long memory versus structural breaks: An overview

We discuss the increasing literature on misspecifying structural breaks or more general trends as long-range dependence. We consider tests on structural breaks in the long-memory regression model as well as the behaviour of estimators of the memory parameter when structural breaks or trends are in the data but long memory is not. Methods for distinguishing both of these phenomena are proposed. The financial support of Volkswagenstiftung is gratefully acknowledged.     

Foundational issues concerning the analysis of censored data

The common approach to analyzing censored data utilizes competing risk models; a class of distribution is first chosen and then the sufficient statistics are identified! An operational Bayesian approach (Barlow 1993) for analyzing censored data would require a somewhat different methodology. In this approach, we first determine potentially observable parameters of interest. We then determine the data summaries (sufficient statistics) for these parameters. Tsai (1994) suggests that the observed sample frequency is sufficient for predicting the population frequency. Invariant probability measures (likelihoods), conditional on the parameters of interest, are then derived based on the principle of sufficiency and the principle of insufficient reason.Research partially supported by the Army Research Office (DAAL03-91-G-0046) grant to the University of California at Berkeley.     

Data depth and correlation

Summary: We describe depth–based graphical displays that show the interdependence of multivariate distributions. The plots involve one–dimensional curves or bivariate scatterplots, so they are easier to interpret than correlation matrices. The correlation curve, modelled on the scale curve of Liu et al. (1999), compares the volume of the observed central regions with the volume under independence. The correlation DD–plot is the scatterplot of depth values under a reference distribution against depth values under independence. The area of the plot gives a measure of distance from independence. Correlation curve and DD-plot require an independence model as a baseline: Besides classical parametric specifications, a nonparametric estimator, derived from the randomization principle, is used. Combining data depth and the notion of quadrant dependence, quadrant correlation trajectories are obtained which allow simultaneous representation of subsets of variables. The properties of the plots for the multivariate normal distribution are investigated. Some real data examples are illustrated. *This work was completed with the support of Ca Foscari University.