Competing risks simulation with the survsim R package

The goal of this work is to describe how the last version available of the survsim R package can be used to simulate a cohort in a competing risks context by means of a cause-specific hazards model following the ideas introduced by Beyersmann in 2009, and also allowing for individual heterogeneity through a random effect. An example of its application based on a real cohort will be discussed.     

Inference for a simultaneous linear partially explosive model with polynomial regression components of different degrees

This paper is concerned with the estimation of the coefficients of simultaneous partially explosive model with polynomial regression components of different degrees in its equations. Since the least squares method breaks down in this case, a three stage estimation procedure is suggested for obtaining CAN estimates of the coefficients.     

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.     

Identification of long memory in GARCH models

Abstract: This work extends the analysis of Baillie, Bollerslev and Mikkelsen (1996) and Bollerslev and Mikkelsen (1996) on the estimation and identification problems of the Fractionally Integrated Generalized Autoregressive Conditional Heteroskedastik (FIGARCH) model. We assess the power of different information criteria and tests in identifying the presence of long memory in the conditional variances. The analysis is performed with a Montecarlo simulation study. In detail, the focus on the Akaike, Hannan-Quinn, Shibata and Schwarz information criteria and on the Jarque-Bera test for normality, Box-Pierce test for residual correlation and Engle test for ARCH effects. This study verifies that information criteria clearly distinguish the presence of long memory while tests do not evidence any difference between the fitted long and short memory models. An empirical application is provided; it analyses, on a high frequency dataset, the returns of the FIB30, the future on the MIB30, the Italian stock market index of highly capitalized firms.Massimiliano Caporin: mcaporin@unive.itThis paper was presented at the SIS 2002 Conference (Italian Statistical society annual meeting) held in Milan, University Bicocca, 5-7 June 2002. A short version of this work can be found in the proceedings of the conference     

Estimation of the signal-to-noise in the linear regression model

In the present paper estimators of the signal-to-noise are given. A simulation study is conducted in order to see how the proposed estimators perform relative to the naive estimator by way of scalar risk comparison. The results favour our suggested estimators.     

Quantile estimation in ultra-high frequency financial data: a comparison between parametric and semiparametric approach

In the context of ACD models for ultra-high frequency data different specifications are available to estimate the conditional mean of intertrade durations, while quantiles estimation has been completely neglected by literature, even if to trading extent it can be more informative. The main problem arising with quantiles estimation is the correct specification of durations probability law: the usual assumption of Exponentially distributed residuals, is very robust for the estimation of parameters of the conditional mean, but dramatically fails the distributional fit. In this paper a semiparametric approach is formalized, and compared with the parametric one, deriving from Exponential assumption. Empirical evidence for a stock of Italian financial market strongly supports the former approach.Paola Zuccolotto: The author wishes to thank Prof. A. Mazzali, Dott. G. De Luca, Dott. M. Sandri for valuable comments.     

Applications in business,medical and industrial statistics of bi-aspect nonparametric tests for location problems

Starting from the theory of the Nonparametric Combination of Dependent Permutation Tests (Pesarin, 1992, 2001), Marozzi (2002a, b) proposed two bi-aspect nonparametric tests for the two-sample and the multi-sample location problems. These tests are shown by simulation to be remarkably more powerful than the traditional parametric and permutation competitors (which can be seen as uni-aspect tests) under heavy-tailed and skewed distributions. After a brief presentation of the bi-aspect idea to location testing problems, three actual applications are discussed. The first one is a problem of business statistics and deals with the analysis of time for service calls. The second one is in medical statistics and deals with the analysis of the effect of cigarette smoking on maternal airway function during pregnancy. The third one is in industrial statistics and deals with the analysis of the setting of machines that produce steel ball bearings. The bi-aspect testing allows us to draw deeper and more informative inference than that allowed by traditional competitors.Marco Marozzi: Part of the research was done when the author was in Dipartimento di Scienze Statistiche, Universitá di Bologna, Italy.     

Normal random numbers lying on spirals and clubs

Two methods for transforming uniformly distributed random numbers into normally distributed random numbers are considered in conjunction with linear congruential generators. The two-dimensional lattice structure of the uniform random numbers is transformed by the Box-Muller method into a spiral structure and by the polar method into a club-shaped structure. The approximation of the two-dimensional normal distribution and the independence of the associated random variables are discussed.     

A generalization and Bayesian interpretation of ridge-type estimators with good prior means

Pliskin (1987) and Trenkler (1988) compared ridge-type estimators with good prior means. From a Bayesian viewpoint, these estimators are special cases of Bayesestimators and the mean square error matrix comparisons can be made in the more general case.     

Maximum likelihood estimators in regression models with infinite variance innovations

In this paper we consider the problem of maximum likelihood (ML) estimation in the classical AR(1) model with i.i.d. symmetric stable innovations with known characteristic exponent and unknown scale parameter. We present an approach that allows us to investigate the properties of ML estimators without making use of numerical procedures. Finally, we introduce a generalization to the multivariate case.     

On some reliability aspects of Pearson family of distributions

We characterize the Pearson family of distributions by finding a relationship between the failure rate and the higher order moments of residual life. We also present a characterization theorem of IFR(DFR) class of distributions in the Pearson family.     

A note on a result for two SUR models

Revankar (1974, p. 190, equation (4.4)) obtains a result for the covariance matrices of the “Aitken” estimators of the regression coefficients parameter matrices of two SUR models. The present note supplies a simpler derivation of this result. It is obtained by using a known result in multivariate statistical analysis, see e.g., Sarkar (1981, p. 560, Theorem 3.1).     

Estimating unobservable signal by Markovian noise induction

A sub threshold signal is transmitted through a channel and may be detected when some noise - with known structure and proportional to some level - is added to the data. There is an optimal noise level, called of stochastic resonance, that corresponds to the minimum variance of the estimators in the problem of recovering unobservable signals. For several noise structures it has been shown the evidence of stochastic resonance effect. Here we study the case when the noise is a Markovian process. We propose consistent estimators of the sub threshold signal and we solve further a problem of hypotheses testing. We also discuss evidence of stochastic resonance for both estimation and hypotheses testing problems via examples.     

A relation for the covariances of order statistics from n independent and non-identically distributed random variables

We derive a simple relation satisfied by the covariances of order statistics in the i.i.d. case and then generalize it to the case when the variables are independent and non-identically distributed. This relation could be employed successfully either to check the calculations or to reduce the amount of direct computations involved in evaluating the covariances of order statistics from an outlier model.     

Higher order moments of order statistics from INID exponential random variables

In this paper we develop recurrence relations for the third and fourth order moments of order statistics from I.NI.D exponential random variables. Recurrence relations for the p-outlier model (with a slippage of p observations) are derived as a special case. Applications of these results will also be described.     

Modelling Uncertainty and Overdispersion in Ordinal Data

In this article we introduce a probability distribution generated by a mixture of discrete random variables to capture uncertainty, feeling, and overdispersion, possibly present in ordinal data surveys. The choice of the components of the new model is motivated by a study on the data generating process. Inferential issues concerning the maximum likelihood estimates and the validation steps are presented; then, some empirical analyses are given to support the usefulness of the approach. Discussion on further extensions of the model ends the article.     

Two point priors and Γ-minimax estimating in families of uniform distributions

It is shown that when a parameter lying in a sufficiently small interval is to be estimated in a family of uniform distributions, a two point prior is least favourable under squared error loss. The unique Bayes estimator with respect to this prior is minimax. The Γ-minimax estimator is derived for sets Γ of priors consisting of all priors that give fixed probabilities to two specified subintervals of the parameter space if a two point prior is least favourable in Γ.     

Gamma-minimax results for the class of unimodal priors

Olman and Shmundak proved 1985 that in estimating a bounded normal mean under squared error loss the Bayes estimator with respect to the uniform distribution on the parameter interval is gamma-minimax when the parameter interval is sufficiently small and the class of priors consists of all symmetric and unimodal distributions. Recently, one of the authors showed that this result remains valid for quite general families of distributions which satisfy some regularity conditions. In the present paper a generalization to the class of unimodal priors with fixed mode is derived. It is proved that the Bayes estimator with respect to a suitable mixture of two uniform distributions is gamma-minimax for sufficiently small parameter intervals. To that end appropriate characterizations of a saddle point in the corresponding statistical games are established. Some results of a numerical study are presented.     

Extending conditional likelihood in models for stratified binary data

The conditional likelihood is widely used in logistic regression models with stratified binary data. In particular, it leads to accurate inference for the parameters of interest, which are common to all strata, eliminating stratum-specific nuisance parameters. The modified profile likelihood is an accurate approximation to the conditional likelihood, but has the advantage of being available for general parametric models. Here, we propose the modified profile likelihood as an ideal extension of the conditional likelihood in generalized linear models for binary data, with generic link function. An important feature is that for the implementation we only need standard outputs of routines for generalized linear models. The accuracy of the method is supported by theoretical properties and is confirmed by simulation results.This research was supported by MIUR COFIN 2001-2003.