The flood algorithm—a multivariate, self-organizing-map-based, robust location and covariance estimator

Self-organizing maps (SOMs) introduced by Kohonen (Biol. Cybern. 43(1):59–69, 1982) are well-known in the field of artificial neural networks. The way SOMs are performing is very intuitive, leading to great popularity and numerous applications (related to statistics: classification, clustering). The result of the unsupervised learning process performed by SOMs is a non-linear, low-dimensional projection of the high-dimensional input data, that preserves certain features of the underlying data, e.g. the topology and probability distribution (Lee and Verleysen in Nonlinear Dimensionality Reduction, Springer, 2007; Kohonen in Self-organizing Maps, 3rd edn., Springer, 2001).     

Heteroskedasticity-consistent covariance matrix estimation:white's estimator and the bootstrap ∗

This paper considers the issue of estimating the covariance matrix of ordinary least squares estimates in a linear regression model when heteroskedasticity is suspected. We perform Monte Carlo simulation on the White estimator, which is commonly used in.

empirical research, and also on some alternatives based on different bootstrapping schemes. Our results reveal that the White estimator can be considerably biased when the sample size is not very large, that bias correction via bootstrap does not work well, and that the weighted bootstrap estimators tend to display smaller biases than the White estimator and its variants, under both homoskedasticity and heteroskedasticity. Our results also reveal that the presence of (potentially) influential observations in the design matrix plays an important role in the finite-sample performance of the heteroskedasticity-consistent estimators.     

Multivariate spatial U-quantiles: A Bahadur–Kiefer representation,a Theil–Sen estimator for multiple regression,and a robust dispersion estimator

A leading multivariate extension of the univariate quantiles is the so-called “spatial” or “geometric” notion, for which sample versions are highly robust and conveniently satisfy a Bahadur–Kiefer representation. Another extension of univariate quantiles has been to univariate U-quantiles, on the basis of which, for example, the well-known Hodges–Lehmann location estimator has a natural formulation. Generalizing both extensions, we introduce multivariate spatial U-quantiles and develop a corresponding Bahadur–Kiefer representation. New statistics based on spatial U-quantiles are presented for nonparametric estimation of multiple regression coefficients, extending the classical Theil–Sen nonparametric simple linear regression slope estimator, and for robust estimation of multivariate dispersion. Some other applications are mentioned as well.     

Robustness and power of parametric, nonparametric, robustified and adaptive tests—The multi-sample location problem

This paper deals with a survey of different types of tests, parametric, nonparametric, robustified and adaptive ones, and with an application to the two-sided c-sample location problem. Some concepts of robustness are discussed, such as breakdown point, influence function, gross-error sensitivity and especially α- and β-robustness. A robustness study on level α in the case of heteroscedasticity and nonnormal distributions is carried out via Monte Carlo methods and also a power comparison of all the tests considered. It turns out that robustified versions of the F-test and Welch-test where the original observations are replaced by its ranks behave well over a broad class of distributions, symmetric ones with different tail weight and asymmetric ones, but, on the whole, an adaptive test is to prefer.     

Optimality of the quasi-score estimator in a mean–variance model with applications to measurement error models

We consider a regression of y$y$ on x$x$ given by a pair of mean and variance functions with a parameter vector θ$\theta$ to be estimated that also appears in the distribution of the regressor variable x$x$. The estimation of θ$\theta$ is based on an extended quasi-score (QS) function. We show that the QS estimator is optimal within a wide class of estimators based on linear-in-y$y$ unbiased estimating functions. Of special interest is the case where the distribution of x$x$ depends only on a subvector α$\alpha$ of θ$\theta$, which may be considered a nuisance parameter. In general, α$\alpha$ must be estimated simultaneously together with the rest of θ$\theta$, but there are cases where α$\alpha$ can be pre-estimated. A major application of this model is the classical measurement error model, where the corrected score (CS) estimator is an alternative to the QS estimator. We derive conditions under which the QS estimator is strictly more efficient than the CS estimator.     

On tests of symmetry,marginal homogeneity and quasi-symmetry in two-way contingency tables based on minimum φ-divergence estimator with constraints

The restricted minimum φ-divergence estimator, [Pardo, J.A., Pardo, L. and Zografos, K., 2002, Minimum φ-divergence estimators with constraints in multinomial populations. Journal of Statistical Planning and Inference, 104, 221–237], is employed to obtain estimates of the cell frequencies of an I×I contingency table under hypotheses of symmetry, marginal homogeneity or quasi-symmetry. The associated φ-divergence statistics are distributed asymptotically as chi-squared distributions under the null hypothesis. The new estimators and test statistics contain, as particular cases, the classical estimators and test statistics previously presented in the literature for the cited problems. A simulation study is presented, for the symmetry problem, to choose the best function φ₂ for estimation and the best function φ₁ for testing.     

Prediction with Additive Models—Simulation and Application with Real Data

Abstract

In this paper we study the predictor behaviour of the additive model. The prediction equation is introduced as well as the computational considerations to select the smoothing parameters through cross-validation. The additive predictor is compared with a partially linear predictor in a broad simulation study and an application to a real case, prediction of the atmospheric concentration of SO₂ in sample stations.     

GEE estimation of the covariance structure of a bivariate panel data model with an application to wage dynamics and the incidence of profit-sharing in West Germany

We propose a generalized estimating equations (GEE) approach to the estimation of the mean and covariance structure of bivariate time series processes of panel data. The one-step approach allows for mixed continuous and discrete dependent variables. A Monte Carlo Study is presented to compare our particular GEE estimator with more standard GEE-estimators. In the empirical illustration, we apply our estimator to the analysis of individual wage dynamics and the incidence of profit-sharing in West Germany. Our findings show that time-invariant unobserved individual ability jointly influences individual wages and participation in profit sharing schemes.     

The exponentiated exponential–geometric distribution: a distribution with decreasing,increasing and unimodal failure rate

In this paper, we proposed a new family of distributions namely exponentiated exponential–geometric (E2G) distribution. The E2G distribution is a straightforwardly generalization of the exponential–geometric (EG) distribution proposed by Adamidis and Loukas [A lifetime distribution with decreasing failure rate, Statist. Probab. Lett. 39 (1998), pp. 35–42], which accommodates increasing, decreasing and unimodal hazard functions. It arises on a latent competing risk scenarios, where the lifetime associated with a particular risk is not observable but only the minimum lifetime value among all risks. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulas for its survival and hazard functions, moments, rth moment of the ith order statistic, mean residual lifetime and modal value. Maximum-likelihood inference is implemented straightforwardly. From a mis-specification simulation study performed in order to assess the extent of the mis-specification errors when testing the EG distribution against the E2G, and we observed that it is usually possible to discriminate between both distributions even for moderate samples with presence of censoring. The practical importance of the new distribution was demonstrated in three applications where we compare the E2G distribution with several lifetime distributions.     

Specific-to-general predictor selection in approximate autoregressions—Monte Carlo evidence and a large scale performance assessment with real data

This paper describes the performance of specific-to-general composition of forecasting models that accord with (approximate) linear autoregressions. Monte Carlo experiments are complemented with ex-ante forecasting results for 97 macroeconomic time series collected for the G7 economies in Stock and Watson (J. Forecast. 23:405–430, 2004). In small samples, the specific-to-general strategy is superior in terms of ex-ante forecasting performance in comparison with a commonly applied strategy of successive model reduction according to weakest parameter significance. Applied to real data, the specific-to-general approach turns out to be preferable. In comparison with successive model reduction, the successive model expansion is less likely to involve overly large losses in forecast accuracy and is particularly recommended if the diagnosed prediction schemes are characterized by a medium to large number of predictors.     

Positive-definite modification of a covariance matrix by minimizing the matrix $$\ell_{\infty}$$ ℓ ∞ norm with applications to portfolio optimization

AStA Advances in Statistical Analysis - The covariance matrix, which should be estimated from the data, plays an important role in many multivariate procedures, and its positive definiteness...     

Population size estimation and heterogeneity in capture–recapture data: a linear regression estimator based on the Conway–Maxwell–Poisson distribution

The purpose of the study is to estimate the population size under a truncated count model that accounts for heterogeneity. The proposed estimator is based on the Conway–Maxwell–Poisson distribution. The benefit of using the Conway–Maxwell–Poisson distribution is that it includes the Bernoulli, the Geometric and the Poisson distributions as special cases and, furthermore, allows for heterogeneity. Parameter estimates can be obtained by exploiting the ratios of successive frequency counts in a weighted linear regression framework. The results of the comparisons with Turing’s, the maximum likelihood Poisson, Zelterman’s and Chao’s estimators reveal that our proposal can be beneficially used. Furthermore, our proposal outperforms its competitors under all heterogeneous settings. The empirical examples consider the homogeneous case and several heterogeneous cases, each with its own features, and provide interesting insights on the behavior of the estimators.     

2m fractional factorial designs of resolution V with high A-efficiency, 7 ⩽ m ⩽ 10

We present 111 2^m fractional factorial designs of resolution V for 7 ⩽ m ⩽ 10. These designs are the best known to the authors with respect to the A-optimality criterion (as of October 1995).     

Mortality,longevity and experiments with the Lee–Carter model

The paper reviews the Lee-Carter modelling framework, illustrated with an application, and then extends the framework through the development of a wider class of generalised, parametric, non-linear models. The choice of error distribution is also generalised. These extensions permit the modelling and extrapolation of age-specific cohort effects as well as the more familiar age-specific period effects: the age-period-cohort version of the model is discussed with a worked example. The paper also provides a comparative study of simulation strategies for assessing risk in mortality rate predictions and the associated forecast estimates of life expectancy and annuity values in both period and cohort perspectives.     

Global and multiple test procedures using ordered p-values—a review

This paper reviews global and multiple tests for the combination ofn hypotheses using the orderedp-values of then individual tests. In 1987, Röhmel and Streitberg presented a general method to construct global level α tests based on orderedp-values when there exists no prior knowledge regarding the joint distribution of the corresponding test statistics. In the case of independent test statistics, construction of global tests is available by means of recursive formulae presented by Bicher (1989), Kornatz (1994) and Finner and Roters (1994). Multiple test procedures can be developed by applying the closed test principle using these global tests as building blocks. Liu (1996) proposed representing closed tests by means of “critical matrices” which contain the critical values of the global tests. Within the framework of these theoretical concepts, well-known global tests and multiple test procedures are classified and the relationships between the different tests are characterised.     

Ranking and estimation of related means in two—way models—a Bayesian approach

A hierarchical Bayesian approach to ranking and selection as well as estimation of related means in two—way models is considered. Using the method of Monte Carlo simulation with importance sampling, we are able to carry out efficiently the three or four dimensional integrations as needed. An example is included to illustrate the methodology.