In this paper we compute the IF of a general class of estimators for grouped data, namely the class of MPE. We find that this IF can be large although it is bounded. Therefore, we propose a more general class of estimators, the MGP-estimators, which include the class of estimators based on the power divergence statistic and permits to define robust estimators. By analogy with Hampel's theorem, we define optimal bounded IF estimators and by a simulation study, we show that under small model contaminations, they are a lot more stable than the classical estimators for grouped data. Finally, our results are applied to a particular real example.
Filtering methods are powerful tools to estimate the hidden state of a statespace model from observations available in real time. However, they are known to be highly sensitive to the presence of small misspecifications of the underlying model and to outliers in the observation process. In this paper, we show that the methodology of robust statistics can be adapted to sequential filtering. We introduce an impact function that quantifies the sensitivity of the state distribution with respect to new data. Since the impact function of standard filters are unbounded even in the simplest cases, we propose filters with bounded impact functions which provide accurate state and parameter inference in the presence of model misspecifications. In particular, the robust particle filter naturally solves the degeneracy problems that plague the bootstrap particle filter (Gordon, Salmond and Smith, 1993) and its many extensions. We illustrate the good properties of robust filters in several examples, including linear state-space models and nonlinear models of stochastic volatility.
Distributional dominance criteria are commonly applied to draw welfare inferences about comparisons, but conclusions drawn from empirical implementations of dominance criteria may be influenced by data contamination. We show the conditions under which this may occur and propose empirical methods to work round the proble using both non-parametric and parametric approaches.
We define rank-based estimators (R-estimators) for semiparametric time series models in whichthe conditional location and scale depend on a Euclidean parameter, while the innovation density isan infinite-dimensional nuisance. Applications include linear and nonlinear models, featuring eitherhomo- or heteroskedasticity (e.g. AR-ARCH and discretely observed diffusions with jumps). We showhow to construct easy-to-implement R-estimators, which achieve semiparametric efficiency at somepredetermined reference density while preserving root-n consistency, irrespective of the actual density.Numerical examples illustrate the good performances of the proposed estimators. An empirical analysisof the log-return and log-transformed two-scale realized volatility concludes the paper.
We approach parameter estimation based on power-divergence using Havrda-Charvat generalized entropy. Unlike other robust estimators relying on divergence measures, the procedure is fully parametric and avoids complications related to bandwidth selection. Hence, it allows for the treatment of multivariate distributions. The parameter estimator is indexed by a single constant q, balancing the trade-off between robustness and efficiency. If q approaches 1, the procedure is maximum likelihood estimation; if q = 1/2, we minimize an empirical version of the Hellinger distance which is fully parametric. We study the mean squared error under contamination by means of a multi-parameter generalization of the change-of-variance function and devise an analytic min-max criterion for selecting q. Optimal q between 1/2 and 1 give remarkable robustness and yet result in negligible losses of efficiency compared to maximum likelihood. The method is considerably accurate for relatively large multivariate problems in presence of a relevant fraction of bad data.
Much of the trading activity in Equity markets is directed to brokerage houses. In exchange they provide so-called "soft dollars" which basically are amounts spent in "research" for identifying profitable trading opportunities. Soft dollars represent about USD 1 out of every USD 10 paid in commissions. Obviously they are costly, and it is interesting for an institutional investor to determine whether soft dollar inputs are worth being used (and indirectly paid for) or not, from a statistical point of view. To address this question, we develop association measures between what broker-dealers predict and what markets realize. Our data are ordinal predictions by two broker-dealers and realized values on several markets, on the same ordinal scale. We develop a structural equation model with latent variables in an ordinal setting which allows us to test broker-dealer predictive ability of financial market movements. We use a multivariate logit model in a latent factor framework, develop a tractable estimator based on a Laplace approximation, and show its consistency and asymptotic normality. Monte Carlo experiments reveal that both the estimation method and the testing procedure perform well in small samples. The method is then used to analyze our dataset.
In affective psychology, there is a persistent controversy about the number, the nature and the definition of the affect structure dimensions. Responding to the methodological criticisms addressed to the preceding studies, we conciliated the principal theories regarding the affect structure with the same experimental setting. In particular, using the semantic items all around the circumplex we found three bipolar independent dimensions and using only the PANAS semantic items, we found two unipolar dimensions. Finally, we propose a heuristic theorization of affect based on a current firmly established in social sciences, coherent from semantics to sociology, but largely ignored by researchers in affective psychology, that allows to postulate that affect is all at once cognition, motivation and behaviour.
In most health survey the state of health of individuals is measured through several different kinds of variables such as qualitative, discrete quantitative or dichotomic ones. From these variables, one aims at building univariate indices of health that summarize the information. To do so, we propose in this paper to use Generalized Linear Latent Variable Models (GLLVM) (see e.g. Bartholomew and Knott 1999), which allows to estimate one or more continuous latent variables from a set of observable ones. As an application, we consider the data from the 1997 Swiss Health Survey and build two health indicators. The first one describes the health status induced merely by the age of the subject, and the second one complements the first one.
This paper proposes a robust estimator for a general class of linear latent variable models (GLLVM) (Moustaki and Knott 2000, Bartholomew and Knott 1999). It is based on a weighted score function that is simple to implement numerically and is made consistent using the basic idea of indirect inference. The need of a robust estimator for these models is motivated by the study of the effect of model deviations such as data contamination on the maximum likelihood estimator (MLE). This is done with the use of the influence function (Hampel 1968, 1974) and the gross error sensitivity (Hampel, Ronchetti, Rousseeuw, and Stahel 1986). Simulation studies show that the MLE can be seriously biased by model deviations. The performance of the robust estimator in terms of bias and variance is compared to the MLE estimator with simulation studies and with a real example from a consumption survey.
