Robust Two-Step Wavelet-Based Inference for Time Series Models

Latent time series models such as (the independent sum of) ARMA(p, q) models with additional stochastic processes are increasingly used for data analysis in biology, ecology, engineering, and economics. Inference on and/or prediction from these models can be highly challenging: (i) the data may contain outliers that can adversely affect the estimation procedure; (ii) the computational complexity can become prohibitive when the time series are extremely large; (iii) model selection adds another layer of (computational) complexity; and (iv) solutions that address (i), (ii), and (iii) simultaneously do not exist in practice. This paper aims at jointly addressing these challenges by proposing a general framework for robust two-step estimation based on a bounded influence M-estimator of the wavelet variance. We first develop the conditions for the joint asymptotic normality of the latter estimator thereby providing the necessary tools to perform (direct) inference for scale-based analysis of signals. Taking advantage of the model-independent weights of this first-step estimator, we then develop the asymptotic properties of two-step robust estimators using the framework of the generalized method of wavelet moments (GMWM). Simulation studies illustrate the good finite sample performance of the robust GMWM estimator and applied examples highlight the practical relevance of the proposed approach

A New Semiparametric Approach to Analysing Conditional Income Distributions

In this paper we explore the application of Generalised Additive Models of Location, Scale and Shape for the analysis of conditional income distributions in Germany following the reunification. We find that conditional income distributions can generally be modelled using the three parameter Dagum distribution and our results hint at an even more pronounced effect of skill-biased technological change than can be observed by standard mean regression

Robust Portfolio Selection.

In this paper, we discuss one of the reasons leading practitionners to the rejection of the Markowitz model and propose a new stastistical method to avoid this problem. To be more precise, we discuss the problem of statistical robustness of the Markowitz optimizer and show that the latter is not robust, meaning that a few extreme assets prices or returns can lead to irrelevant 'optimal' portfolios. We then propose a robust Markowitz optimizer and show that it is far more stable than the classical version.INVESTMENTS ; MODELS ; STATISTICAL ANALYSIS ; PRICES

Bounded-influence robust estimation in generalized linear latent variable models

Latent variable models are used for analyzing multivariate data. Recently, generalized linear latent variable models for categorical, metric, and mixed-type responses estimated via maximum likelihood (ML) have been proposed. Model deviations, such as data contamination, are shown analytically, using the influence function and through a simulation study, to seriously affect ML estimation. This article proposes a robust estimator that is made consistent using the basic principle of indirect inference and can be easily numerically implemented. The performance of the robust estimator is significantly better than that of the ML estimators in terms of both bias and variance. A real example from a consumption survey is used to highlight the consequences in practice of the choice of the estimator

Robust stochastic dominance: a semi-parametric approach

Lorenz curve, M-estimators, Pareto model, welfare dominance,