Robust Estimation Procedure Research Articles

Linear models for the impact of order flow on prices. II. The Mixture Transition Distribution model

Modelling the impact of the order flow on asset prices is of primary importance to understand the behaviour of financial markets. Part I of this paper reported the remarkable improvements in the description of the price dynamics which can be obtained when one incorporates the impact of past returns on the future order flow. However, impact models presented in Part I consider the order flow as an exogenous process, only characterised by its two-point correlations. This assumption seriously limits the forecasting ability of the model. Here we attempt to model directly the stream of discrete events with a so-called Mixture Transition Distribution (MTD) framework, introduced originally by Raftery [J. R. Stat. Soc. Ser. B, 1985, 528–539]. We distinguish between price-changing and non price-changing events and combine them with the order sign in order to reduce the order flow dynamics to the dynamics of a four-state discrete random variable. The MTD represents a parsimonious approximation of a full high-order Markov chain. The new approach captures with adequate realism the conditional correlation functions between signed events for both small and large tick stocks and signature plots. From a methodological point of view, constraining the MTD within the class of ergodic Markov models, and exploiting the buy–sell symmetry of the data, we propose a weak restriction on the transition matrices which solves the problem of identifiability of mixture models. In spite of the large number of parameters, this translates into a feasible and robust estimation procedure. Out-of-sample analyses demonstrate that the model does not overfit the data.

Using response ratios for meta-analyzing single-case designs with behavioral outcomes

Methods for meta-analyzing single-case designs (SCDs) are needed to inform evidence-based practice in clinical and school settings and to draw broader and more defensible generalizations in areas where SCDs comprise a large part of the research base. The most widely used outcomes in single-case research are measures of behavior collected using systematic direct observation, which typically take the form of rates or proportions. For studies that use such measures, one simple and intuitive way to quantify effect sizes is in terms of proportionate change from baseline, using an effect size known as the log response ratio. This paper describes methods for estimating log response ratios and combining the estimates using meta-analysis. The methods are based on a simple model for comparing two phases, where the level of the outcome is stable within each phase and the repeated outcome measurements are independent. Although auto-correlation will lead to biased estimates of the sampling variance of the effect size, meta-analysis of response ratios can be conducted with robust variance estimation procedures that remain valid even when sampling variance estimates are biased. The methods are demonstrated using data from a recent meta-analysis on group contingency interventions for student problem behavior.

A Revisit to Estimation of Beta Risk and an Analysis of Stock Market through Copula Transformation and Winsorization with S&P 500 Index as Proxy

We consider the problem of reliable estimation of market betas. Estimation using least squares can be very sensitive to underlying assumptions of normality and the presence of outliers, whereas various robust estimation procedures have a certain degree of arbitrariness in their implementation. This is especially of concern because returns for various equities may have very different statistical distributions. Our approach is to bring all estimation problems to a common platform through bivariate Gaussian copula transformation where, in view of the linearity of regression, correlation is a meaningful measure of dependence. We then carry out the estimation of betas by combining it with the winsorized relative volatility of the asset. Extensive analysis of the U.S. market with the S&P 500 as proxy indicates that, when the data show departure from assumptions, our approach provides more stable estimates of betas than least squares, and estimates are essentially the same when assumptions are met. Improvement is realized in up to 53% of instances.

Vision System for Coarsely Estimating Motion Parameters for Unknown Fast Moving Objects in Space

Motivated by biological interests in analyzing navigation behaviors of flying animals, we attempt to build a system measuring their motion states. To do this, in this paper, we build a vision system to detect unknown fast moving objects within a given space, calculating their motion parameters represented by positions and poses. We proposed a novel method to detect reliable interest points from images of moving objects, which can be hardly detected by general purpose interest point detectors. 3D points reconstructed using these interest points are then grouped and maintained for detected objects, according to a careful schedule, considering appearance and perspective changes. In the estimation step, a method is introduced to adapt the robust estimation procedure used for dense point set to the case for sparse set, reducing the potential risk of greatly biased estimation. Experiments are conducted against real scenes, showing the capability of the system of detecting multiple unknown moving objects and estimating their positions and poses.

Simultaneous estimation based on empirical likelihood and general maximum likelihood estimation

One typical problem in simultaneous estimation of mean values is estimating means of normal distributions, however when normality or any other distribution is not specified, more robust estimation procedures are demanded. A new estimation procedure is proposed based on empirical likelihood which does not request any specific distributional assumption. The new idea is based on incorporating empirical likelihood with general maximum likelihood estimation. One well-known nonparametric estimator, the linear empirical Bayes estimator, can be interpreted as an estimator based on empirical likelihood under some framework and it is shown that the proposed procedure can improve the linear empirical Bayes estimator. Numerical studies are presented to compare the proposed estimator with some existing estimators. The proposed estimator is applied to the problem of estimating mean values corresponding to high valued observations. Simulations and real data example of gene expression are provided.

Robust sparse Gaussian graphical modeling

Gaussian graphical modeling has been widely used to explore various network structures, such as gene regulatory networks and social networks. We often use a penalized maximum likelihood approach with the $L_1$ penalty for learning a high-dimensional graphical model. However, the penalized maximum likelihood procedure is sensitive to outliers. To overcome this problem, we introduce a robust estimation procedure based on the $\gamma$-divergence. The proposed method has a redescending property, which is known as a desirable property in robust statistics. The parameter estimation procedure is constructed using the Majorize-Minimization algorithm, which guarantees that the objective function monotonically decreases at each iteration. Extensive simulation studies showed that our procedure performed much better than the existing methods, in particular, when the contamination ratio was large. Two real data analyses were carried out to illustrate the usefulness of our proposed procedure.

Robust mixture multivariate linear regression by multivariate Laplace distribution

Assuming that the error terms follow a multivariate Laplace distribution, we propose a robust estimation procedure for mixture of multivariate linear regression models in this paper. Using the fact that the multivariate Laplace distribution is a scale mixture of the multivariate standard normal distribution, an efficient EM algorithm is designed to implement the proposed robust estimation procedure. The performance of the proposed algorithm is thoroughly evaluated by some simulation and comparison studies.

Robust estimation for the varying coefficient partially nonlinear models

In this paper, we propose a robust estimation procedure based on the exponential squared loss (ESL) function for the varying coefficient partially nonlinear model. Under some conditions, the asymptotic properties of proposed estimators are established. Furthermore, we develop a new minorization–maximization (MM) algorithm to calculate the estimates for both non-parametric and parametric parts, and introduce a data-driven procedure to select the tuning parameters. Simulation studies illustrate that the proposed method is more robust and efficient than the classical least squares technique when there are outliers in the dataset. Finally, we apply the proposed methodology to analyze a real dataset. The results reveal that the proposed has better the predictive ability.

Augmented estimation for t-year survival with censored regression models.

Reliable and accurate risk prediction is fundamental for successful management of clinical conditions. Estimating comprehensive risk prediction models precisely, however, is a difficult task, especially when the outcome of interest is time to a rare event and the number of candidate predictors, p, is not very small. Another challenge in developing accurate risk models arises from potential model misspecification. Time-specific generalized linear models estimated with inverse censoring probability weighting are robust to model misspecification, but may be inefficient in the rare event setting. To improve the efficiency of such robust estimation procedures, various augmentation methods have been proposed in the literature. These procedures can also leverage auxiliary variables such as intermediate outcomes that are predictive of event risk. However, most existing methods do not perform well in the rare event setting, especially when p is not small. In this article, we propose a two-step, imputation-based augmentation procedure that can improve estimation efficiency and that is robust to model misspecification. We also develop regularized augmentation procedures for settings where p is not small, along with procedures to improve the estimation of individualized treatment effect in risk reduction. Numerical studies suggest that our proposed methods substantially outperform existing methods in efficiency gains. The proposed methods are applied to an AIDS clinical trial for treating HIV-infected patients.

Robust Test of Long Run Risk and Valuation Risk Model

This paper tests the long run risk and valuation risk model using a robust estimation procedure. The persistent long run component of consumption growth process is proxied by a news based index that is created using a random forest algorithm. This news index is shown to predict aggregate long term consumption growth with an R-square of 57% and is robust to inclusion of other commonly used predictors. I theoretically derive an estimatable bias term in adjusted Euler equation of the model that arises due to measurement error in consumption data and show that this bias term is non-zero. Using a three pass estimation procedure that accounts for this bias, I show that the long run risk and valuation risk model fails to explain cross section of equity returns. This contrasts to the results from regular two pass Fama-MacBeth estimation procedure that implies that the same model explains the cross section of asset returns with statistically significant risk premia estimates.

Robust fitting of mixtures of factor analyzers using the trimmed likelihood estimator

ABSTRACTMixtures of factor analyzers (MFAs) have been popularly used to cluster the high-dimensional data. However, the traditional estimation method is based on the normality assumptions of random terms and thus is sensitive to outliers. In this article, we introduce a robust estimation procedure of MFAs using the trimmed likelihood estimator. We use a simulation study and a real data application to demonstrate the robustness of the trimmed estimation procedure and compare it with the traditional normality-based maximum likelihood estimate.

A Bayesian procedure for evaluating the frequency of calibration factor updates in highway safety manual (HSM) applications

The Highway Safety Manual (HSM) presents statistical models to quantitatively estimate an agency’s safety performance. The models were developed using data from only a few U.S. states. To account for the effects of the local attributes and temporal factors on crash occurrence, agencies are required to calibrate the HSM-default models for crash predictions. The manual suggests updating calibration factors every two to three years, or preferably on an annual basis. Given that the calibration process involves substantial time, effort, and resources, a comprehensive analysis of the required calibration factor update frequency is valuable to the agencies. Accordingly, the objective of this study is to evaluate the HSM’s recommendation and determine the required frequency of calibration factor updates. A robust Bayesian estimation procedure is used to assess the variation between calibration factors computed annually, biennially, and triennially using data collected from over 2400 miles of segments and over 700 intersections on urban and suburban facilities in Florida. Bayesian model yields a posterior distribution of the model parameters that give credible information to infer whether the difference between calibration factors computed at specified intervals is credibly different from the null value which represents unaltered calibration factors between the comparison years or in other words, zero difference. The concept of the null value is extended to include the range of values that are practically equivalent to zero. Bayesian inference shows that calibration factors based on total crash frequency are required to be updated every two years in cases where the variations between calibration factors are not greater than 0.01. When the variations are between 0.01 and 0.05, calibration factors based on total crash frequency could be updated every three years.

A Bayesian view of doubly robust causal inference: Table 1.

In causal inference confounding may be controlled either through regression adjustment in an outcome model, or through propensity score adjustment or inverse probability of treatment weighting, or both. The latter approaches, which are based on modelling of the treatment assignment mechanism and their doubly robust extensions have been difficult to motivate using formal Bayesian arguments, in principle, for likelihood-based inferences, the treatment assignment model can play no part in inferences concerning the expected outcomes if the models are assumed to be correctly specified. On the other hand, forcing dependency between the outcome and treatment assignment models by allowing the former to be misspecified results in loss of the balancing property of the propensity scores and the loss of any double robustness. In this paper, we explain in the framework of misspecified models why doubly robust inferences cannot arise from purely likelihood-based arguments, and demonstrate this through simulations. As an alternative to Bayesian propensity score analysis, we propose a Bayesian posterior predictive approach for constructing doubly robust estimation procedures. Our approach appropriately decouples the outcome and treatment assignment models by incorporating the inverse treatment assignment probabilities in Bayesian causal inferences as importance sampling weights in Monte Carlo integration.

Data-Adaptive Bias-Reduced Doubly Robust Estimation.

Doubly robust estimators have now been proposed for a variety of target parameters in the causal inference and missing data literature. These consistently estimate the parameter of interest under a semiparametric model when one of two nuisance working models is correctly specified, regardless of which. The recently proposed bias-reduced doubly robust estimation procedure aims to partially retain this robustness in more realistic settings where both working models are misspecified. These so-called bias-reduced doubly robust estimators make use of special (finite-dimensional) nuisance parameter estimators that are designed to locally minimize the squared asymptotic bias of the doubly robust estimator in certain directions of these finite-dimensional nuisance parameters under misspecification of both parametric working models. In this article, we extend this idea to incorporate the use of data-adaptive estimators (infinite-dimensional nuisance parameters), by exploiting the bias reduction estimation principle in the direction of only one nuisance parameter. We additionally provide an asymptotic linearity theorem which gives the influence function of the proposed doubly robust estimator under correct specification of a parametric nuisance working model for the missingness mechanism/propensity score but a possibly misspecified (finite- or infinite-dimensional) outcome working model. Simulation studies confirm the desirable finite-sample performance of the proposed estimators relative to a variety of other doubly robust estimators.

A robust forecasting framework based on the Kalman filtering approach with a twofold parameter tuning procedure: Application to solar and photovoltaic prediction

This paper presents a framework which relies on the linear dynamical Kalman filter to perform a reliable prediction for solar and photovoltaic production. The method is convenient for real-time forecasting and we describe its use to perform these predictions for different time horizons, between one minute and one hour ahead. The dataset used is a set of measurements of solar irradiance and PV power production measured in a sub-tropical zone: Guadeloupe. In this zone, fluctuating meteorological conditions can occur, with highly variable atmospheric events having severe impact in the solar irradiance and the PV power. In such conditions, heterogeneous ramp events are observed making difficult to control and manage these sources of energy. The present work hopes to build a suitable statistical method, based on bayesian inference and state-space modeling, able to predict the evolution of solar radiation and PV production. We develop a forecast method based on the Kalman filter combined with a robust parameter estimation procedure built with an Auto Regressive model or with an Expectation–Maximisation algorithm. The model is built to run with univariate or multivariate data according to their availability. The model is used here to forecast the univariate solar and PV data and also PV with exogenous data such as cloud cover and air temperature. The accuracy of this technique is studied with a set of performance criterion including the root mean square error and the mean bias error. We compare the results for the different tests performed, from one minute to one hour ahead, to the simple persistence model. The performance of our technique exceeds by far the traditional persistence model with a skill score improvement around 39% and 31%, respectively for PV production and GHI, for one hour ahead forecast.

Estimating Quantile Families of Loss Distributions for Non-Life Insurance Modelling via L-Moments

This paper discusses different classes of loss models in non-life insurance settings. It then overviews the class Tukey transform loss models that have not yet been widely considered in non-life insurance modelling, but offer opportunities to produce flexible skewness and kurtosis features often required in loss modelling. In addition, these loss models admit explicit quantile specifications which make them directly relevant for quantile based risk measure calculations. We detail various parameterizations and sub-families of the Tukey transform based models, such as the g-and-h, g-and-k and g-and-j models, including their properties of relevance to loss modelling.One of the challenges with such models is to perform robust estimation for the loss model parameters that will be amenable to practitioners when fitting such models. In this paper we develop a novel, efficient and robust estimation procedure for estimation of model parameters in this family Tukey transform models, based on L-moments. It is shown to be more robust and efficient than current state of the art methods of estimation for such families of loss models and is simple to implement for practical purposes.

Hyperspectral Anomaly Detectors Using Robust Estimators

Anomaly detection methods are devoted to target detection schemes in which no a priori information about the spectra of the targets of interest is available. This paper reviews classical anomaly detection schemes such as the widely spread Reed–Xiaoli detector and some of its variations. Moreover, the Mahalanobis distance-based detector, rigorously derived from a Kelly’s test-based approach, is analyzed and its exact distribution is derived when both mean vector and covariance matrix are unknown and have to be estimated. Although, most of these techniques are based on Gaussian distribution, we also propose here ways to extend them to non-Gaussian framework. For this purpose, elliptical distributions are considered for background statistical characterization. Through this assumption, this paper describes robust estimation procedures (M-estimators of location and scale) more suitable for non-Gaussian environment. We show that using them as plug-in estimators in anomaly detectors leads to some great improvement in the detection process. Finally, the theoretical contribution is validated through simulations and on real hyperspectral scenes.

Robust evaluation of fit indices to fake-good perturbation of ordinal data

This study extended the findings of a former simulation study (Multivar Behav Res 47:519–546, 2012) to evaluate the sensitivity of a large set of SEM-based fit indices to fake-good ordinal data. In the new simulation study we manipulated a comprehensive set of factors (including 3 robust estimation procedures and 3 different faking good models) that could influence the performance of 8 widely used fit indices. The simulation study conditions were chosen to highlight the differences among the fit indices, as well as to cover a wide variety of conditions. Our results demonstrated empirically that the normed fit index (NFI) turned out to be the most reliable fit index with a high sensitivity to fake perturbations. This result was evident in all the simulation design conditions except for those characterized by slight faking levels of perturbations. Interestingly, unlike NFI, the comparative fit index seemed to be highly insensitive to fake data when robust estimation conditions were considered. On the basis of the results of the simulation study we proposed a simple qualitative criterion to evaluate the impact of faking on statistical results.

Robust Predictions of Catalyst Deactivation of Atmospheric Residual Desulfurization

A robust parameter estimation procedure was proposed to obtain accurate, confident parameters for the atmospheric residue desulfurization (ARDS) model in this work. A comprehensive ARDS model includes too many parameters such as deactivation and loading parameters. However, past studies have used data fitting in the early phases of reactor system life testing to obtain the parameters. This procedure was found to be too sensitive to the initial estimates used in fitting. In order to use the ARDS model for designing reactor systems and evaluating operating strategies, a robust parameter estimation procedure must be available. In this work, we demonstrate that the kinetic and deactivation parameters should be obtained from kinetic tests and accelerated test data, respectively for individual catalysts. Only loading parameters such as contact efficiencies should be obtained using early life test data. The procedure was validated with long-term experimental data. The results showed that the procedure could be applied on different catalyst systems as well, which allows the model to predict mid-term and long-term performance well during a life test. The procedure described here will substantially improve the robustness of model predictions in the refining industry.

Long‐term pattern of population dynamics in the field vole from central Europe: cyclic pattern with amplitude dampening

AbstractThe subject of population cycles is regarded as controversial due to a number of unsettled questions such as whether or not cyclic patterns are governed by the same processes at high and low latitudes in Europe. Recent evidence suggests that the dynamics at high and low latitudes share the common temporal pattern of vole dynamics referred to as collapsing population cycles. Despite concurrent interest, the key contention around the causal mechanisms that drive population cycles remains a hot topic in ecology. The aims of this study are to supplement information on the seasonal population dynamics of the field vole Microtus agrestis in the Czech Republic by analysing 25 years of time series data. By applying robust estimation procedures, we estimated several parameters to describe population dynamics, such as population variability, amplitude dampening, cycle period, order of the dynamics and the structure of density dependence. The parameters indicate that field vole dynamics in central Europe are highly variable, cyclic dynamics of order two, with peaks in abundance occurring regularly at intervals of 4–5 years. In addition to exhibiting population cycles, the field vole populations show a pattern of dampened amplitude as observed elsewhere in Europe, including northern latitudes. By analysing temporal trends in seasonal abundances, population growth rates and environmental temperatures, we did not obtain evidence to support the hypothesis that amplitude dampening results from the negative effect of increasingly mild winters on winter population growth rates.