Estimating Function Approach Research Articles

Credit default swap spreads modeling and forecasting with a stochastic square-root three-factor model

In this study, we consider the CIR3 model, a three-factor stochastic model with correlated trends and volatilities for modeling and forecasting credit default swap (CDS) spreads. After recalling existence and uniqueness results, together with a generalized Feller condition to ensure positivity, we use a Lamperti-type transform to rewrite our SDEs system in a form in which the stochastic part of the leading process is uncorrelated with those of its mean and volatility processes. Finally, we calibrate the model through the estimating function approach for ergodic diffusions and simulate the CDS prices by discretizing our (transformed) system. These findings contribute to a deeper understanding of stochastic models with correlated trends and volatilities, with applications in pricing, trading and risk assessment.

Identification of stochastic nonlinear models using optimal estimating functions

The first part of the paper examines the asymptotic properties of linear prediction error method estimators, which were recently suggested for the identification of nonlinear stochastic dynamical models. It is shown that their accuracy depends not only on how the model is parameterized, but also on the shape of the unknown distribution of the data. Therefore, it is not obvious in general which linear prediction error method should be preferred. In the second part, the estimating functions approach is introduced and used to construct estimators that are asymptotically optimal with respect to a specific class of estimators. These estimators rely on partial probabilistic parametric models, and therefore neither require the computations of the likelihood function nor any marginalization integrals. The convergence and consistency of the proposed estimators are established under standard regularity and identifiability assumptions akin to those of prediction error methods. The paper is concluded by several numerical simulation examples.

Causal inference of latent classes in complex survey data with the estimating equation framework.

Latent class analysis (LCA) has been effectively used to cluster multiple survey items. However, causal inference with an exposure variable, identified by an LCA model, is challenging because (1) the exposure variable is unobserved and harbors the uncertainty of estimating parameters in the LCA model and (2) confounding bias adjustments need to be done with the unobserved LCA-driven exposure variable. In addition to these challenges, complex survey design features and survey weights must be accounted for if they are present. Our solutions to these issues are to (1) assess point estimates with the expected estimating function approach and (2) modify the survey design weights with LCA-based propensity scores. This paper aims to introduce a statistical procedure to apply the estimating equation approach to assessing the effects of LCA-driven cause in complex survey data using an example of the National Health and Nutrition Examination Survey.

Generalized value at risk forecasting

In this paper, using estimating function approach, a new optimal volatility estimator is introduced and based on the recursive form of the estimator a data-driven generalized EWMA model for value at risk (VaR) forecast is proposed. An appropriate data-driven model for volatility is identified by the relationship between absolute deviation and standard deviation for symmetric distributions with finite variance. It is shown that the asymptotic variance of the proposed volatility estimator is smaller than that of conventional estimators and is more appropriate for financial data with larger kurtosis. For IBM, Microsoft, Apple stocks and SP 500 index the proposed method is used to identify the model, estimate the volatility, and obtain minimum mean square error(MMSE) forecasts of VaR.

Double Poisson-Tweedie Regression Models.

In this paper, we further extend the recently proposed Poisson-Tweedie regression models to include a linear predictor for the dispersion as well as for the expectation of the count response variable. The family of the considered models is specified using only second-moments assumptions, where the variance of the count response has the form μ+ϕμp $\mu + \phi \mu^p$, where µ is the expectation, ϕ and p are the dispersion and power parameters, respectively. Parameter estimations are carried out using an estimating function approach obtained by combining the quasi-score and Pearson estimating functions. The performance of the fitting algorithm is investigated through simulation studies. The results showed that our estimating function approach provides consistent estimators for both mean and dispersion parameters. The class of models is motivated by a data set concerning CD4 counting in HIV-positive pregnant women assisted in a public hospital in Curitiba, Paraná, Brazil. Specifically, we investigate the effects of a set of covariates in both expectation and dispersion structures. Our results showed that women living out of the capital Curitiba, with viral load equal or larger than 1000 copies and with previous diagnostic of HIV infection, present lower levels of CD4 cell count. Furthermore, we detected that the time to initiate the antiretroviral therapy decreases the data dispersion. The data set and R code are available as supplementary materials.

Quasi-beta Longitudinal Regression Model Applied to Water Quality Index Data

We propose a new class of regression models to deal with longitudinal continuous bounded data. The model is specified using second-moment assumptions, and we employ an estimating function approach for parameter estimation and inference. The main advantage of the proposed approach is that it does not need to assume a multivariate probability distribution for the response vector. The fitting procedure is easily implemented using a simple and efficient Newton scoring algorithm. Thus, the quasi-beta longitudinal regression model can easily handle data in the unit interval, including exact zeros and ones. The covariance structure is defined in terms of a matrix linear predictor composed by known matrices. A simulation study was conducted to check the properties of the estimating function estimators of the regression and dispersion parameter estimators. The NORTA algorithm (NORmal To Anything) was used to simulate correlated beta random variables. The results of this simulation study showed that the estimators are consistent and unbiased for large samples. The model is motivated by a data set concerning the water quality index, whose goal is to investigate the effect of dams on the water quality index measured on power plant reservoirs. Furthermore, diagnostic techniques were adapted to the proposed models, such as DFFITS, DFBETAS, Cook’s distance and half-normal plots with simulated envelope. The R code and data set are available in the supplementary material.

Flexible quasi-beta regression models for continuous bounded data

We propose a flexible class of regression models for continuous bounded data based on second-moment assumptions. The mean structure is modelled by means of a link function and a linear predictor, while the mean and variance relationship has the form [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text] are the mean, dispersion and power parameters respectively. The models are fitted by using an estimating function approach where the quasi-score and Pearson estimating functions are employed for the estimation of the regression and dispersion parameters respectively. The flexible quasi-beta regression model can automatically adapt to the underlying bounded data distribution by the estimation of the power parameter. Furthermore, the model can easily handle data with exact zeroes and ones in a unified way and has the Bernoulli mean and variance relationship as a limiting case. The computational implementation of the proposed model is fast, relying on a simple Newton scoring algorithm. Simulation studies, using datasets generated from simplex and beta regression models show that the estimating function estimators are unbiased and consistent for the regression coefficients. We illustrate the flexibility of the quasi-beta regression model to deal with bounded data with two examples. We provide an R implementation and the datasets as supplementary materials.

Generalized Value at Risk Forecasting

In this paper, using estimating function approach, a new optimal volatility estimator is introduced, and, based on the recursive form of the estimator, a data-driven generalized EWMA model for VaR forecast is proposed. An appropriate data-driven model for volatility is identified by the relationship between the absolute deviation and the standard deviation for symmetric distributions with finite variance. It is shown that the asymptotic variance of the proposed volatility estimator is smaller than that of conventional estimators and is more appropriate for financial data with larger kurtosis. For IBM, Microsoft, and Apple stocks the proposed method is used to identify the model, estimate the volatility, and obtain VaR forecasts.

Multiple Response Variables Regression Models in R: The mcglm Package

This article describes the R package mcglm implemented for fitting multivariate covariance generalized linear models (McGLMs). McGLMs provide a general statistical modeling framework for normal and non-normal multivariate data analysis, designed to handle multivariate response variables, along with a wide range of temporal and spatial correlation structures defined in terms of a covariance link function and a matrix linear predictor involving known symmetric matrices. The models take non-normality into account in the conventional way by means of a variance function, and the mean structure is modeled by means of a link function and a linear predictor. The models are fitted using an estimating function approach based on second-moment assumptions. This provides a unified approach to a wide variety of different types of response variables and covariance structures, including multivariate extensions of repeated measures, time series, longitudinal, genetic, spatial and spatio-temporal structures. The mcglm package allows a flexible specification of the mean and covariance structures, and explicitly deals with multivariate response variables, through a user friendly formula interface similar to the ordinary glm function. Illustrations in this article cover a wide range of applications from the traditional one response variable Gaussian mixed models to multivariate spatial models for areal data using the multivariate Tweedie distribution. Additional features, such as robust and bias-corrected standard errors for regression parameters, residual analysis, measures of goodness-of-fit and model selection using the score information criterion are discussed through six worked examples. The mcglm package is a full R implementation based on the Matrix package which provides efficient access to BLAS (basic linear algebra subroutines), Lapack (dense matrix), TAUCS (sparse matrix) and UMFPACK (sparse matrix) routines for efficient linear algebra in R.

Comparison of pivotals for confidence bounds and intervals for the mean of a stationary time series

ABSTRACTWe construct new pivotals to obtain confidence bounds and confidence intervals for the mean of a stationary process. These follow the approach based on estimating functions. The new pivotals are compared with the standard pivotal based on studentization. We study the first four cumulants of each of these pivotals and explain why the pivotals based on the estimating function approach result in better coverage probabilities. Some simulation results comparing these pivotals have been reported.

Extended Poisson–Tweedie: Properties and regression models for count data

We propose a new class of discrete generalized linear models based on the class of Poisson–Tweedie factorial dispersion models with variance of the form [Formula: see text], where [Formula: see text] is the mean and [Formula: see text] and [Formula: see text] are the dispersion and Tweedie power parameters, respectively. The models are fitted by using an estimating function approach obtained by combining the quasi-score and Pearson estimating functions for the estimation of the regression and dispersion parameters, respectively. This provides a flexible and efficient regression methodology for a comprehensive family of count models including Hermite, Neyman Type A, Pólya–Aeppli, negative binomial and Poisson-inverse Gaussian. The estimating function approach allows us to extend the Poisson–Tweedie distributions to deal with underdispersed count data by allowing negative values for the dispersion parameter [Formula: see text]. Furthermore, the Poisson–Tweedie family can automatically adapt to highly skewed count data with excessive zeros, without the need to introduce zero-inflated or hurdle components, by the simple estimation of the power parameter. Thus, the proposed models offer a unified framework to deal with under-, equi-, overdispersed, zero-inflated and heavy-tailed count data. The computational implementation of the proposed models is fast, relying only on a simple Newton scoring algorithm. Simulation studies showed that the estimating function approach provides unbiased and consistent estimators for both regression and dispersion parameters. We highlight the ability of the Poisson–Tweedie distributions to deal with count data through a consideration of dispersion, zero-inflated and heavy tail indices, and illustrate its application with four data analyses. We provide an R implementation and the datasets as supplementary materials.

Doubly robust estimation of generalized partial linear models for longitudinal data with dropouts.

We develop a doubly robust estimation of generalized partial linear models for longitudinal data with dropouts. Our method extends the highly efficient aggregate unbiased estimating function approach proposed in Qu et al. (2010) to a doubly robust one in the sense that under missing at random (MAR), our estimator is consistent when either the linear conditional mean condition is satisfied or a model for the dropout process is correctly specified. We begin with a generalized linear model for the marginal mean, and then move forward to a generalized partial linear model, allowing for nonparametric covariate effect by using the regression spline smoothing approximation. We establish the asymptotic theory for the proposed method and use simulation studies to compare its finite sample performance with that of Qu's method, the complete-case generalized estimating equation (GEE) and the inverse-probability weighted GEE. The proposed method is finally illustrated using data from a longitudinal cohort study.

Estimation of parametric failure time distributions based on interval-censored data with irregular dependent follow-up.

Event history studies based on disease clinic data often face several complications. Specifically, patients may visit the clinic irregularly, and the intermittent observation times could depend on disease-related variables; this can cause a failure time outcome to be dependently interval-censored. We propose a weighted estimating function approach so that dependently interval-censored failure times can be analysed consistently. A so-called inverse-intensity-of-visit weight is employed to adjust for the informative inspection times. Left truncation of failure times can also be easily handled. Additionally, in observational studies, treatment assignments are typically non-randomized and may depend on disease-related variables. An inverse-probability-of-treatment weight is applied to estimating functions to further adjust for measured confounders. Simulation studies are conducted to examine the finite sample performances of the proposed estimators. Finally, the Toronto Psoriatic Arthritis Cohort Study is used for illustration. Copyright © 2017 John Wiley & Sons, Ltd.

Estimation for Wrapped Zero Inflated Poisson and Wrapped Poisson Distributions

There has been a growing interest in discrete circular models such as wrapped zero inflated Poisson and wrapped Poisson distributions and the trigonometric moments (see Brobbey et al., 2016 and Girija et al., 2014). Also, characteristic functions of stable processes have been used to study the estimation of the model parameters using estimating function approach (see Thavaneswaran et al., 2013). One difficulty in estimating the circular mean and the resultant mean length parameter of wrapped Poisson (WP) or wrapped zero inflated Poisson (WZIP) is that neither the likelihood of WP/WZIP random variable nor the score function is available in closed form, which leads one to use either trigonometric method of moment estimation (TMME) or an estimating function approach. In this paper, we study the estimation of WZIP distribution and WP distribution using estimating functions and obtain the closed form expression of the information matrix. We also derive the asymptotic distribution of the tangent of the mean direction for both the WZIP and WP distributions.

Estimation, filtering and smoothing in the stochastic conditional duration model: an estimating function approach

Stochastic conditional duration models are widely used in the financial econometrics literature to model the duration between transactions in a financial market. Even though there are developments in terms of modelling aspects, estimation, filtering and smoothing are still being investigated by researchers in this area. Almost all the existing procedures are highly computational intensive because of the complexity of the likelihood function. In this paper, we suggest a new procedure for estimation, filtering and smoothing in stochastic conditional duration models, based on estimating functions. Simulation studies indicate that the suggested procedure performs well and also fast in terms of computation. Copyright © 2016 John Wiley & Sons, Ltd.

Wrapped Zero-inflated Poisson Distribution and Its Properties

Recently, there has been a growing interest in discrete valued wrapped distributions and the trigonometric moments.<br />Characteristic functions of stable processes have been used to study the estimation of the model parameters using<br />estimating function approach (Thavaneswaran et al., 2013). In this paper, we introduce a new discrete circular distribution,<br />the wrapped zero-inflated Poisson distribution and derive its population characteristics.<br /><br />

Merging multiple longitudinal studies with study-specific missing covariates: A joint estimating function approach.

Merging multiple datasets collected from studies with identical or similar scientific objectives is often undertaken in practice to increase statistical power. This article concerns the development of an effective statistical method that enables to merge multiple longitudinal datasets subject to various heterogeneous characteristics, such as different follow-up schedules and study-specific missing covariates (e.g., covariates observed in some studies but missing in other studies). The presence of study-specific missing covariates presents great statistical methodology challenge in data merging and analysis. We propose a joint estimating function approach to addressing this challenge, in which a novel nonparametric estimating function constructed via splines-based sieve approximation is utilized to bridge estimating equations from studies with missing covariates to those with fully observed covariates. Under mild regularity conditions, we show that the proposed estimator is consistent and asymptotically normal. We evaluate finite-sample performances of the proposed method through simulation studies. In comparison to the conventional multiple imputation approach, our method exhibits smaller estimation bias. We provide an illustrative data analysis using longitudinal cohorts collected in Mexico City to assess the effect of lead exposures on children's somatic growth.

Implementation of the Estimating Functions Approach in Asset Returns Volatility Forecasting Using First Order Asymmetric GARCH Models

This paper implements the method of estimating functions (EF) in the modelling and forecasting of financial returns volatility. This estimation approach incorporates higher order moments which are common in most financial time series, into modelling, leading to a substantial gain of information and overall efficiency benefits. The two models considered in this paper provide a better in-sample-fit under the estimating functions approach relative to the traditional maximum likely-hood estimation (MLE) approach when fitted to empirical time series. On this ground, the EF approach is employed in the first order EGARCH and GJR-GARCH models to forecast the volatility of two market indices from the USA and Japanese stock markets. The loss functions, mean square error (MSE) and mean absolute error (MAE), have been utilized in evaluating the predictive ability of the EGARCH vis-a-vis the GJR-GARCH model.

Quasi-likelihood for Spatial Point Processes.

Fitting regression models for intensity functions of spatial point processes is of great interest in ecological and epidemiological studies of association between spatially referenced events and geographical or environmental covariates. When Cox or cluster process models are used to accommodate clustering not accounted for by the available covariates, likelihood based inference becomes computationally cumbersome due to the complicated nature of the likelihood function and the associated score function. It is therefore of interest to consider alternative more easily computable estimating functions. We derive the optimal estimating function in a class of first-order estimating functions. The optimal estimating function depends on the solution of a certain Fredholm integral equation which in practise is solved numerically. The derivation of the optimal estimating function has close similarities to the derivation of quasi-likelihood for standard data sets. The approximate solution is further equivalent to a quasi-likelihood score for binary spatial data. We therefore use the term quasi-likelihood for our optimal estimating function approach. We demonstrate in a simulation study and a data example that our quasi-likelihood method for spatial point processes is both statistically and computationally efficient.

A combined estimating function approach for fitting stationary point process models

A composite likelihood technique based on pairwise contributions provides a computationally simple but potentially inefficient approach for fitting spatial point process models. We propose a new estimation procedure that improves the efficiency. Our approach combines estimating functions derived from pairwise composite likelihood estimation and estimating functions that account for correlations among the pairwise contributions. Our method can be used to fit a variety of parametric spatial point process models and can yield more efficient estimators for the clustering parameters than pairwise composite likelihood estimation. We demonstrate the efficacy of our proposed method through a simulation study and an application to the longleaf pine data.