Quasi-likelihood Estimation Research Articles

Quasi-likelihood estimation of the arrival time of an ultra-wideband quasi-radio signal with unknown amplitude and initial phase

The problem of estimating the time of arrival of a signal is relevant in the fields of radio and hydrolocation, radio astronomy, remote observation and sensing, etc. The useful signal is often described by a quasi-deterministic function of time, which can be regular or discontinuous. In recent years, problems of processing ultra-wideband signals have been of significant interest. Among the many UWB signals, it is customary to distinguish a separate class of ultra-wideband quasi-radio signals, the structure of which is similar to the structure of narrowband radio signals, but the condition of relative narrowband for which may not be met. Algorithms for estimating the arrival time of regular ultra-wideband quasi-radio signals have been studied in the existing literature. In this case, the synthesis and analysis of an algorithm for quasi-plausible estimation of the arrival time of a discontinuous signal of finite duration and arbitrary shape is of practical interest. The purpose of the work is to synthesize and analyze a quasi-likelihood algorithm for estimating the time of arrival of a discontinuous ultra-wideband quasi-radio signal with an unknown amplitude and initial phase against a background of white Gaussian noise. In this work, closed asymptotically exact expressions for the bias and scattering of the estimate are obtained, which make it possible to study the effectiveness of the synthesized algorithm, as well as compare its effectiveness with special cases of signal models - narrowband and wideband radio and video signals. The results of the study make it possible to determine losses in the accuracy of estimation the signal arrival time due to a priori ignorance of the initial phase and shape of the modulating function of the signal. Depending on the required accuracy of estimate the time of arrival of an ultra-wideband quasi-radio signal, it is possible to optimize the parameters of the transmitted signals and determine the limits of applicability of the designed radio system.

Measurement error–tolerant Poisson regression for Valley Fever incidence prediction

The incidence of Valley Fever can be predicted using a Poisson regression model, which links the expected incidence count to influential covariates with model coefficients. In real-world practice, the estimated model coefficients are sensitive to the inevitable measurement errors in the covariates, which are usually manifested as classical errors and/or Berkson errors. While conventional methods have separately addressed each type of error, the joint consideration of both, referred to as mixture measurement error in this article, is currently absent from the existing literature, leaving model coefficient estimators with significant biases. This article presents a measurement-error tolerant Poisson regression to mitigate the impacts of the mixture measurement error in covariates of health-care data analysis. An error-structureadapted quasi-likelihood estimation method is proposed to enhance the accuracy of model estimation. The effectiveness of the proposed method is demonstrated through a numerical case study built upon a Valley Fever investigation, validating its improved estimation accuracy and robustness.

Inference for possibly misspecified generalized linear models with nonpolynomial-dimensional nuisance parameters

Summary It is routine practice in statistical modelling to first select variables and then make inference for the selected model as in stepwise regression. Such inference is made upon the assumption that the selected model is true. However, without this assumption, one would not know the validity of the inference. Similar problems also exist in high-dimensional regression with regularization. To address these problems, we propose a dimension-reduced generalized likelihood ratio test for generalized linear models with nonpolynomial dimensionality, based on quasilikelihood estimation that allows for misspecification of the conditional variance. The test has nearly oracle performance when using the correct amount of shrinkage and has robust performance against the choice of regularization parameter across a large range. We further develop an adaptive data-driven dimension-reduced generalized likelihood ratio test and prove that, with probability going to one, it is an oracle generalized likelihood ratio test. However, in ultrahigh-dimensional models the penalized estimation may produce spuriously important variables that deteriorate the performance of the test. To tackle this problem, we introduce a cross-fitted dimension-reduced generalized likelihood ratio test, which is not only free of spurious effects, but robust against the choice of regularization parameter. We establish limiting distributions of the proposed tests. Their advantages are highlighted via theoretical and empirical comparisons to some competitive tests. An application to breast cancer data illustrates the use of our proposed methodology.

On efficiency of locally D -optimal designs under heteroscedasticity and non-Gaussianity

On efficiency of locally <i>D</i> -optimal designs under heteroscedasticity and non-Gaussianity

New ridge parameter estimators for the quasi-Poisson ridge regression model

The quasi-Poisson regression model is used for count data and is preferred over the Poisson regression model in the case of over-dispersed count data. The quasi-likelihood estimator is used to estimate the regression coefficients of the quasi-Poisson regression model. The quasi-likelihood estimator gives sub-optimal estimates if regressors are highly correlated—multicollinearity issue. Biased estimation methods are often used to overcome the multicollinearity issue in the regression model. In this study, we explore the ridge estimator for the quasi-Poisson regression model to mitigate the multicollinearity issue. Furthermore, we propose various ridge parameter estimators for this model. We derive the theoretical properties of the ridge estimator and compare its performance with the quasi-likelihood estimator in terms of matrix and scalar mean squared error. We further compared the proposed estimator numerically through a Monte Carlo simulation study and a real-life application. We found that both the simulation and application results show the superiority of the ridge estimator, particularly with the best ridge parameter estimator, over the quasi-likelihood estimator in the presence of multicollinearity issue.

Self-exciting threshold -valued autoregressive processes for non-stationary time series of counts

To handle non-stationary integer-valued time series of counts with piecewise characteristics and linear trends, this paper introduced a class of self-exciting threshold Z -valued autoregressive processes. The process is defined with a free type distribution for the innovation, which enhances the flexibility of the model. The basic probabilistic and statistical properties of the proposed model are discussed. Conditional least squares (CLS) estimator and modified quasi-likelihood (MQL) estimator, as well as their asymptotic properties are obtained. A searching algorithm for estimating the threshold parameter is also provided. Some simulation studies are conducted to show the performances of the proposed methods. Finally, an application to a real data example is provided.

An alternative derivation of weak convergence concerning quasi-likelihood estimation with a small-sample correction for simultaneous testing

Often arises in counting data analysis that both violation of distributional assumption and large-scale over-dispersion substantially impair the validity of the methods for multiple comparisons. For over-dispersed data fitting to the generalized linear models, we describe the simultaneous inference method in assessing a sequence of estimable functions based on the root using the quasi-likelihood estimation of the regression coefficients. A new method for deriving the limiting distributions of the score function and the root under a list of mild regularity conditions is presented. This approach has a close connection to the asymptotic normality of the root in general linear models that it provides a heuristic analogy for classroom presentation. Hence, researchers can routinely estimate quantiles based on the limiting distribution of the root for simultaneous inference. We apply the percentile bootstrap method to estimate the quantiles as a resampling-based alternative. As will be shown, the simultaneous test based on both the approximation methods above is anti-conservative in designs with small sample sizes. We propose the simultaneous testing method using Efron's bias-corrected percentile bootstrapping procedure as an improvement. In small-sample designs, we demonstrate through the simulation study that the proposed method provides a viable alternative to the large-sample and the percentile bootstrap approximation methods. Moreover, the proposed method persists in controlling the familywise error rate in simultaneous testing for highly over-dispersed data from substantially small-sample designs, where the percentile-t bootstrap method provides a liberal test.

Квазиправдоподобный алгоритм оценки частоты сверхширокополосного квазирадиосигнала с неизвестной длительностью

The quasi-likelihood frequency estimation algorithm of an ultra-wideband quasi-radio signal with an unknown duration, observed with white Gaussian noise, is studied. When synthesizing the frequency estimation algorithm, instead of an unknown duration, some of its expected value was used. The dependence of the variance of the frequency estimate of an ultra-wideband quasi-radio signal on the signal-to-noise ratio for various values of the duration detuning and the dependence of the frequency estimate bias on the duration detuning for various values of the narrowband parameter are obtained. It has been established that the duration detuning has a significant effect on the efficiency of frequency estimation of an ultra-wideband quasi-radio signal, while at large values of the narrowband parameter, the obtained expressions coincide with the known expressions for the variance and bias of the frequency estimate of narrowband radio signal. Recommendations on the use of the synthesized algorithm in practical applications are formulated.

Effective estimation of nonlinear errors-in-variables models

Model variables are inevitably affected and interfered by measurement errors in statistical models inference. In this paper, we investigate the effective estimators of unknown operators in the nonlinear errors-in-variables models. By combining the maximum quasi-likelihood approach and the nonparametric local estimation method, a modified approximate maximum quasi-likelihood estimators are applied to evaluate the unknown parameters of the models. Under some mild assumptions, the consistency and asymptotic normality of the corresponding estimators are established. In order to further illustrate the advantages of the modified approach, we utilize simulation examples and actual data of monozygotic twins for analysis. The results visually show the robustness of the modified estimator as well as higher precision and accuracy.

Optimal estimating function for weak location‐scale dynamic models

Estimating functions provide a very general framework for the statistical inference of dynamic models under weak assumptions. We consider a class of time series models consisting in the parametrization of the first two conditional moments which – by contrast with classical location‐scale dynamic models – do not impose further constraints on the conditional distribution/moments. Quasi‐likelihood estimators (QLE) are obtained by solving estimating equations deduced from those two conditional moments. Conditions ensuring the existence and asymptotic properties (consistency and asymptotic normality) of such estimators are provided. We propose optimal QLEs in Godambe's sense, deduced from a condition obtained by Chandra and Taniguchi (2001, Annals of the Institute of Statistical Mathematics 53, 125–141). The particular case of the quasi‐maximum likelihood estimators is considered. For pure location models, a data‐driven procedure for optimally choosing the QLE is proposed. Our results are illustrated via Monte Carlo experiments and real financial data.

Threshold estimation for jump-diffusions under small noise asymptotics

We consider parameter estimation of stochastic differential equations driven by a Wiener process and a compound Poisson process as small noises. The goal is to give a threshold-type quasi-likelihood estimator and show its consistency and asymptotic normality under new asymptotics. One of the novelties of the paper is that we give a new localization argument, which enables us to avoid truncation in the contrast function that has been used in earlier works and to deal with a wider class of jumps in threshold estimation than ever before.

A novel stochastic semi-parametric frontier-based three-stage DEA window model to evaluate China's industrial green economic efficiency

Traditional three-stage data envelopment analysis (DEA) models do not consider the problem of functional form and multicollinearity. This study develops a new stochastic semi-parametric frontier-based three-stage DEA model. The frontier incorporates the effects of both external environmental factors and statistical noise on efficiency. We adopt the StoNED (stochastic non-smooth envelopment of data) approach and use the quasi-likelihood estimation method to estimate the parameters of inefficiency term and stochastic noise. We conduct Monte Carlo experiments to examine the performance of the new frontier under different circumstances. Our results show that the new frontier provides a more realistic and accuracy estimator for efficiency measures. An empirical analysis is used to evaluate green economic efficiency (GEE) in China. We empirically compare different models and the results show that external environmental factors cause significant differences. We provide each provincial average GEE evaluated by the improved QLE-StoNED model, which are outperforms compared with other recently developed estimators. And a gradient difference emerges in the GEE among the eastern, central and western areas of China. The results also offer practical implications for the harmonious development of industrial production and a green economy in China.

Efficient penalized generalized linear mixed models for variable selection and genetic risk prediction in high-dimensional data.

Sparse regularized regression methods are now widely used in genome-wide association studies (GWAS) to address the multiple testing burden that limits discovery of potentially important predictors. Linear mixed models (LMMs) have become an attractive alternative to principal components (PCs) adjustment to account for population structure and relatedness in high-dimensional penalized models. However, their use in binary trait GWAS rely on the invalid assumption that the residual variance does not depend on the estimated regression coefficients. Moreover, LMMs use a single spectral decomposition of the covariance matrix of the responses, which is no longer possible in generalized linear mixed models (GLMMs). We introduce a new method called pglmm, a penalized GLMM that allows to simultaneously select genetic markers and estimate their effects, accounting for between-individual correlations and binary nature of the trait. We develop a computationally efficient algorithm based on penalized quasi-likelihood estimation that allows to scale regularized mixed models on high-dimensional binary trait GWAS. We show through simulations that when the dimensionality of the relatedness matrix is high, penalized LMM and logistic regression with PC adjustment fail to select important predictors, and have inferior prediction accuracy compared to pglmm. Further, we demonstrate through the analysis of two polygenic binary traits in a subset of 6731 related individuals from the UK Biobank data with 320K SNPs that our method can achieve higher predictive performance, while also selecting fewer predictors than a sparse regularized logistic lasso with PC adjustment. Our Julia package PenalizedGLMM.jl is publicly available on github: https://github.com/julstpierre/PenalizedGLMM. Supplementary data are available at Bioinformatics online.

COVID-19 hospitalizations and patients' age at admission: The neglected importance of data variability for containment policies.

An excess in the daily fluctuation of COVID-19 in hospital admissions could cause uncertainty and delays in the implementation of care interventions. This study aims to characterize a possible source of extravariability in the number of hospitalizations for COVID-19 by considering age at admission as a potential explanatory factor. Age at hospitalization provides a clear idea of the epidemiological impact of the disease, as the elderly population is more at risk of severe COVID-19 outcomes. Administrative data for the Veneto region, Northern Italy from February 1, 2020, to November 20, 2021, were considered. An inferential approach based on quasi-likelihood estimates through the generalized estimation equation (GEE) Poisson link function was used to quantify the overdispersion. The daily variation in the number of hospitalizations in the Veneto region that lagged at 3, 7, 10, and 15 days was associated with the number of news items retrieved from Global Database of Events, Language, and Tone (GDELT) regarding containment interventions to determine whether the magnitude of the past variation in daily hospitalizations could impact the number of preventive policies. This study demonstrated a significant increase in the pattern of hospitalizations for COVID-19 in Veneto beginning in December 2020. Age at admission affected the excess variability in the number of admissions. This effect increased as age increased. Specifically, the dispersion was significantly lower in people under 30 years of age. From an epidemiological point of view, controlling the overdispersion of hospitalizations and the variables characterizing this phenomenon is crucial. In this context, the policies should prevent the spread of the virus in particular in the elderly, as the uncontrolled diffusion in this age group would result in an extra variability in daily hospitalizations. This study demonstrated that the overdispersion, together with the increase in hospitalizations, results in a lagged inflation of the containment policies. However, all these interventions represent strategies designed to contain a mechanism that has already been triggered. Further efforts should be directed toward preventive policies aimed at protecting the most fragile subjects, such as the elderly. Therefore, it is essential to implement containment strategies before the occurrence of potentially out-of-control situations, resulting in congestion in hospitals and health services.

Association between household air pollution from solid fuel use and risk of chronic diseases and their multimorbidity among Chinese adults

BackgroundGiven the increasing burden of chronic conditions, multimorbidity is now a priority for public health systems worldwide. However, the relationship between household air pollution (HAP) exposure with multimorbidity remains unclear. MethodsWe used three waves data (2011, 2013, and 2015) including 19,295 participants aged ≥ 45 years from the China Health and Retirement Longitudinal Study, to investigate the association between HAP exposure from solid fuel use for heating and cooking with the risk of chronic multimorbidity. Multimorbidity was defined as the coexistence of two or more of 15 chronic diseases (hypertension, diabetes, dyslipidemia, heart disease, stroke, cardiovascular disease, chronic lung disease, asthma, kidney disease, liver disease, digestive disease, cancer, psychiatric disease, memory-related disease, and arthritis). Multiple logistic regression investigated the association between solid fuel use for heating and cooking, separately or simultaneously, with the risk of multimorbidity. Poisson regression with quasi-likelihood estimation explored whether solid fuel exposure could increase the number of morbidities. Stratified analyses and sensitivity analyses examined the effect modification and robustness of the association. ResultsOf the 19,295 participants (mean age: 58.9 years), 40.9 % have multimorbidity. Compared with participants who used clean fuels for heating and cooking, the risk was higher in mixed fuel (adjusted odds ratio, aOR = 1.26, 95 %CI:1.16–1.36) and solid fuel users (aOR = 1.81, 1.67–1.98) separately. HAP from solid fuel use was positively associated with an increased number of morbidities (adjusted β = 0.329, 0.290 to 0.368), after controlling for confounders. Those living in a one-story building, with poor household cleanliness have a higher risk of multimorbidity. No significant modifications of those associations by the socio-demographic and behaviour characteristics was observed. ConclusionsHAP from solid fuel use is associated with a high risk of chronic multimorbidity in Chinese adults. Our findings provide important implications for reducing chronic disease burden by restricting solid fuel use.

EXPONENTIAL REALIZED GARCH-ITÔ VOLATILITY MODELS

This paper introduces a novel Itô diffusion process to model high-frequency financial data that can accommodate low-frequency volatility dynamics by embedding the discrete-time nonlinear exponential generalized autoregressive conditional heteroskedasticity (GARCH) structure with log-integrated volatility in a continuous instantaneous volatility process. The key feature of the proposed model is that, unlike existing GARCH-Itô models, the instantaneous volatility process has a nonlinear structure, which ensures that the log-integrated volatilities have the realized GARCH structure. We call this the exponential realized GARCH-Itô model. Given the autoregressive structure of the log-integrated volatility, we propose a quasi-likelihood estimation procedure for parameter estimation and establish its asymptotic properties. We conduct a simulation study to check the finite-sample performance of the proposed model and an empirical study with 50 assets among the S&amp;P 500 compositions. Numerical studies show the advantages of the proposed model.

Bootstrap method for misspecified ergodic Lévy driven stochastic differential equation models

In this paper, we consider possibly misspecified stochastic differential equation models driven by Lévy processes. Regardless of whether the driving noise is Gaussian or not, Gaussian quasi-likelihood estimator can estimate unknown parameters in the drift and scale coefficients. However, in the misspecified case, the asymptotic distribution of the estimator varies by the correction of the misspecification bias, and consistent estimators for the asymptotic variance proposed in the correctly specified case may lose theoretical validity. As one of its solutions, we propose a bootstrap method for approximating the asymptotic distribution. We show that our bootstrap method theoretically works in both correctly specified case and misspecified case without assuming the precise distribution of the driving noise.

Forecasting Model of Air Pollution Index using Generalized Autoregressive Conditional Heteroskedasticity Family (GARCH)

The Air Pollution Index (API) of Malaysia has increased consistently in recent decades, becoming a serious environment issue concern. In this paper, we analyzed daily integer value time series data for API in Sarawak from January to June in 2019 using generalized autoregressive conditional heteroskedasticity (GARCH) family for discrete case namely poisson integer value GARCH (INGARCH), negative binomial integer value GARCH (NBINGARCH) and integer value autoregressive conditional heteroskedasticity (INARCH) models. The parameters of the models will be estimated using quasi likelihood estimator (QLE) and we compare their Akaike information criterion (AIC) to determine the best model fitted the data. The results showed that INGARCH (1,1) and INARCH (1,0) performed inconsistent results since the conventional methods of NBINGARCH (1,1) outperformed the performance of INGARCH (1,1) and INARCH (1,0). However, consistet results were achieved as the NBINGARCH (1,1) gave the smallest forecasting error compared to INGARCH (1,1) and INARCH (1,0). The findings are very important for controlling the API results in future and taking protection measure for conservation of the air.

Estimation of ergodic square-root diffusion under high-frequency sampling

Gaussian quasi-likelihood estimation of the parameter in the square-root diffusion process is studied under high-frequency sampling. Different from previous studies under low-frequency sampling, high-frequency of data leads to a very simple form of the asymptotic covariance matrix. Through easy-to-compute preliminary contrast functions, a practical two-stage manner without numerical optimization is formulated to conduct not only an asymptotically efficient estimation of the drift parameters but also a high-precision estimator of the diffusion parameter. Simulation experiments are given to illustrate the results.

Quasi-likelihood Estimation in Fractional Levy SPDEs from Poisson Sampling

We study the quasi-likelihood estimator of the drift parameter in the stochastic partial differential equations driven by a cylindrical fractional Levy process when the process is observed at the arrival times of a Poisson process. We use a two stage estimation procedure. We first estimate the intensity of the Poisson process. Then we plug-in this estimate in the quasi-likelihood to estimate the drift parameter. We obtain the strong consistency and the asymptotic normality of the estimators.