Time-invariant Coefficients Research Articles

The constant solution method for solving large-scale differential Sylvester matrix equations with time invariant coefficients

The constant solution method for solving large-scale differential Sylvester matrix equations with time invariant coefficients

Asynchronous and error-prone longitudinal data analysis via functional calibration.

In many longitudinal settings, time-varying covariates may not be measured at the same time as responses and are often prone to measurement error. Naive last-observation-carried-forward methods incur estimation biases, and existing kernel-based methods suffer from slow convergence rates and large variations. To address these challenges, we propose a new functional calibration approach to efficiently learn longitudinal covariate processes based on sparse functional data with measurement error. Our approach, stemming from functional principal component analysis, calibrates the unobserved synchronized covariate values from the observed asynchronous and error-prone covariate values, and is broadly applicable to asynchronous longitudinal regression with time-invariant or time-varying coefficients. For regression with time-invariant coefficients, our estimator is asymptotically unbiased, root-n consistent, and asymptotically normal; for time-varying coefficient models, our estimator has the optimal varying coefficient model convergence rate with inflated asymptotic variance from the calibration. In both cases, our estimators present asymptotic properties superior to the existing methods. The feasibility and usability of the proposed methods are verified by simulations and an application to the Study of Women's Health Across the Nation, a large-scale multisite longitudinal study on women's health duringmidlife.

Identification of an impulse response through a model of ARX structure

Polynomial parametric models of ARX structure are becoming increasingly popular for characterizing heat transfer for linear thermal systems with time invariant coefficients. This stems from their robustness when applied to inverse problems, either for model reduction, for experimental model identification or for inverse input problems. Their parsimonious character allows to get residuals of very low levels with a limited number of coefficients. This paper shows, on a theoretical algebraic basis, that ARX models can be deduced from convolutive models.

Quantile estimation of semiparametric model with time-varying coefficients for panel count data.

Panel count data frequently occurs in follow-up studies, such as medical research, social sciences, reliability studies, and tumorigenicity experiences. This type data has been extensively studied by various statistical models with time-invariant regression coefficients. However, the assumption of invariant coefficients may be violated in some reality, and the temporal covariate effects would be of great interest in research studies. This motivates us to consider a more flexible time-varying coefficient model. For statistical inference of the unknown functions, the quantile regression approach based on the B-spline approximation is developed. Asymptotic results on the convergence of the estimators are provided. Some simulation studies are presented to assess the finite-sample performance of the estimators. Finally, two applications of bladder cancer data and US flight delay data are analyzed by the proposed method.

Bayesian Modelling of Time-Varying Conditional Heteroscedasticity

Conditional heteroscedastic (CH) models are routinely used to analyze financial datasets. The classical models such as ARCH-GARCH with time-invariant coefficients are often inadequate to describe frequent changes over time due to market variability. However, we can achieve significantly better insight by considering the time-varying analogs of these models. In this paper, we propose a Bayesian approach to the estimation of such models and develop a computationally efficient MCMC algorithm based on Hamiltonian Monte Carlo (HMC) sampling. We also established posterior contraction rates with increasing sample size in terms of the average Hellinger metric. The performance of our method is compared with frequentist estimates and estimates from the time constant analogs. To conclude the paper we obtain time-varying parameter estimates for some popular Forex (currency conversion rate) and stock market datasets.

An additive hazards frailty model with semi-varying coefficients.

Proportional hazards frailty models have been extensively investigated and used to analyze clustered and recurrent failure times data. However, the proportional hazards assumption in the models may not always hold in practice. In this paper, we propose an additive hazards frailty model with semi-varying coefficients, which allows some covariate effects to be time-invariant while other covariate effects to be time-varying. The time-varying and time-invariant regression coefficients are estimated by a set of estimating equations, whereas the frailty parameter is estimated by the moment method. The large sample properties of the proposed estimators are established. The finite sample performance of the estimators is examined by simulation studies. The proposed model and estimation are illustrated with an analysis of data from a rehospitalization study of colorectal cancer patients.

New discrete-time zeroing neural network for solving time-variant underdetermined nonlinear systems under bound constraint

Many industrial applications result in the constrained underdetermined nonlinear system (UNS) that needs to be solved. The existing solutions are reported to the constrained UNS with time-invariant coefficients, and they may not perform well for the time-variant case. In this paper, we attempt to address the above limitation by providing a new discrete-time zeroing neural network (DTZNN) for solving the time-variant UNS (TVUNS) under bound constraint. Specifically, the bound-constrained TVUNS (BC-TVUNS) is first transformed into a mixed nonlinear system by introducing a nonnegative variable. Then, a continuous-time ZNN (CTZNN) model is established to solve such a mixed system as well as the BC-TVUNS. By employing a special difference formula to discretize the CTZNN model, the new DTZNN model is thus proposed to obtain the solution of the BC-TVUNS. Theoretical analysis and comparative numerical results are presented to validate the effectiveness of the proposed DTZNN model over the previous DTZNN models. The DTZNN application potential is further indicated on the basis of the simulations on a dual-arm redundant robot using the proposed model.

Dynamic logistic state space prediction model for clinical decision making.

Prediction modeling for clinical decision making is of great importance and needed to be updated frequently with the changes of patient population and clinical practice. Existing methods are either done in an ad hoc fashion, such as model recalibration or focus on studying the relationship between predictors and outcome and less so for the purpose of prediction. In this article, we propose a dynamic logistic state space model to continuously update the parameters whenever new information becomes available. The proposed model allows for both time-varying and time-invariant coefficients. The varying coefficients are modeled using smoothing splines to account for their smooth trends over time. The smoothing parameters are objectively chosen by maximum likelihood. The model is updated using batch data accumulated at prespecified time intervals, which allows for better approximation of the underlying binomial density function. In the simulation, we show that the new model has significantly higher prediction accuracy compared to existing methods. We apply the method to predict 1 year survival after lung transplantation using the United Network for Organ Sharingdata.

Weight calibration to improve efficiency for estimating pure risks from the additive hazards model with the nested case-control design.

We study the efficiency of covariate-specific estimates of pure risk (one minus the survival function) when some covariates are only available for case-control samples nested in a cohort. We focus on the semiparametric additive hazards model in which the hazard function equals a baseline hazard plus a linear combination of covariates with either time-varying or time-invariant coefficients. A published approach uses the design-based inclusion probabilities to reweight the nested case-control data. We obtain more efficient estimates of pure risks by calibrating the design weights to data available in the entire cohort, for both time-varying and time-invariant covariate coefficients. We develop explicit variance formulas for the weight-calibrated estimates based on influence functions. Simulations show the improvement in precision by using weight calibration and confirm the consistency of variance estimators and the validity of inference based on asymptotic normality. Examples are provided using data from the Prostate, Lung, Colorectal, and Ovarian Cancer Screening Trial Study (PLCO).

Asymptotic properties of QMLE for seasonal threshold GARCH model with periodic coefficients

Periodic models for volatility process constitute an alternative representation for the seasonal patterns observed in data exhibits a strong seasonal volatility driven by periodic coefficients of high and law variation. Moreover, these varying-parameters can arise also when seasonality is incorporated into the theory of economic decision-making So, in this paper, we propose an extension of time-invariant coefficients threshold GARCH (TGARCH) processes to periodically time-varying coefficients (PTGARCH) one. This parametrization allows us to describe the dynamic volatility through a TGARCH model within each regime (or season), and therefore a new stylized fact that characterize the volatility by seasonal patterns. Hence, theoretical probabilistic properties of this model are derived. The necessary and sufficient conditions which ensure the strict stationarity and ergodicity (in periodic sense) solution of PTGARCH are given. We extend the standard results of the popular quasi-maximum likelihood estimator (QMLE) for estimating the unknown parameters in model. More precisely, the strong consistency and the asymptotic normality of QMLE are studied for the cases when the innovation process is an i.i.d (Strong case) or is not (Semi-strong case). A Monte Carlo study is further conducted to examine the finite sample properties of the QMLE. The simulation results reveal that the QMLE is approximately unbiased and consistent for modest sample sizes when the stationarity conditions hold. Empirical work on the exchange rates of the Algerian Dinar against the single European currency (Euro) shows that our approach also outperforms and fits the data well.

QMLE for Periodic Time-Varying Asymmetric $$\log $$ GARCH Models

This paper establishes probabilistic and statistical properties of the extension of time-invariant coefficients asymmetric $$\log $$ GARCH processes to periodically time-varying coefficients ($$P\log $$ GARCH) one. In these models, the parameters of $$\log -$$volatility are allowed to switch periodically between different seasons. The main motivations of this new model are able to capture the asymmetry and hence leverage effect, in addition, the volatility coefficients are not a subject to positivity constraints. So, some probabilistic properties of asymmetric $$P\log $$ GARCH models have been obtained, especially, sufficient conditions ensuring the existence of stationary, causal, ergodic (in periodic sense) solution and moments properties are given. Furthermore, we establish the strong consistency and the asymptotic normality of the quasi-maximum likelihood estimator (QMLE) under extremely strong assumptions. Finally, we carry out a simulation study of the performance of the QML and the $$P\log $$ GARCH is applied to model the crude oil prices of Algerian Saharan Blend.

Self-Interference Cancellation With Frequency Offset and Nonlinear Distortion Suppression for Cooperative Jamming Communications

Cooperative jamming is envisioned as a key technique to enhance the wireless secrecy. With the help of a cooperative node, confidential communications are ensured by emitting a jamming signal to combat against eavesdropping. Concurrently, this jamming signal also propagates into the legitimate node through the multipath wireless channel, then becomes the self-interference (SI). In this letter, a nonlinear SI cancellation scheme is proposed by jointly taking into account the frequency offset, the power amplifier nonlinearity, and the multipath effect. These practical imperfections induced SI is first formulated based on a memory polynomial model. After a Taylor series expansion to the SI, the time-invariant coefficients from the SI are derived and subsequently estimated to yield a SI cancelling signal. Simulation results show that the proposed scheme has a significant SI cancellation improvement over the current method, and extends the transmit power range to provide a better security performance.

QML Estimation of Asymmetric Markov Switching GARCH(p, q) Processes

In this paper, I propose a natural extension of time-invariant coefficients threshold GARCH (TGARCH) processes to time-varying one, in which the associated volatility switch between different regimes due to dependency of its coefficients on unobservable (latent) time homogeneous Markov chain with finite state space (MS-TGARCH). These models are showed to be capable to capture some phenomena observed for most financial time series, among others, the asymmetric patterns, leverage effects, dependency without correlation and tail heaviness. So, some theoretical probabilistic properties of such models are discussed, in particular, we establish firstly necessary and sufficient conditions ensuring the strict stationarity and ergodicity for solution process of MS-TGARCH. Secondary, we extend the standard results for the limit theory of the popular quasi-maximum likelihood estimator (QMLE) for estimating the unknown parameters involved in model and we examine thus the strong consistency of such estimates. The finite-sample properties of QMLE are illustrated by a Monte Carlo study. Our proposed model is applied to model the exchange rates of the Algerian Dinar against the single European currency (Euro).

Linear optimal control of time delay systems via Hermite wavelet

To solve the time delay optimal control problem with quadratic performance index, a direct numerical method based on Hermite wavelet has been proposed in the present study. The idea is to convert the time delay optimal control problem into a quadratic programming problem. To do so, various time functions in the system are expanded as their truncated series and the properties of the operational matrices of integration, delay and product of two Hermite wavelet vectors are used as well. These matrices are utilized to reduce the solution of optimal control with time delay system, to the solution of a quadratic programming with linear constraints. Finally, three examples of time varying and time invariant coefficients are given to compare the results with some of the existing methods.

Fouling detection in a shell and tube heat exchanger using variation of its thermal impulse responses: Methodological approach and numerical verification

A new method for fouling detection in a heat exchanger is proposed. This method is based on the sensitivity of its impulse response (time version of its transfer function) with fouling. The concept is validated here numerically for a shell and tube heat exchanger in steady state regime, perturbed thermally by a transient surface source. This method is presented here, on a theoretical ground. It can be implemented online, whatever the geometric and structural characteristics of the setup. It only requires the use of regular temperature sensors and actuators. The only condition concern the equations of the model of the heat exchanger which have to be linear with time invariant coefficients.

Uncertainties in the South African wind load design formulation

This paper presents an investigation of the uncertainties inherent in the South African formulation of design wind loads on structures, as stipulated by SANS 10160-3:2011. The investigation follows from the identification of anomalous values in the existing South African probabilistic wind load models during a reliability assessment of SANS 10160. The primary wind load components which have the greatest effect on the total wind load uncertainty are identified as the time variant free-field wind pressure, followed by the time invariant pressure coefficients and terrain roughness factors. A rational and transparent reliability framework for the quantification of the uncertainties inherent in the formulation of these components is then presented. Probabilistic models of these components were developed following independent investigations of each component. The results from these investigations show that the existing probabilistic wind load models underestimate the uncertainty of the wind load components, particularly when considering the time invariant components.

Optimal maintainability of manpower system with time invariant coefficients

In manpower control studies, it is is well known that in attaining a desired structure from a given structure or maintaining a given desired structure, it is possible to achieve these using different values of the control variable. Therefore, there is need to evaluate these control values for optimality. In this paper, we present the optimal controllability via attainability, of a manpower system represented as a stochastic differential equation with time invariant coefficients. We also give criterion for maintainability of the system.

Self-Interference Cancellation With Nonlinearity and Phase-Noise Suppression in Full-Duplex Systems

This paper addresses the self-interference (SI) cancellation for full-duplex operation in the presence of imperfect radio-frequency (RF) components. In particular, we develop a new scheme to jointly estimate and cancel the in-phase/quadrature mixer imbalance, power amplifier nonlinearities, up-/down-conversion phase noise, and the SI channel. First, we develop a detailed baseband model that captures the most significant transceiver RF imperfections, for both separate- and common-oscillator structures used in the up- and down-conversions. Then, a basis expansion model is derived to approximate the time-varying phase noise and to transform the problem of estimating the time-varying phase noise into the estimation of a set of time-invariant coefficients. Subsequently, the likelihood function is derived in the presence of the unknown intended signal to formulate the joint estimation of the intended channel, SI channel, nonlinear impairments, and phase noise, under the maximum likelihood (ML) criterion. An iterative procedure is developed to find the ML estimate of the different parameters based on the known transmitted data, the known pilot symbols, and the statistics of the unknown intended signal received from the intended transmitter. The full use of the received signal significantly reduces the required number of pilot symbols as compared to training-based techniques. We consider the two pilot-insertion structures used in LTE for the frequency-multiplexed pilots and the time-multiplexed pilots. Simulation results indicate that the proposed ML algorithms can offer a superior SI-cancellation performance with the resulting intended-signal-to-SI-and-noise ratio very close to the intended-signal-to-noise ratio.

Complete and Simplified Models for Estimating Vibration Instability of Cyclically Symmetric Ring Structures: Comparison and Verification

In-plane vibration of cyclically symmetric ring structures is examined with emphasis on the comparison of instabilities estimated by complete and simplified models. The aim of this paper is to understand under what conditions and to what degree the simplified models can approach the complete model. Previous studies develop time-variant models and employ perturbation method by assuming weak support. This work casts the rotating-load problem into a nonrotating load problem. A complete model with time-invariant coefficients is developed in rotating-support-fixed frame, where the bending and extensional deformations are incorporated. It is then reduced into two simplified ones based on different deformation restrictions. Due to the time-invariant effect observed in the rotating-support-fixed frame, the eigenvalues are formulated directly by using classical vibration theory and compared based on a sample structure. The comparisons verify that the two types of models are comparable only for weak support. Furthermore, the simplified models cannot accurately predict all unstable behaviors in particular for strong support. The eigenvalues are different even in comparable regions. For verification purpose, the time-invariant models are transformed into time-variant ones in the inertial frame, based on which instabilities are estimated by using Floquét theory. Consistence between the time-invariant and -variant models verifies the comparisons.

Regression analysis of sparse asynchronous longitudinal data.

We consider estimation of regression models for sparse asynchronous longitudinal observations, where time-dependent responses and covariates are observed intermittently within subjects. Unlike with synchronous data, where the response and covariates are observed at the same time point, with asynchronous data, the observation times are mismatched. Simple kernel-weighted estimating equations are proposed for generalized linear models with either time invariant or time-dependent coefficients under smoothness assumptions for the covariate processes which are similar to those for synchronous data. For models with either time invariant or time-dependent coefficients, the estimators are consistent and asymptotically normal but converge at slower rates than those achieved with synchronous data. Simulation studies evidence that the methods perform well with realistic sample sizes and may be superior to a naive application of methods for synchronous data based on an ad hoc last value carried forward approach. The practical utility of the methods is illustrated on data from a study on human immunodeficiency virus.