Nonparametric Impulse Response Research Articles

What Do Data on Millions of U.S. Workers Reveal About Lifecycle Earnings Dynamics?

We study individual male earnings dynamics over the life cycle using panel data on millions of U.S. workers. Using nonparametric methods, we first show that the distribution of earnings changes exhibits substantial deviations from lognormality, such as negative skewness and very high kurtosis. Further, the extent of these nonnormalities varies significantly with age and earnings level, peaking around age 50 and between the 70th and 90th percentiles of the earnings distribution. Second, we estimate nonparametric impulse response functions and find important asymmetries: Positive changes for high‐income individuals are quite transitory, whereas negative ones are very persistent; the opposite is true for low‐income individuals. Third, we turn to long‐run outcomes and find substantial heterogeneity in the cumulative growth rates of earnings and the total number of years individuals spend nonemployed between ages 25 and 55. Finally, by targeting these rich sets of moments, we estimate stochastic processes for earnings that range from the simple to the complex. Our preferred specification features normal mixture innovations to both persistent and transitory components and includes state‐dependent long‐term nonemployment shocks with a realization probability that varies with age and earnings.

EMG-Torque Dynamics Change With Contraction Bandwidth.

An accurate model for ElectroMyoGram (EMG)-torque dynamics has many uses. One of its applications which has gained high attention among researchers is its use, in estimating the muscle contraction level for the efficient control of prosthesis. In this paper, the dynamic relationship between the surface EMG and torque during isometric contractions at the human ankle was studied using system identification techniques. Subjects voluntarily modulated their ankle torque in dorsiflexion direction, by activating their tibialis anterior muscle, while tracking a pseudo-random binary sequence in a torque matching task. The effects of contraction bandwidth, described by torque spectrum, on EMG-torque dynamics were evaluated by varying the visual command switching time. Nonparametric impulse response functions (IRF) were estimated between the processed surface EMG and torque. It was demonstrated that: 1) at low contraction bandwidths, the identified IRFs had unphysiological anticipatory (i.e., non-causal) components, whose amplitude decreased as the contraction bandwidth increased. We hypothesized that this non-causal behavior arose, because the EMG input contained a component due to feedback from the output torque, i.e., it was recorded from within a closed-loop. Vision was not the feedback source since the non-causal behavior persisted when visual feedback was removed. Repeating the identification using a nonparametric closed-loop identification algorithm yielded causal IRFs at all bandwidths, supporting this hypothesis. 2) EMG-torque dynamics became faster and the bandwidth of system increased as contraction modulation rate increased. Thus, accurate prediction of torque from EMG signals must take into account the contraction bandwidth sensitivity of this system.

Closed-loop identification of the dynamic relation between surface EMG and torque at the human ankle

This work studies the dynamic relationship between the electrical activity produced in skeletal muscles and recorded using electromyogram(EMG), and torque at the healthy human ankle during isometric contractions. Subjects were instructed to voluntarily modulate their ankle torque by tracking a pseudo-random visual command signal. Impulse response functions (IRF) estimated between the EMG and torque records had an unphysiological anticipatory component suggesting that the estimated IRF was biased because the data were recorded in closed-loop. Applying a closed-loop identification algorithm that modeled the EMG-torque relation as a nonparametric impulse response function, and the noise as an autoregressive-moving-average process gave unbiased results. The EMG-torque IRF had second-order, low-pass, dynamics, whose properties varied with the mean torque.

A unified impulse response model for DCE‐MRI

We describe the gamma capillary transit time model, a generalized impulse response model for DCE-MRI that mathematically unifies the Tofts-Kety, extended Tofts-Kety, adiabatic tissue homogeneity, and two-compartment exchange models. By including a parameter (α⁻¹) representing the width of the distribution of capillary transit times within a tissue voxel, the GCTT model discriminates tissues having relatively monodisperse transit time distributions from those having a large degree of heterogeneity. All five models were compared using in vivo data acquired in three brain tumors (one glioblastoma multiforme, one pleomorphic xanthoastrocytoma, and one anaplastic meningioma) and Monte Carlo simulations. Our principal findings are : (1) The four most commonly used models for dynamic contrast-enhanced magnetic resonance imaging can be unified within a single formalism. (2) Application of the GCTT model to in vivo data incurs only modest penalties in parameter uncertainty and computational cost. (3) Measured nonparametric impulse response functions in human brain tumors are well described by the GCTT model. (4) Estimation of α⁻¹ is feasible but achieving statistical significance requires higher SNR than is typically obtained in single voxel dynamic contrast-enhanced magnetic resonance imaging data. These results suggest that the GCTT model may be useful for extraction of information about tumor physiology beyond what is obtained using current modeling methodologies.

Trunk stiffness and dynamics during active extension exertions

Spinal stability is related to the recruitment and control of active muscle stiffness. Stochastic system identification techniques were used to calculate the effective stiffness and dynamics of the trunk during active trunk extension exertions. Twenty-one healthy adult subjects (10 males, 11 females) wore a harness with a cable attached to a servomotor such that isotonic flexion preloads of 100, 135, and 170 N were applied at the T10 level of the trunk. A pseudorandom stochastic force sequence (bandwidth 0–10 Hz, amplitude ±30 N) was superimposed on the preload causing small amplitude trunk movements. Nonparametric impulse response functions of trunk dynamics were computed and revealed that the system exhibited underdamped second-order behavior. Second-order trunk dynamics were determined by calculating the best least-squares fit to the IRF. The quality of the model was quantified by comparing estimated and observed displacement variance accounted for (VAF), and quality of the second-order fits was calculated as a percentage and referred to as fit accuracy. Mean VAF and fit accuracy were 87.8 ± 4.0 % and 96.0 ± 4.3 % , respectively, indicating that the model accurately represented active trunk kinematic response. The accuracy of the kinematic representation was not influenced by preload or gender. Mean effective stiffness was 2.78 ± 0.96 N / mm and increased significantly with preload ( p < 0.001 ), but did not vary with gender ( p = 0.425 ). Mean effective damping was 314 ± 72 N s/m and effective trunk mass was 37.0 ± 9.3 kg . We conclude that stochastic system identification techniques should be used to calculate effective trunk stiffness and dynamics.

Identification of physiological systems: a robust method for non-parametric impulse response estimation.

The identification of non-parametric impulse response functions (IRFs) from noisy finite-length data records is analysed using the techniques of matrix perturbation theory. Based on these findings, a method for IRF estimation is developed that is more robust than existing techniques, particularly when the input is non-white. Furthermore, methods are developed for computing confidence bounds on the resulting IRF estimates. Monte Carlo simulations are used to assess the capabilities of this new method and to demonstrate its superiority over classical techniques. An application to the identification of dynamic ankle stiffness in humans is presented.

An Operational Method for Nonparametric Analysis of Feedback Control Systems

An operational method of analysis using nonparametric impulse response models is proposed for the nonparametric analysis and design of feedback control systems. It is based on the algebra of convolution quotients, and represents common results such as closed-loop transfer functions in symbolic forms, which closely resemble those for conventional parametric analysis. In design applications, controllers are also expressed symbolically by means of convolution quotients. A deconvolution algorithm is proposed to compute the convolution quotients, and permits these symbolic forms to be evaluated and applied to nonparametric analysis and design.

Manipulator control design using a nonparametric method

A nonparametric method based on nonparametric impulse response (IR) models is applied to the control system design of a two-degree-of-freedom direct drive manipulator. Linearized models of the manipulator system are obtained by a direct test method and are in the form of nonparametric IRs. The controllers are also represented by nonparametric IR models, and are implemented as finite-impulse response (FIR) digital filters. Satisfactory control performance is achieved in the experimental verification of the non-parametric designs.

Non-parametric controller synthesis for NMP plants

A non-parametric method for controller synthesis developed earlier is extended to non-minimum-phase (NMP) plants represented by non-parametric impulse response (IR) models. The authors are not aware of the existence of other non-parametric design techniques for NMP plants. The proposed method borrows ideas from Predictive Control, and its effectiveness is confirmed by design examples.

Impulse Response Estimation Via Parametric Methods

Parameter estimation with the nonparametric impulse response model gives unbiased results, but suffers from the large number of parameters. By simple structuring of the measurement vector they can be considerably reduced and an identification tool is obtained, that combines the advantages of parametric and nonparametric methods: It is appropriate for on-line identification, no a-priori knowledge about order or dead time of the process is required and it is insensitive to noise. Computationally efficient algorithms are given for the reconstruction of the continuous-time impulse response from the reduced impulse response sequence and for on-line computation of the parameters of the continuous-time transfer function.

Dynamic relationship between EMG and torque at the human ankle: variation with contraction level and modulation.

Stochastic system identification techniques were used to determine the dynamic relationship between the electromyogram (EMG) and torque in the ankle muscles of normal human subjects. EMG and torque were recorded while subjects modulated ankle torque by tracking a computer-generated stochastic waveform. Nonparametric impulse response functions (IRFs) relating EMG to ankle torque were computed and parameterised by determining the parameters of the second-order system which provided the best least-squares fit. Two sets of experiments were carried out. In the first, the mean level of torque was varied from 5 per cent of the maximum voluntary contraction (MVC) to 30 per cent MVC while the depth of modulation was held constant at ±5 per cent of MVC. In the second series of experiments the mean torque was held constant at 25 per cent MVC while the depth of modulation was varied from ±2.5 per cent to ±25 per cent. The major findings were: (1) A second-order, low-pass filter provided a good quasilinear model of the EMG/force dynamics under all conditions; (2) The model parameters depended only weakly on the mean level of torque; (3) In contrast, the model parameters depended strongly on the amplitude with which the contraction was modulated; the natural frequency increased significantly with the depth of modulation.