Network and panel quantile effects via distribution regression

This article reviews recent advances in fixed effects estimation of panel data models for long panels, where the number of time periods is relatively large. We focus on semiparametric models with unobserved individual and time effects, where the distribution of the outcome variable, conditional on covariates and unobserved effects, is specified parametrically while the distribution of the unobserved effects is left unrestricted. In contrast to existing reviews on long panels, we discuss models with both individual and time effects, split-panel jackknife bias corrections, unbalanced panels, distribution and quantile effects, and other extensions. Understanding and correcting the incidental parameter bias caused by the estimation of many fixed effects are our main focuses, and the unifying theme is that the order of this bias is given by the simple formula p/ n for all models discussed, with p being the number of estimated parameters and n the total sample size.

This article reviews recent advances in fixed effect estimation of panel data models for long panels, where the number of time periods is relatively large. We focus on semiparametric models with unobserved individual and time effects, where the distribution of the outcome variable conditional on covariates and unobserved effects is specified parametrically, while the distribution of the unobserved effects is left unrestricted. Compared to existing reviews on long panels (Arellano & Hahn, 2007; a section in Arellano & Bonhomme, 2011) we discuss models with both individual and time effects, split-panel Jackknife bias corrections, unbalanced panels, distribution and quantile effects, and other extensions. Understanding and correcting the incidental parameter bias caused by the estimation of many fixed effects is our main focus, and the unifying theme is that the order of this bias is given by the simple formula p/n for all models discussed, with p the number of estimated parameters and n the total sample size.

We study a nonlinear panel data model in which the fixed effects are assumed to have finite support. The fixed effects estimator is known to have the incidental parameters problem. We contribute to the literature by making a qualitative observation that the incidental parameters problem in this model may not be not as severe as in the conventional case. Because fixed effects have finite support, the probability of correctly identifying the fixed effect converges to one even when the cross sectional dimension grows as fast as some exponential function of the time dimension. As a consequence, the finite sample bias of the fixed effects estimator is expected to be small.

Fixed effects estimators of panel models can be severely biased because of the well-known incidental parameters problem. We show that this bias can be reduced by using a panel jackknife or an analytical bias correction motivated by large T. We give bias corrections for averages over the fixed effects, as well as model parameters. We find large bias reductions from using these approaches in examples. We consider asymptotics where T grows with n, as an approximation to the properties of the estimators in econometric applications. We show that if T grows at the same rate as n the fixed effects estimator is asymptotically biased, so that asymptotic confidence intervals are incorrect, but that they are correct for the panel jackknife. We show T growing faster than n1/3 suffices for correctness of the analytic correction, a property we also conjecture for the jackknife.

The lack of study among the economic forecasting literature that can empirically proves the hypothesis of being more powerfulness of dynamic neural networks in comparison with the static neural networks models for forecasting, is the most important motivation of this study. In this paper, the utilization of NNARX as a nonlinear dynamic neural network model, ANN as a nonlinear static neural network model and ARIMA as a linear model were compared to forecast poultry retail price. As a case study on Iranian poultry retail price, we compare forecast performance of these models for three forecasts (1, 2 and 4 week ahead). Results show that NNARX and ANN models outperform ARIMA model, and also NNARX model outperforms ANN model for all three forecasts.

A non-linear congestion network model for planning internal movement in the Hajj

A Penalty Function Approach to Bias Reduction in Non-linear Panel Models with Fixed Effects

The current study proposes a novel network control structure based on local and remote placed control elements, together with a nonlinear network transmission model recently proposed by the authors. For rejecting the disturbance effect of the network, a switched PD compensator is proposed. The control design methodology encompasses both analytical and numerical methods, so that both the stabilization and the tracking control objectives are met. The stability is assessed by considering the overall system as a switched linear system. Finally, the results are validated on a numerical example.

Heterogeneity is omnipresent across all living systems. Diversity enriches the dynamical repertoire of these systems but remains challenging to reconcile with their manifest robustness and dynamical persistence over time, a fundamental feature called resilience. To better understand the mechanism underlying resilience in neural circuits, we considered a nonlinear network model, extracting the relationship between excitability heterogeneity and resilience. To measure resilience, we quantified the number of stationary states of this network, and how they are affected by various control parameters. We analyzed both analytically and numerically gradient and non-gradient systems modeled as non-linear sparse neural networks evolving over long time scales. Our analysis shows that neuronal heterogeneity quenches the number of stationary states while decreasing the susceptibility to bifurcations: a phenomenon known as trivialization. Heterogeneity was found to implement a homeostatic control mechanism enhancing network resilience to changes in network size and connection probability by quenching the system's dynamic volatility.

In this paper, firstly, a basic nonlinear magnetic network model considering iron saturations is proposed for a three-phase 12-stator-slot/10-rotor-pole flux-switching permanent magnet (FSPM) machine. This model is built under cylindrical coordinates and enables the open-circuit air-gap flux-density distributions, phase permanent magnet (PM) flux-linkage, and electromotive- force (EMF) to be predicted with acceptable accuracy. However, large discrepancies are found in the predictions of armature inductances. Then, the basic model is modified by taking into account the localized saturation effect. As a result, the electromagnetic performance can be predicted more accurately, especially for the air-gap flux-density distributions. Furthermore, two improved models are proposed by adding bypass-bridge branches in stator network, to enhance the calculating accuracy of both saturated and unsaturated armature inductances. Finally, the predicted results from the four magnetic network models are validated by both 2D finite element analysis (FEA) and experimental measurements on a machine prototype. Overall, comparisons indicate that the model with bypass-bridge branches between stator teeth and back irons exhibits best performances.

We consider a situation where a distribution is being estimated by the empirical distribution of noisy measurements. The measurements errors are allowed to be heteroskedastic and their variance may depend on the realization of the underlying random variable. We use an asymptotic embedding where the noise shrinks with the sample size to calculate the leading bias arising from the presence of noise. Conditions are obtained under which this bias is asymptotically non-negligible. Analytical and jackknife corrections for the empirical distribution are derived that recenter the limit distribution and yield confidence intervals with correct coverage in large samples. Similar adjustments are presented for nonparametric estimators of the density and quantile function. Our approach can be connected to corrections for selection bias and shrinkage estimation. Simulation results confirm the much improved sampling behavior of the corrected estimators. An empirical application to the estimation of a stochastic-frontier model is also provided.

Linear multiple regression (LMR) and nonlinear polynomial network (NPN) models were developed from data collected from ISO 8178-4 (1996) test cycle B-type tests (ISO) and an expanded set of tests (EXP) to predict hydrocarbon (HC) emissions from a diesel engine. LMR using the ISO training data (R2 = 0.94) resulted in overfitting of the model as applied to the evaluation data (R2 = 0.49). LMR based on the expanded data (R2 = 0.68) was a better LMR model when applied to the evaluation data (R2 = 0.64). NPN using the expanded training data (R2 = 0.99) resulted in the best model when applied to the evaluation data (R2 = 0.98) and is preferred for predicting HC when the larger set of test mode data are available. NPN using the ISO training data (R2 = 0.99) resulted in a satisfactory fit for the evaluation data (R2 = 0.91), although with a higher average absolute error (0.52 vs. 0.42 g/kWh) than NPN using the EXP training data. This model was also considered suitable for predicting HC. Results of this initial study suggest that data could be collected during ISO 8178-4 emission tests and modeled with NPN to predict HC emissions for a diesel engine operating at various constant speeds and loads.

Cortical sensory neurons are commonly characterized using the receptive field, the linear dependence of their response on the stimulus. In primary auditory cortex neurons can be characterized by their spectrotemporal receptive fields, the spectral and temporal features of a sound that linearly drive a neuron. However, receptive fields do not capture the fact that the response of a cortical neuron results from the complex nonlinear network in which it is embedded. By fitting a nonlinear feedforward network model (a network receptive field) to cortical responses to natural sounds, we reveal that primary auditory cortical neurons are sensitive over a substantially larger spectrotemporal domain than is seen in their standard spectrotemporal receptive fields. Furthermore, the network receptive field, a parsimonious network consisting of 1–7 sub-receptive fields that interact nonlinearly, consistently better predicts neural responses to auditory stimuli than the standard receptive fields. The network receptive field reveals separate excitatory and inhibitory sub-fields with different nonlinear properties, and interaction of the sub-fields gives rise to important operations such as gain control and conjunctive feature detection. The conjunctive effects, where neurons respond only if several specific features are present together, enable increased selectivity for particular complex spectrotemporal structures, and may constitute an important stage in sound recognition. In conclusion, we demonstrate that fitting auditory cortical neural responses with feedforward network models expands on simple linear receptive field models in a manner that yields substantially improved predictive power and reveals key nonlinear aspects of cortical processing, while remaining easy to interpret in a physiological context.

Active Queue Management (AQM) has been widely used for congestion avoidance in TCP networks. Although numerous AQM schemes have been proposed to regulate a queue size close to a reference level as RED, PI controller, PID Controller, Adaptive prediction controller (APC) and neural network using the Back-Propagation (BP) most of them are incapable of adequately adapting to TCP network dynamics due to TCP's non-linearity and time-varying stochastic properties. In this paper, we design a nonlinear neural network controller using the non-linear model of TCP network. Genetic algorithms are used to train the nonlinear neural controller. We evaluate the performances of the proposed neural network AQM approach via simulation experiments. The proposed approach yields superior performance with faster transient response, larger throughput, and higher link utilization, as compared to other schemes.

Because of the incidental parameters problem, the fixed effects maximum likelihood estimator in a nonlinear panel data model is in general inconsistent when the time series lengthTis short and fixed. Even ifTapproaches infinity but at a rate not faster than the cross sectional sample sizen, the fixed effects estimator is still asymptotically biased. This paper proposes using the standard bootstrap andk-step bootstrap to correct the bias. We establish the asymptotic validity of the bootstrap bias corrections for both model parameters and average marginal effects. Our results apply to static models as well as some dynamic Markov models. Monte Carlo simulations show that our procedures are effective in reducing the bias of the fixed effects estimator and improving the coverage accuracy of the associated confidence interval.