Sieve Inference on Semi-nonparametric Time Series Models

The method of sieves has been widely used in estimating semiparametric and nonparametric models. In this paper, we first provide a general theory on the asymptotic normality of plug-in sieve M estimators of possibly irregular functionals of semi/nonparametric time series models. Next, we establish a surprising result that the asymptotic variances of plug-in sieve M estimators of irregular (i.e., slower than root-T estimable) functionals do not depend on temporal dependence. Nevertheless, ignoring the temporal dependence in small samples may not lead to accurate inference. We then propose an easy-to-compute and more accurate inference procedure based on a "pre-asymptotic" sieve variance estimator that captures temporal dependence. We construct a "pre-asymptotic" Wald statistic using an orthonormal series long run variance (OS-LRV) estimator. For sieve M estimators of both regular (i.e., root-T estimable) and irregular functionals, a scaled "pre-asymptotic" Wald statistic is asymptotically F distributed when the series number of terms in the OS-LRV estimator is held fixed. Simulations indicate that our scaled "pre-asymptotic" Wald test with F critical values has more accurate size in finite samples than the usual Wald test with chi-square critical values.Weak dependence, Sieve M estimation, Sieve Riesz representor, Irregular functional, Misspecification, Pre-asymptotic variance, Orthogonal series long run variance estimation, F distribution

Acoustic vibration response and power generation characteristics of airborne acoustic generator system

Aiming at the problem of insufficient power supply in modern intelligent fuze, it is of great theoretical significance and practical guidance to study the relationship between acoustic vibration response and power generation characteristics of airborne piezoelectric generators and maximum energy output. Theoretical analysis and experimental verification show that: 1. As long as the frequency of the acoustic wave induced by the flow coincides with the frequency of the acoustical modal in the cavity, a sinusoidal vibration excitation signal will be generated in the cavity; 2. With the increase of the flow rate, the frequency of the vibration signal coupled by the fluid sound source also increases. If the frequency of the acoustic wave is near the anti-resonance frequency of the piezoelectric vibrator, the displacement amplitude of the piezoelectric vibrator increases greatly. The maximum output open circuit voltage is the maximum power generated when the external circuit is connected; 3. The amplitude of the open circuit voltage of the electromechanical coupling output is linear with the amplitude of the displacement of the piezoelectric vibrator, the frequency is the same, the phase angle is the same, and the displacement and the exciting force of the piezoelectric vibrator have the characteristics of the same frequencies and backward phases, the maximum displacement of the piezoelectric vibrator is related to the amplitude of the exciting force and the angular frequency of the exciting force. This characteristic can be used to solve the piezoelectric stress factor under different initial conditions from the experimental point of view

Neural Network Models Using Thermal Sensations and Occupants’ Behavior for Predicting Thermal Comfort

It is important to create comfortable indoor environments for building occupants. This study developed neural network (NN) models for predicting thermal comfort in indoor environments by using thermal sensations and occupants’ behavior. The models were trained by data on air temperature, relative humidity, clothing insulation, metabolic rate, thermal sensations, and occupants’ behavior collected in ten offices. The models were able to predict similar acceptable air temperature ranges in offices, from 20.6℃ to 25℃ in winter and from 20.6℃ to 25.6℃ in summer. The comfort zone obtained by the NN model using thermal sensations in the ten offices was narrower than the comfort zone in ASHRAE Standard 55, but that obtained by the NN model using behaviors was wider than the ASHRAE comfort zone. This investigation demonstrates alternative approaches to the prediction of thermal comfort

Sieve Semiparametric Two-Step GMM under Weak Dependence

This paper considers semiparametric two-step GMM estimation and inference with weakly dependent data, where unknown nuisance functions are estimated via sieve extremum estimation in the first step. We show that although the asymptotic variance of the second-step GMM estimator may not have a closed form expression, it can be well approximated by sieve variances that have simple closed form expressions. We present consistent or robust variance estimation, Wald tests and Hansen’s (1982) over-identification tests for the second step GMM that properly reflect the first-step estimated functions and the weak dependence of the data. Our sieve semiparametric two-step GMM inference procedures are shown to be numerically equivalent to the ones computed as if the first step were parametric. A new consistent random-perturbation estimator of the derivative of the expectation of the non-smooth moment function is also provided

Solving Inverse Problems with Reinforcement Learning

In this paper, we formally introduce, with rigorous derivations, the use of reinforcement learning to the field of inverse problems by designing an iterative algorithm, called REINFORCE-IP, for solving a general type of non-linear inverse problem. By choosing specific probability models for the action-selection rule, we connect our approach to the conventional regularization methods of Tikhonov regularization and iterative regularization. For the numerical implementation of our approach, we parameterize the solution-searching rule with the help of neural networks and iteratively improve the parameter using a reinforcement-learning algorithm~-- REINFORCE. Under standard assumptions we prove the almost sure convergence of the parameter to a locally optimal value. Our work provides two typical examples (non-linear integral equations and parameter-identification problems in partial differential equations) of how reinforcement learning can be applied in solving non-linear inverse problems. Our numerical experiments show that REINFORCE-IP is an efficient algorithm that can escape from local minimums and identify multi-solutions for inverse problems with non-uniqueness.Comment: 33 pages, 10 figure