This paper investigates the asymptotic properties of quasi-maximum likelihood estimators for spatial dynamic panel data with fixed effects, when both the number of individuals
n
and the number of ...time periods
T
are large. We consider the case where
T
is asymptotically large relative to
n
, the case where
T
is asymptotically proportional to
n
, and the case where
n
is asymptotically large relative to
T
. In the case where
T
is asymptotically large relative to
n
, the estimators are
n
T
consistent and asymptotically normal, with the limit distribution centered around 0. When
n
is asymptotically proportional to
T
, the estimators are
n
T
consistent and asymptotically normal, but the limit distribution is not centered around 0; and when
n
is large relative to
T
, the estimators are
T
consistent, and have a degenerate limit distribution. The estimators of the fixed effects are
T
consistent and asymptotically normal. We also propose a bias correction for our estimators. We show that when
T
grows faster than
n
1
/
3
, the correction will asymptotically eliminate the bias and yield a centered confidence interval.
Remaining useful life (RUL) prediction has attracted more and more attention in recent years because of its significance in predictive maintenance. The degradation processes of systems from the same ...population are generally different from one another due to their various operational conditions and health states. This behavior is defined as unit-to-unit variability (UtUV), which brings difficulty to RUL prediction. To handle this problem, this paper develops a Wiener-process-model (WPM)-based method for RUL prediction with the consideration of the UtUV. In this method, an age- and state-dependent WPM is specially designed to describe the various degradation processes of different units. A unit maximum likelihood estimation (UMLE) algorithm is proposed to estimate the UtUV parameter according to the measurements of training units, without any restriction to the distribution pattern of the parameter. The UtUV parameter is further updated via particle filtering (PF) according to the measurements of the testing unit. In the particle updating process, a fuzzy resampling algorithm is developed to handle the sample impoverishment problem of PF. With the updated parameter, the RUL is predicted through a degradation process simulation algorithm. The effectiveness of the proposed method is verified through a simulation study and a turbofan engine degradation dataset.
A joint sparse representation (JSR) method has shown superior performance for the classification of hyperspectral images (HSIs). However, it is prone to be affected by outliers in the HSI spatial ...neighborhood. In order to improve the robustness of JSR, we propose a maximum likelihood estimation (MLE)-based JSR (MLEJSR) model, which replaces the traditional quadratic loss function with an MLE-like estimator for measuring the joint approximation error. The MLE-like estimator is actually a function of coding residuals. Given some priors on the coding residuals, the MLEJSR model can be easily converted to an iteratively reweighted JSR problem. Choosing a reasonable weight function, the effect of inhomogeneous neighboring pixels or outliers can be dramatically reduced. We provide a theoretical analysis of MLEJSR from the viewpoint of recovery error and evaluate its empirical performance on three public hyperspectral data sets. Both the theoretical and experimental results demonstrate the effectiveness of our proposed MLEJSR method, especially in the case of large noise.
Recently, various algorithms for data-driven simulation and control have been proposed based on the Willems' fundamental lemma. However, when collected data are noisy, these methods lead to ...ill-conditioned data-driven model structures. In this article, we present a maximum likelihood framework to obtain an optimal data-driven model, the signal matrix model, in the presence of output noise. Data compression and noise-level estimation schemes are also proposed to apply the algorithm efficiently to large datasets and unknown noise-level scenarios. Two approaches in system identification and receding horizon control are developed based on the derived optimal estimator. The first one identifies a finite impulse response model. This approach improves the least-squares estimator with less restrictive assumptions. The second one applies the signal matrix model as the predictor in predictive control. The control performance is shown to be better than existing data-driven predictive control algorithms, especially under high noise levels. Both approaches demonstrate that the derived estimator provides a promising framework to apply data-driven algorithms to noisy data.
The β-model for random graphs is commonly used for representing pairwise interactions in a network with degree heterogeneity. Going beyond pairwise interactions, Stasi et al. 45 introduced the ...hypergraph β-model for capturing degree heterogeneity in networks with higher-order (multi-way) interactions. In this paper we initiate the rigorous study of the hypergraph β-model with multiple layers, which allows for hyperedges of different sizes across the layers. To begin with, we derive the rates of convergence of the maximum likelihood (ML) estimates and establish their minimax rate optimality. We also derive the limiting distribution of the ML estimates and construct asymptotically valid confidence intervals for the model parameters. Next, we consider the goodness-of-fit problem in the hypergraph β-model. Specifically, we establish the asymptotic normality of the likelihood ratio (LR) test under the null hypothesis, derive its detection threshold, and also its limiting power at the threshold. Interestingly, the detection threshold of the LR test turns out to be minimax optimal, that is, all tests are asymptotically powerless below this threshold. The theoretical results are further validated in numerical experiments. In addition to developing the theoretical framework for estimation and inference for hypergraph β-models, the above results fill a number of gaps in the graph β-model literature, such as the minimax optimality of the ML estimates and the non-null properties of the LR test, which, to the best of our knowledge, have not been studied before.
In power systems, state estimation is a widely investigated method to collate field measurements and power flow equations to derive the most-likely state of the observed networks. In the literature, ...it is commonly assumed that all measurements are characterized by zero-mean Gaussian noise. However, it has been shown that this assumption might be unacceptable, e.g., in the case of the so-called pseudo-measurements. In this paper, a state estimator is presented that can model (pseudo-)measurement uncertainty with any continuous distribution, without approximations. This is possible by reformulating state estimation as a maximum-likelihood estimation-based constrained optimization problem, in a more generic fashion than conventional implementations. To realistically describe distribution networks, three-phase unbalanced power flow equations are used. Trade-offs between accuracy and computational effort of different uncertainty modeling methods are presented using the IEEE European Low Voltage Test Feeder.
GENERALIZED RANDOM FORESTS Athey, Susan; Tibshirani, Julie; Wager, Stefan
The Annals of statistics,
04/2019, Volume:
47, Issue:
2
Journal Article
Peer reviewed
Open access
We propose generalized random forests, a method for nonparametric statistical estimation based on random forests (Breiman Mach. Learn. 45 (2001) 5–32) that can be used to fit any quantity of interest ...identified as the solution to a set of local moment equations. Following the literature on local maximum likelihood estimation, our method considers a weighted set of nearby training examples; however, instead of using classical kernel weighting functions that are prone to a strong curse of dimensionality, we use an adaptive weighting function derived from a forest designed to express heterogeneity in the specified quantity of interest. We propose a flexible, computationally efficient algorithm for growing generalized random forests, develop a large sample theory for our method showing that our estimates are consistent and asymptotically Gaussian and provide an estimator for their asymptotic variance that enables valid confidence intervals. We use our approach to develop new methods for three statistical tasks: nonparametric quantile regression, conditional average partial effect estimation and heterogeneous treatment effect estimation via instrumental variables. A software implementation, grf for R and C++, is available from CRAN.
In massive multiple-input multiple-output (MIMO) systems, it may not be power efficient to have a pair of high-resolution analog-to-digital converters (ADCs) for each antenna element. In this paper, ...a near maximum likelihood (nML) detector for uplink multiuser massive MIMO systems is proposed where each antenna is connected to a pair of one-bit ADCs, i.e., one for each real and imaginary component of the baseband signal. The exhaustive search over all the possible transmitted vectors required in the original maximum likelihood (ML) detection problem is relaxed to formulate an ML estimation problem. Then, the ML estimation problem is converted into a convex optimization problem which can be efficiently solved. Using the solution, the base station can perform simple symbol-by-symbol detection for the transmitted signals from multiple users. To further improve detection performance, we also develop a two-stage nML detector that exploits the structures of both the original ML and the proposed (one-stage) nML detectors. Numerical results show that the proposed nML detectors are efficient enough to simultaneously support multiple uplink users adopting higher-order constellations, e.g., 16 quadrature amplitude modulation. Since our detectors exploit the channel state information as part of the detection, an ML channel estimation technique with one-bit ADCs that shares the same structure with our proposed nML detector is also developed. The proposed detectors and channel estimator provide a complete low power solution for the uplink of a massive MIMO system.
The estimation of absorption time distributions of Markov jump processes is an important task in various branches of statistics and applied probability. While the time‐homogeneous case is classic, ...the time‐inhomogeneous case has recently received increased attention due to its added flexibility and advances in computational power. However, commuting sub‐intensity matrices are assumed, which in various cases limits the parsimonious properties of the resulting representation. This paper develops the theory required to solve the general case through maximum likelihood estimation, and in particular, using the expectation‐maximization algorithm. A reduction to a piecewise constant intensity matrix function is proposed in order to provide succinct representations, where a parametric linear model binds the intensities together. Practical aspects are discussed and illustrated through the estimation of notoriously demanding theoretical distributions and real data, from the perspective of matrix analytic methods.
Superconducting nanowire single photon detectors (SNSPDs) have attracted considerable attention in the field of free-space optical communications, especially for ultra-long-distance communications. ...Calibrating the inherent time delay in the optoelectronic circuit of SNSPD arrays is critical to enabling photon detection with high time accuracy. In this paper, we propose two methods for estimating the inherent timing error: Gaussian fitting calibration (GFC) and maximum-likelihood calibration (MLC). In particular, MLC estimates the timing error by taking into account the deadtime and jitter characteristics of SNSPD. Experimental results demonstrate the effectiveness of the proposed methods.
•Novel Gaussian fitting and maximum-likelihood methods proposed for SNSPD time delay calibration.•Maximum-likelihood calibration considers SNSPD deadtime and jitter to improve accuracy.•Experiments validate effectiveness of proposed methods, with MLC providing unbiased estimates.
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