First-order Estimators Research Articles

Nonparametric second-order estimation for spatiotemporal point patterns.

Many existing methodologies for analyzing spatiotemporal point patterns are developed based on the assumption of stationarity in both space and time for the second-order intensity or pair correlation. In practice, however, such an assumption often lacks validity or proves to be unrealistic. In this paper, we propose a novel and flexible nonparametric approach for estimating the second-order characteristics of spatiotemporal point processes, accommodating non-stationary temporal correlations. Our proposed method employs kernel smoothing and effectively accounts for spatial and temporal correlations differently. Under a spatially increasing-domain asymptotic framework, we establish consistency of the proposed estimators, which can be constructed using different first-order intensity estimators to enhance practicality. Simulation results reveal that our method, in comparison with existing approaches, significantly improves statistical efficiency. An application to a COVID-19 dataset further illustrates the flexibility and interpretability of our procedure.

Is Newey–West optimal among first-order kernels?

Newey–West (1987) standard errors are the dominant standard errors used for heteroskedasticity and autocorrelation robust (HAR) inference in time series regression. The Newey–West estimator uses the Bartlett kernel, which is a first-order kernel, meaning that its characteristic exponent, q, is equal to 1, where q is defined as the largest value of r for which the quantity k[r](0)=limt→0|t|−r(k(0)−k(t)) is defined and finite. This raises the apparently uninvestigated question of whether the Bartlett kernel is optimal among first-order kernels. We demonstrate that, for q<2, there is no optimal qth-order kernel for HAR testing in the Gaussian location model or for minimizing the MSE in spectral density estimation. In fact, for any q<2, the space of qth-order positive-semidefinite kernels is not closed and, moreover, all continuous qth-order kernels can be decomposed into a weighted sum of qth and second-order kernels, which suggests that there is no meaningful notion of ‘pure’ qth-order kernels for q<2. Nevertheless, it is possible to rank any given collection of qth-order kernels using the functional Iq[k]=k[q](0)1/q∫k2(t)dt with smaller values corresponding to better asymptotic performance. We examine the value of Iq[k] for a wide variety of first-order estimators and find that none improve upon the Bartlett kernel. These comparisons provide additional justification for the continued use of the Newey–West estimator with testing-optimal smoothing parameters and fixed-b critical values despite the lack of optimality of Bartlett among first-order kernels.

DC Motor Speed Regulator via Active Damping Injection and Angular Acceleration Estimation Techniques

This paper suggests a novel model-based nonlinear DC motor speed regulator without the use of a current sensor. The current dynamics, machine parameters and mismatched load variations are considered. The proposed controller is designed to include an active damping term that regulates the motor speed in accordance with the first-order low-pass filter dynamics through the pole-zero cancellation. Meanwhile, the angular acceleration and its reference are obtained from simple first-order estimators using only the speed information. The effectiveness is experimentally verified using hardware comprising the QUBE-Servo2, myRIO-1900, and LabVIEW.

Sensorless non‐linear position‐stabilising control for magnetic levitation systems

This study presents a solution to the position stabilisation problem for non-linear magnetic levitation systems using the only position measurement. This considers parameter and load variations without the use of current and velocity feedback. The features are given as follows: (i) the removal of current and velocity feedback by the proposed first-order state estimators without system parameters, (ii) securing of improved closed-loop robustness from the combination of active damping and specified feedback gain with the closed-loop system order reduced to 1 and (iii) proof of performance recovery and offset-free in the absence of regulation error integral actions. The numerical simulations verify the performance and robustness improvements through realistic scenarios.

Estimating Fish Species Richness across Multiple Watersheds

Assessing fish species richness at the scale of an entire watershed or multiple watersheds is important when designing conservation areas and maintaining aquatic biodiversity. Estimating biodiversity at this scale requires considering the effects of habitat heterogeneity within and across drainages on the species-area relationship (SAR). I examined the SAR using unusually complete data to assess fish species richness in minimally disturbed watersheds on large public lands in the Sand Hills ecoregion, southeastern United States of America (USA). My objectives were to compare (1) true richness with estimates produced by different species richness estimators and sampling designs and (2) species richness among reservations. Accurate estimates were obtained for five contiguous watersheds (780 km2 total) by using Chao 2 or first-order jackknife estimators, coupled with (1) a stratified design that apportioned sampling effort over 25 sample sites based on major spatial correlates of assemblage composition, including stream size and drainage basin identity and (2) sufficient sampling effort to collect enough individuals to include rare species. The greatest species richness was in streams within a large land holding characterized by greater instream habitat diversity, less disturbed land coverage, more forested land, and closer proximity to source pools than other reservations. Species richness in these streams was within the range observed in high diversity Neotropical and Indomalayan realms.

Impact of Human Capital Inequality on Total Factor Productivity in China

This paper investigates the impact of human capital inequality on Total Factor Productivity (TFP) in China. Approaching this question in dynamic panel data over 18 years and 29 provinces with first-order difference GMM and system GMM estimators reveals: human capital inequality has a significant negative effect on TFP, and high-quality human capital has a significant positive effect on TFP.

Second-Order Inference for the Mean of a Variable Missing at Random.

We present a second-order estimator of the mean of a variable subject to missingness, under the missing at random assumption. The estimator improves upon existing methods by using an approximate second-order expansion of the parameter functional, in addition to the first-order expansion employed by standard doubly robust methods. This results in weaker assumptions about the convergence rates necessary to establish consistency, local efficiency, and asymptotic linearity. The general estimation strategy is developed under the targeted minimum loss-based estimation (TMLE) framework. We present a simulation comparing the sensitivity of the first and second-order estimators to the convergence rate of the initial estimators of the outcome regression and missingness score. In our simulation, the second-order TMLE always had a coverage probability equal or closer to the nominal value 0.95, compared to its first-order counterpart. In the best-case scenario, the proposed second-order TMLE had a coverage probability of 0.86 when the first-order TMLE had a coverage probability of zero. We also present a novel first-order estimator inspired by a second-order expansion of the parameter functional. This estimator only requires one-dimensional smoothing, whereas implementation of the second-order TMLE generally requires kernel smoothing on the covariate space. The first-order estimator proposed is expected to have improved finite sample performance compared to existing first-order estimators. In the best-case scenario of our simulation study, the novel first-order TMLE improved the coverage probability from 0 to 0.90. We provide an illustration of our methods using a publicly available dataset to determine the effect of an anticoagulant on health outcomes of patients undergoing percutaneous coronary intervention. We provide R code implementing the proposed estimator.

Doubly-Selective Channel Estimation Using Data-Dependent Superimposed Training and Exponential Basis Models

Channel estimation for single-user frequency- selective time-varying channels is considered using superimposed training. The time-varying channel is assumed to be well- approximated by a complex exponential basis expansion model (CE-BEM). A periodic (non-random) training sequence is arithmetically added (superimposed) at low power to the information sequence at the transmitter before modulation and transmission. In existing first-order statistics-based channel estimators, the information sequence acts as interference resulting in a poor signal-to-noise ratio (SNR). In this paper a data-dependent superimposed training sequence is used to cancel out the effects of the unknown information sequence at the receiver on channel estimation. A performance analysis is presented. We also consider the issue of superimposed training power allocation. Several illustrative computer simulation examples are presented.

Efficient information theoretic inference for conditional moment restrictions

The generalised method of moments estimator may be substantially biased in finite samples, especially so when there are large numbers of unconditional moment conditions. This paper develops a class of first-order equivalent semi-parametric efficient estimators and tests for conditional moment restrictions models based on a local or kernel-weighted version of the Cressie–Read power divergence family of discrepancies. This approach is similar in spirit to the empirical likelihood methods of Kitamura et al. [2004. Empirical likelihood-based inference in conditional moment restrictions models. Econometrica 72, 1667–1714] and Tripathi and Kitamura [2003. Testing conditional moment restrictions. Annals of Statistics 31, 2059–2095]. These efficient local methods avoid the necessity of explicit estimation of the conditional Jacobian and variance matrices of the conditional moment restrictions and provide empirical conditional probabilities for the observations.

Decentralized model reference adaptive control without restriction on subsystem relative degrees

When the direct model reference adaptive control (MRAC) scheme with first-order local estimators is employed to design totally decentralized controllers, the stability result can only be applied to a system with all of its nominal subsystem relative degrees less than or equal to two. In this paper, this restriction is relaxed and it is achieved by employing the parameter projection together with static normalization. To implement the local controllers, no a priori knowledge of the subsystem unmodeled dynamics and no information exchange between subsystems are required. Global stability is established for the closed-loop system and small in the mean tracking error is ensured. With this analysis, the class of interactions and subsystem unmodeled dynamics can be enlarged to include those having infinite memory.

More Higher-Order Efficiency: Concentration Probability

Based on concentration probability of estimators about a true parameter, third-order asymptotic efficiency of the first-order bias-adjusted MLE within the class of first-order bias-adjusted estimators has been well established in a variety of probability models. In this paper we consider the class of second-order bias-adjusted Fisher consistent estimators of a structural parameter vector on the basis of an i.i.d. sample drawn from a curved exponential-type distribution, and study the asymptotic concentration probability, about a true parameter vector, of these estimators up to the fifth-order. In particular, (i) we show that third-order efficient estimators are always fourth-order efficient; (ii) a necessary and sufficient condition for fifth-order efficiency is provided; and finally (iii) the MLE is shown to be fifth-order efficient.

Switching-based signal estimation with digital implementation

A first-order signal derivative estimator via bang–bang switching is presented in this paper. The derivative estimator can be used as a direct derivative estimation of smooth and bounded input signals. Digital implementation shows the effectiveness of the derivative estimator. High-order signal differentiation can be obtained by concatenating a set of the proposed first-order derivative estimators.

Second-Order Pitman Admissibility and Pitman Closeness: The Multiparameter Case and Stein-Rule Estimators

In a multiparameter estimation problem, for first-order efficient estimators, second-order Pitman admissibility, and Pitman closeness properties are studied. Bearing in mind the dominant role of Stein-rule estimators in multiparameter estimation theory, such second-order properties are also studied for shrinkage maximum likelihood estimators.

Extraction of forest stand parameters from panchromatic and multispectral SPOT-1 data

Abstract The main objective of this paper is to determine the extent to which forest structural variables can be estimated from SPOT-1 panchromatic and multispectral radiance. The test site is the state-owned Pynven forest, featuring a large amount of evenly-aged pine stands from which those with Corsican pine (Pinus nigra Am. var. Calabrica Loud.) are selected. Investigated image parameters include waveband, first-order statistics estimators and sample window size. The forest stand parameters are stand density, stand age, average tree diameter, stand basal area, average canopy height and stand volume. Empirical linear models are constructed based on Bartlett's three-group method, followed by inversion and validation using an independent test data set. The green and red SPOT-1 waveband are useless for forest stand parameter estimation, and the arithmetic mean of sample window radiance is the only usable estimator from the set of tested statistical measures. Stand density and average canopy height can sati...

A Review of Methods for Prediction of Potential Fish Production with Application to the Great Lakes and Lake Winnipeg

Methods for estimating fish production in aquatic ecosystems range from simple empirically derived estimators, such as morphoedaphic indices, to complex ecosystem simulation models. As first-order estimators, the former are attractive to managers because they are simple and relatively inexpensive to apply and interpret. Application of the latter group has been limited because many of the data inputs are difficult and expensive to obtain. Between these extremes are several models, such as the biomass–size spectrum model, that provide useful information for moderate expenditures of time and effort. Existing and new methods are reviewed in the light of production theory and several are applied to Great Lakes and Lake Winnipeg data. Eight empirical models derived from limnological variables were selected from the literature and used to estimate potential fish yield for the Great Lakes and Lake Winnipeg. The models predicted a fairly narrow range of potential yields, but when compared with historic yields, none was consistent for all lakes. The best overall empirically derived estimator of potential yield in the Great Lakes was the morphoedaphic index. Potential fish production estimated from invertebrate production with Borgmann's biomass – size spectrum model was considerably greater than historic yields or the yield estimates from the empirical models. In a third approach, we calculated life history parameters for "small" and "large" fish in the Great Lakes and combined these with Borgmann's production model, empirical information on population production/biomass ratios from the literature, and classical population dynamics theory to estimate potential production and optimum sustained yield for each group. Historic sustained yield, as a percentage of optimum sustained yield, varied from a low of 6 for "small" Lake Ontario fish to 100 for "large" Lake Erie fish.

A method for reducing multipath artifacts in ultrasonic computed tomography

Estimates of ultrasonic attenuation based on first-order or moment spectral estimators are often confused by multipath propagation effects. The magnitude of error in attenuation estimates due to multipath for the frequency shift technique is described. A parametric model of multipath propagation effects on the frequency spectrum is introduced and an optimization technique is used to estimate the coefficients of the model. The attenuation estimation performances of the model estimation technique, the frequency shift technique, and a cepstral liftering technique are compared.

Jacknife estimation of functions of stratum means

SUMMARY The jackknife method of investigating and reducing the bias in nonlinear estimates of parameters is applied to stratified samples from a multivariate population of finite size. Attention is focused on estimators that can be expressed as functions of sample means. As in other applications of the jackknife method, an approximate relationship between the bias in an estimator and the sample size is exploited to reduce this bias by employing a linear combination of an estimate computed from all the data and several estimates each computed after omitting part of the data. Unlike some other applications to stratified sampling, however, where the data omitted are those for a group of sampling units that cut across all strata, the present application involves omitting just one sampling unit at a time, thereby compacting the region where approximate relationships are assumed to hold, and increasing the stability of the variance estimates. The relationships are derived by an analytic approach. Results are carried out far enough for use in second-order jackknife estimates of parameters and variances so as to eliminate bias to third-order moments of the variables observed. When there is just one stratum, the first-order estimators defined by equations (4.3) and (6-1), which are unbiased to second-order moments, are asymptotically the same -as those proposed by Tukey (1958).