Asymptotic Bias in Parameter Estimation of AR-Processes Using Recursive Least Squares with Exponential Forgetting

Fitting N-mixture models to count data with unmodeled heterogeneity: Bias, diagnostics, and alternative approaches

The misspecification of gravity spatial interaction models has recently been described by the author. The bias in parameter estimates that results from such misspecification appears to produce the ‘map pattern effect’ or ‘spatial structure bias’ in estimated distance-decay parameters. A further aspect of the misspecification bias in gravity parameter estimates is explored here. The severity of the bias is shown to vary in a predictable manner with variations in spatial structure. In particular, the bias is shown to be dependent upon the pattern of accessibility that exists within a spatial system. The relevant aspects of this pattern are discussed for intraurban and interurban (or interregional) flow matrices. It is shown that from an examination of the spatial structure of centres in a spatial system it is possible, a priori, to identify whether significant bias will arise in the calibration of a gravity model. Certain configurations of centres are shown theoretically to produce maximal bias. The author thus answers the question, “why do gravity parameter estimates appear to be biased in some systems but not in others?”

This work proposes and evaluates two methods (CM1 and CM2) for detecting non-compliance using concentration-time data and for obtaining estimates of population pharmacokinetic model parameters in a population with prevalent non-compliance. CM1 estimates individual residual variability (RV) and identifies subjects with higher than average RV as non-compliant. Exclusion of subjects with high RV from the analysis dataset reduces the bias in the estimates of the model parameters. Various methods of identification and exclusion of non-compliant subjects were tested, compared, and shown to reduce or eliminate bias in parameter estimates associated with non-compliance. The tested methods were (i) a pre-defined cutoff value of the random effect on RV, (ii) sequential exclusion of subjects with the highest RV percentiles, and (iii) use of a mixture model for RV. CM2 is applicable for the data with a specific sampling pattern that includes a potentially non-compliant outpatient part with several trough samples followed by a dense profile after the inpatient (compliant) dose. It relies only on the doses known to be administered (e.g., inpatient doses). In this method, all concentration measurements during the outpatient part of the study (except the trough value immediately preceding the inpatient dose) are removed from the dataset and an additional parameter (individual relative bioavailability of the outpatient doses) is introduced. For a number of simulated datasets with various sampling schemes and non-compliance patterns the proposed methods allowed to identify subjects with compliance problems and to reduce or eliminate bias in the estimates of the model parameters.

The traditional Stochastic Frontier Model (SFM) suffers from a very restrictive assumption of independence of its error components and also limited ability to address heterogeneity (inefficiency effects) satisfactorily, thereby leading to potential biases in the estimation of model parameters, identification of inefficiency effect variables influencing efficiency and, ultimately, efficiency scores. This paper aims to investigate the consequences of ignoring any dependency in error components and heterogeneity in the stochastic frontier model, and proposes a copula-based SFM with heterogeneity to resolve such weaknesses based on a simulation study to prove its superiority over the traditional SFM, followed by an empirical application on a sample of rice producers from northern Thailand. We demonstrate that the proposed model, i.e., copula-based SFM with dependent error components and heterogeneity, is unbiased and robust. The simulation experiments show that the traditional SFM can cause biases in parameter estimation and severe overestimation of technical efficiency. The traditional SFM with heterogeneity also has similar consequences. However, just ignoring heterogeneity does not have a great impact on parameter estimation and technical efficiency compared to the consequence of ignoring dependency in error components. The empirical application of the proposed model results show that land, labor and material inputs are all significant drivers of rice production in our copula-based SFM with dependent error components and heterogeneity, whereas in the traditional SFM model only the land variable seems to be a significant driver of rice production. The mean technical efficiency (MTE) score was also overestimated by two points in the traditional SFM, i.e., MTE = 0.88 versus 0.86. Finally, results of the copula-based SFM with dependent error components and heterogeneity reveals that both subsistence pressure and the use of hired labor are significantly associated with technical inefficiency, whereas the traditional SFM could identify the effect of hired labor use only. Therefore, caution is necessary when interpreting results from the conventional SFM as the results may be biased, incomplete and/or inadequate.

Understanding of fish growth, the spatial variability in individual growth, and the potential drivers of such variability is a fundamental component of many ecological investigations. However, sampling gears are always size-selective, and this selectivity can result in biased parameter estimates that can lead to, for example, biased stock assessments that use growth estimates. Using seven flathead catfish (Pylodictis olivaris) populations from across the USA as an example, we investigated to what degree the incorporation of gear selectivity in growth models reduces size-selective bias in the estimation of growth parameters during macroscale investigations of fish growth. We developed a series of simulation scenarios by combining different sampling methods to obtain fish samples and different gear selectivity assumptions to estimate parameters. Results showed that the efficacy of incorporating gear selectivity in growth models to reduce size-selective sampling bias during macroscale investigations depends on multiple factors, including (i) the size distribution of small and large fish in the sample (which is a function of sampling methods), and (ii) consistency of sampling methods across populations. Incorporation of gear selectivity may reduce bias when data are lacking for large fish and when sampling methods are inconsistent across populations. Demographics of the sampled populations and the growth parameter of interest can also affect the utility of directly incorporating gear selectivity into growth models. Because multiple factors can influence the efficacy of incorporating gear selectivity into growth models, the decision to do so likely needs to be made on a case-by-case basis. This study extends the existing gear selectivity research by focusing on macroscale fish growth investigations across multiple populations and provides guidance on how to handle gear selectivity assumptions during such investigations.

Detection of Mastitis in Dairy Cattle by Use of Mixture Models for Repeated Somatic Cell Scores: A Bayesian Approach via Gibbs Sampling

Abstract. The asymptotic bias to terms of order T‐1, where T is the observed series length, is studied for estimators of the coefficients and disturbance variance in an AR(p) model. Reduction of the asymptotic bias by tapering is established and, if the tapering function is defined appropriately to depend on T, not only is the asymptotic bias reduced, but the asymptotic distribution of the estimators is not altered. In addition, the asymptotic biases of other time series parameter estimators constructed from the sample covariance function, such as several types of spectral estimators, can also be reduced by tapering.

Researchers often collect longitudinal data to model change over time in a phenomenon of interest. Inevitably, there will be some variation across individuals in specific time intervals between assessments. In this simulation study of growth curve modeling, we investigate how ignoring individual differences in time points when modeling change over time relates to convergence and admissibility of solutions, bias in estimates of parameters, efficiency, power to detect change over time, and Type I error rate. We manipulated magnitude of the individual differences in assessment times, distribution of assessment times, magnitude of change over time, number of time points, and sample size. In contrast to the correct analysis, ignoring individual differences in time points frequently led to inadmissible solutions, especially with few time points and small samples, regardless of the specific magnitude of individual differences that were ignored. Mean intercept and slope were generally estimated without bias. Ignoring individual differences in time points sometimes yielded overestimated intercept and slope variances and underestimated intercept–slope covariance and residual variance. Parameter efficiency as well as power and Type I error rates for the linear slope were unaffected by the type of analysis.

This article describes a Monte Carlo study of 2 methods for treating incomplete nonnormal data. Skewed, kurtotic data sets conforming to a single structured model, but varying in sample size, percentage of data missing, and missing-data mechanism, were produced. An asymptotically distribution-free available-case (ADFAC) method and structured-model expectation-maximization (EM) with nonnormality corrections were applied to these data sets, and the 2 methods were then compared in terms of bias in parameter estimates, bias in standard-error estimates, efficiency of parameter estimates, and model chi-squares. The results favored the nonnormality corrected EM over the ADFAC method in almost all respects, the only important exceptions involving (a) bias in standard-error estimates with large samples and (b) mixed results with respect to the efficiency of parameter estimates.

A Bayesian procedure is presented for parameter estimation in nonlinear flood event models. We derive a pooling diagnostic using Bayes factors to identify when it is reasonable to pool model parameters across storm events. A case study involving a quasi‐distributed, nonlinear flood event model and five watersheds in the southwest of Western Australia is presented to illustrate the capabilities and utility of the procedure. The results indicate that Markov chain Monte Carlo methods based on the Metropolis‐Hastings algorithm are useful tools for parameter estimation. We find that pooling is not justified for the model and data at hand. This suggests that current practices in nonlinear flood event modeling may be in need of urgent review.

A kernel functional representation of linear time-varying systems is employed in conjunction with B-spline functional approximation techniques to construct non-asymptotic state and parameter estimators for LTV systems. Total observability of the estimated system must be assumed. Practical identifiability conditions for parametric estimation are also stated. In the absence of output measurement noise the observer provides almost exact reconstruction of the system state and delivers high fidelity functional estimates of the time varying system parameters. It also shares the usual superior features of algebraic observers such as independence of the initial conditions of the system and good noise attenuation properties. Other advantages of the kernel and B-spline based identification of linear time-varying systems are elucidated.

System identification methods have extensive application in the aerospace industry’s experimental stability and control studies. Accurate aerodynamic modeling and system identification are necessary because they enable performance evaluation, flight simulation, control system design, fault detection, and model aircraft’s complex non-linear behavior. Various estimation methods yield different levels of accuracies with varying complexity and computational time requirements. The primary motivation of such studies is the accurate quantification of process noise. This research evaluates the performance of two recursive parameter estimation methods, viz.; First is the Fourier Transform Regression (FTR). The second approach describes the Extended version of Recursive Least Square (EFRLS), where E.F. refers to the Extended Forgetting factor. Also, the computational viability of these methods was analyzed for real-time application in aerodynamic parameter estimation for both linear and non-linear systems. While the first method utilizes the frequency domain to evaluate aerodynamic parameters, the second method works when noise covariances are unknown. The performance of both methods was assessed by benchmarking against parameter estimates from established methods like Extended Kalman Filter (EKF), Unscented Kalman Filter (UNKF), and Output Error Method (OEM).

When variable selection with stepwise regression and model fitting are conducted on the same data set, competition for inclusion in the model induces a selection bias in coefficient estimators away from zero. In proportional hazards regression with right-censored data, selection bias inflates the absolute value of parameter estimate of selected parameters, while the omission of other variables may shrink coefficients toward zero. This paper explores the extent of the bias in parameter estimates from stepwise proportional hazards regression and proposes a bootstrap method, similar to those proposed by Miller (Subset Selection in Regression, 2nd edn. Chapman & Hall/CRC, 2002) for linear regression, to correct for selection bias. We also use bootstrap methods to estimate the standard error of the adjusted estimators. Simulation results show that substantial biases could be present in uncorrected stepwise estimators and, for binary covariates, could exceed 250% of the true parameter value. The simulations also show that the conditional mean of the proposed bootstrap bias-corrected parameter estimator, given that a variable is selected, is moved closer to the unconditional mean of the standard partial likelihood estimator in the chosen model, and to the population value of the parameter. We also explore the effect of the adjustment on estimates of log relative risk, given the values of the covariates in a selected model. The proposed method is illustrated with data sets in primary biliary cirrhosis and in multiple myeloma from the Eastern Cooperative Oncology Group.

Gravitational-wave (GW) astronomy seeks to extract information about astrophysical systems from the GW signals they emit. For coalescing compact-binary sources this requires accurate model templates for the inspiral and, potentially, the subsequent merger and ringdown. Models with frequency-domain waveforms that terminate abruptly in the sensitive band of the detector are often used for parameter-estimation studies. We show that the abrupt waveform termination contains significant information that affects parameter-estimation accuracy. If the sharp cutoff is not physically motivated, this extra information can lead to misleadingly good accuracy claims. We also show that using waveforms with a cutoff as templates to recover complete signals can lead to biases in parameter estimates. We evaluate when the information content in the cutoff is likely to be important in both cases. We also point out that the standard Fisher matrix formalism, frequently employed for approximately predicting parameter-estimation accuracy, cannot properly incorporate an abrupt cutoff that is present in both signals and templates; this observation explains some previously unexpected results found in the literature. These effects emphasize the importance of using complete waveforms with accurate merger and ringdown phases for parameter estimation.

Population pharmacokinetic (PK) data collected from routine clinical practice offers a rich source of valuable information. However, in observational population PK data, accurate time information for blood samples is often missing, resulting in measurement errors (ME) in the sampling time variable. The goal of this study was to investigate the effects on model parameters when a scheduled time is used instead of the actual blood sampling time, and to propose ME correction methods. Simulation studies were conducted based on two major factors: the curvature in PK profiles and the size of ME. As ME correction methods, transform both sides (TBS) models were developed with application of Box-Cox power transformation and Taylor expansion. The TBS models were compared to a conventional population PK model using simulations. The most important determinant of bias due to time ME was the degree of curvature (nonlinearity) in PK profiles; the smaller the curvature around sampling times, the smaller the associated bias. The second important determinant was the magnitude of ME; the larger the ME, the larger the bias. The proposed TBS models performed better than a conventional population PK modeling when curvature and ME were substantial. Time ME in sampling time can lead to bias on the parameter estimators. The following practical recommendations are provided: 1) when the curvature of PK profiles is small, conventional population PK modeling is robust to even large ME; and 2) when the curvature is moderate or large, the proposed methodology reduces bias in parameter estimates.