Order Selection Procedure Research Articles

Temporal evolution of the extreme excursions of multivariate k$$ k $$th order Markov processes with application to oceanographic data

AbstractWe develop two models for the temporal evolution of extreme events of multivariate th order Markov processes. The foundation of our methodology lies in the conditional extremes model of Heffernan and Tawn (Journal of the Royal Statistical Society: Series B (Methodology), 2014, 66, 497–546), and it naturally extends the work of Winter and Tawn (Journal of the Royal Statistical Society: Series C (Applied Statistics), 2016, 65, 345–365; Extremes, 2017, 20, 393–415) and Tendijck et al. (Environmetrics 2019, 30, e2541) to include multivariate random variables. We use cross‐validation‐type techniques to develop a model order selection procedure, and we test our models on two‐dimensional meteorological‐oceanographic data with directional covariates for a location in the northern North Sea. We conclude that the newly‐developed models perform better than the widely used historical matching methodology for these data.

Local Polynomial Order in Regression Discontinuity Designs

Treatment effect estimates in regression discontinuity (RD) designs are often sensitive to the choice of bandwidth and polynomial order, the two important ingredients of widely used local regression methods. While Imbens and Kalyanaraman and Calonico, Cattaneo, and Titiunik provided guidance on bandwidth, the sensitivity to polynomial order still poses a conundrum to RD practitioners. It is understood in the econometric literature that applying the argument of bias reduction does not help resolve this conundrum, since it would always lead to preferring higher orders. We therefore extend the frameworks of Imbens and Kalyanaraman and Calonico, Cattaneo, and Titiunik and use the asymptotic mean squared error of the local regression RD estimator as the criterion to guide polynomial order selection. We show in Monte Carlo simulations that the proposed order selection procedure performs well, particularly in large sample sizes typically found in empirical RD applications. This procedure extends easily to fuzzy regression discontinuity and regression kink designs.

Wasserstein autoregressive models for density time series

Data consisting of time‐indexed distributions of cross‐sectional or intraday returns have been extensively studied in finance, and provide one example in which the data atoms consist of serially dependent probability distributions. Motivated by such data, we propose an autoregressive model for density time series by exploiting the tangent space structure on the space of distributions that is induced by the Wasserstein metric. The densities themselves are not assumed to have any specific parametric form, leading to flexible forecasting of future unobserved densities. The main estimation targets in the order‐p Wasserstein autoregressive model are Wasserstein autocorrelations and the vector‐valued autoregressive parameter. We propose suitable estimators and establish their asymptotic normality, which is verified in a simulation study. The new order‐p Wasserstein autoregressive model leads to a prediction algorithm, which includes a data driven order selection procedure. Its performance is compared to existing prediction procedures via application to four financial return data sets, where a variety of metrics are used to quantify forecasting accuracy. For most metrics, the proposed model outperforms existing methods in two of the data sets, while the best empirical performance in the other two data sets is attained by existing methods based on functional transformations of the densities.

MNDL Sparsity Order Selection for Compressed Sensing with Application in ECG Compression.

One of the main challenges in sparse signal recovery in compressed sensing framework is determining the sparsity order. Most model order selection methods introduce a penalty term for the number of parameters, however do not consider the variance of the observation and measurement noise. Minimum Noiseless Description Length (MNDL), on the other hand, considers these factors and provides a more robust results in order selection. Nevertheless, it requires noise variance (equivalently SNR) estimate for the order selection procedure. In this paper, a new method is introduced to estimate the variance of the observation noise within the MNDL order selection method. The fully automated method simultaneously provides the SNR estimate and sparsity order and does not require any prior partial knowledge or assumption on the noise variance. Simulation results for ECG compression show advantages of the proposed automated MNDL over the existing approaches in the sense of parameter estimation error and SNR improvement.

Reliability and agreement of the IsoKai isokinetic lift test - A test used for admission to the Swedish Armed Forces.

This study was performed to evaluate the reliability and agreement of the IsoKai isokinetic lift test as it is currently administered in admission to the Swedish Armed Forces. The study included an intrarater (n = 534) and interrater reliability sample (n = 137), of Swedish male conscripts who performed the test on two test occasions about two hours apart. Two-to-four lifts were performed at each occasion, and the highest mean (IsoKaiMF) and peak force (IsoKaiPF) produced (N) were used for evaluation. All intraclass coefficients showed excellent reliability. The interrater analyses resulted in intraclass coefficients of 0.942 (95% CI; 0.920–0.959) and 0.858 (95% CI; 0.806–0.896) for the IsoKaiMF and IsoKaiPF, respectively, while the corresponding coefficients for the intrarater analyses were 0.935 (95% CI; 0.923–0.946) and 0.865 (95% CI; 0.842–0.886). Agreement, the capability of a test to detect changes, was assessed by the standard error of measurement (SEM/SEM%) and the smallest real difference (SRD/SRD%). These estimate indicated that it is possible to achieve measurements relevant to use in real practice with the IsoKai isokinetic lift test. Bland and Altman analyses revealed no systematic errors in either sample. Based on these findings, the IsoKai isokinetic lift test is suggested to be a highly reliable test for maximal dynamic muscular strength. The test could be of use in selection procedures in order to accurately evaluate maximal dynamic muscular strength, and for evaluating longitudinal changes in strength.

Use of different chemometric approaches for an estimation of soil properties at field scale with near infrared spectroscopy

AbstractVisible and near infrared spectroscopy (vis‐NIRS) may be useful for an estimation of soil properties in arable fields, but the quality of results are often variable depending on the applied chemometric approach. Partial least squares regression (PLSR) may be replaced by approaches which employ supervised learning methods or variable selection procedures in order to increase the proportion of informative wavelengths used in the estimation procedure, to reduce the noise of the spectra and to find the best fitting solution. Objectives were (1) to compare the usefulness of PLSR with either PLSR combined with a genetic algorithm (GA‐PLSR) or support vector machine regression (SVMR) for an estimation of soil organic carbon (SOC), total nitrogen (N), pH, cation exchange capacity (CEC) and soil texture for surface soils (0–5 cm, n = 144) of an arable field in Bangalore (India) and (2) to test and optimize different calibration strategies for GA‐PLSR for an improved estimation of soil properties. PLSR was useful for an estimation of SOC, N, sand and clay. In the cross‐validation (n = 96), accuracies of estimated soil properties generally decreased in the order GA‐PLSR > SVMR > PLSR. However, the order of estimation accuracies for the random validation sample (n = 48) changed to SVMR > GA‐PLSR > PLSR for SOC, N, pH, and CEC, whereas for clay the order changed to SVMR > PLSR > GA‐PLSR. A sequential procedure, which used the most frequently selected wavelengths of the GA‐PLSR runs, proved to be useful for an improved estimation of SOC and N. Overall, SVMR especially improved estimations of SOC and clay, whereas GA‐PLSR was particularly useful for SOC and N and it was the only approach which successfully estimated CEC in cross‐validation and validation.

Model order selection in periodic long memory models

An automatic model order selection procedure for k-factor Gegenbauer processes is proposed. The procedure is based on sequential tests of the maximum of the periodogram and semiparametric estimators of the model parameters. As a byproduct, a generalized version of Walker’s large sample g-test is introduced that allows to test for persistent periodicity in stationary short memory processes. Simulation studies show that the model order selection procedure performs well in identifying the correct order under various circumstances. An application to Californian electricity load data illustrates its value in empirical analyses and allows new insights into the periodicity of this process that has been the subject of several studies.

Hidden Markov Models With Applications in Cell Adhesion Experiments

Estimation of the number of hidden states is challenging in hidden Markov models. Motivated by the analysis of a specific type of cell adhesion experiments, a new framework based on a hidden Markov model and double penalized order selection is proposed. The order selection procedure is shown to be consistent in estimating the number of states. A modified expectation–maximization algorithm is introduced to efficiently estimate parameters in the model. Simulations show that the proposed framework outperforms existing methods. Applications of the proposed methodology to real data demonstrate the accuracy of estimating receptor–ligand bond lifetimes and waiting times which are essential in kinetic parameter estimation. Supplementary materials for this article are available online.

A black box method for solving the complex exponentials approximation problem

A common problem, arising in many different applied contexts, consists in estimating the number of exponentially damped sinusoids whose weighted sum best fits a finite set of noisy data and in estimating their parameters. Many different methods exist to this purpose. The best of them are based on approximate Maximum Likelihood estimators, assuming to know the number of damped sinusoids, which can then be estimated by an order selection procedure. As the problem can be severely ill posed, a stochastic perturbation method is proposed which provides better results than Maximum Likelihood based methods when the signal-to-noise ratio is low. The method depends on some hyperparameters which turn out to be essentially independent of the application. Therefore they can be fixed once and for all, giving rise to a black box method.

Order selection in nonlinear time series models with application to the study of cell memory

Cell adhesion experiments are biomechanical experiments studying the binding of a cell to another cell at the level of single molecules. Such a study plays an important role in tumor metastasis in cancer study. Motivated by analyzing a repeated cell adhesion experiment, a new class of nonlinear time series models with an order selection procedure is developed in this paper. Due to the nonlinearity, there are two types of overfitting. Therefore, a double penalized approach is introduced for order selection. To implement this approach, a global optimization algorithm using mixed integer programming is discussed. The procedure is shown to be asymptotically consistent in estimating both the order and parameters of the proposed model. Simulations show that the new order selection approach outperforms standard methods. The finite-sample performance of the estimator is also examined via a simulation study. The application of the proposed methodology to a T-cell experiment provides a better understanding of the kinetics and mechanics of cell adhesion, including quantifying the memory effect on a repeated unbinding force experiment and identifying the order of the memory.

Model identification for infinite variance autoregressive processes

We consider model identification for infinite variance autoregressive time series processes. It is shown that a consistent estimate of autoregressive model order can be obtained by minimizing Akaike’s information criterion, and we use all-pass models to identify noncausal autoregressive processes and estimate the order of noncausality (the number of roots of the autoregressive polynomial inside the unit circle in the complex plane). We examine the performance of the order selection procedures for finite samples via simulation, and use the techniques to fit a noncausal autoregressive model to stock market trading volume data.

A Simulation Integrated Investment Project Ranking and Selection Approach

Enterprises are confronted with several project alternatives that they assume to gain revenue in the future, but their own economical resources are limited to carry out all alternatives. Therefore, a decision process arises to prioritize and select among alternatives according to the predetermined goals and criteria to reach the maximum utilization. On the other hand, in project evaluation, the values of project parameters are often assumed to be known with complete certainty. However, project parameters normally change during a life cycle of the project, and it is necessary to consider uncertainty and risk phenomena while evaluating projects. Simulation-based project evaluation approaches enable to make more reliable investment decision since they permit to include future uncertainty and risk in analysis process. In this article, a novel simulation-based optimal decision approach is proposed for evaluating and comparing investment projects under uncertain and/or risky environments. The phases of the proposed approach are; (a) developing the effectiveness measure formulation of a project, (b) identifying and checking all controllable project parameters that affect the measure, (c) developing simulation model for the measure, and (d) performing the project ranking and selection procedures in order to rank and select the projects. Three ranking and selection procedures, previously used for comparing performances of the different production/service systems, are embedded in the proposed approach.

GANC: Greedy agglomerative normalized cut for graph clustering

This paper describes a graph clustering algorithm that aims to minimize the normalized cut criterion and has a model order selection procedure. The performance of the proposed algorithm is comparable to spectral approaches in terms of minimizing normalized cut. However unlike spectral approaches, the proposed algorithm scales to graphs with millions of nodes and edges. The algorithm consists of three components that are processed sequentially: a greedy agglomerative hierarchical clustering procedure, model order selection, and a local refinement.

Energy-efficient collaborative tracking in wireless sensor networks

In this paper, the problem of collaborative tracking of mobile nodes in wireless sensor networks is addressed. Aiming at an efficient resource exploitation, the research adopts a strategy of combining target tracking with node selection procedures in order to select informative sensors to minimise the energy consumption of the tracking task. We layout a cluster-based architecture to address the limitations in computational power, battery capacity and communication capacities of the sensor devices. We consider the computation of the Posterior Cramer-Rao Bound (PCRB) on the tracking accuracy based on Received Signal Strength (RSS) measurements. To track mobile nodes two particle filters are used: the bootstrap particle filter and the unscented one, both in the centralised and in the distributed manner. Their performances are compared through simulation with the theoretical lower PCRB. The node selection problem is formulated as a cross-layer energy minimisation problem, whose solution is addressed by a greedy-type algorithm, both in the static scenario and in the dynamic scenario.

An Information-Theoretic Approach for Energy-Efficient Collaborative Tracking in Wireless Sensor Networks

The problem of collaborative tracking of mobile nodes in wireless sensor networks is addressed. By using a novel metric derived from the energy model in LEACH (W.B. Heinzelman, A.P. Chandrakasan and H. Balakrishnan, Energy-Efficient Communication Protocol for Wireless Microsensor Networks, in: Proceedings of the 33rd Hawaii International Conference on System Sciences (HICSS '00), 2000) and aiming at an efficient resource solution, the approach adopts a strategy of combining target tracking with node selection procedures in order to select informative sensors to minimize the energy consumption of the tracking task. We layout a cluster-based architecture to address the limitations in computational power, battery capacity and communication capacities of the sensor devices. The computation of the posterior Cramer-Rao bound (PCRB) based on received signal strength measurements has been considered. To track mobile nodes two particle filters are used: the bootstrap particle filter and the unscented particle filter, both in the centralized and in the distributed manner. Their performances are compared with the theoretical lower bound PCRB. To save energy, a node selection procedure based on greedy algorithms is proposed. The node selection problem is formulated as a cross-layer optimization problem and it is solved using greedy algorithms.

Closed loop identification method using a subspace approach

This paper presents a free model reduction closed loop subspace identification method for multivariable systems operating in a well posed closed loop environment. This allows to determine the impulse response of the system from the identification of the control system sensitivity functions. The rational behind the proposed method is twofold. Firstly, the general purpose design features of the subspace system identification approach and its inherent numerical robustness. Secondly, the model reduction performed in the available subspace identification is removed by a proper order selection procedure. A bias analysis is carried out to emphasize the robustness features.

Work order release and input sequencing for a printed circuit board assembly cell

The problem of work order release and input sequencing for a printed circuit board assembly cell is addressed. Some of the placement machines in the assembly cell are highly flexible and their setup is changed according to the component requirements of released orders. The selection of work orders to form a new batch to be released into the shop floor and the sequencing of individual orders within a batch are two problems which are solved repeatedly. For solving the work order selection problem a MILP model is solved and its results for the overall system performance are compared to a bottleneck oriented heuristic. The system performance is measured by a simulation model of the respective cell. In addition, local dispatching and sequencing rules are applied within the simulation model in order to model the material flows. The computational experiments start with evaluating the different work order selection procedures. A numerical study for different order arrival processes is conducted and the contribution of input sequencing to the system performance is discussed. The experiments are based on concrete industry data.

Residential rehabilitation for drug users: a review of 13 months' intake to a therapeutic community.

Residential rehabilitation based on 'therapeutic community' treatment for drug users is a treatment option which is attractive to GPs and others referring drug users for treatment. Whilst there is evidence that maintenance-based programmes for drug users are effective, there have been fewer attempts to evaluate the effectiveness of abstinence-based programmes which are relatively more intensive and expensive interventions. This paper reports and evaluates the outcomes for 13 months' intake of 138 drug users to a residential community. We carried out a retrospective cohort study using existing clinical and residential record data. The setting is a residential rehabilitation centre run by the charity Phoenix House in Sheffield, UK, offering a 1-year programme for heroin addicts including community detoxification overseen by primary care specialist doctors and residential rehabilitation. Participants were all patients who entered treatment between 1 February 1998 and 28 February 1999 inclusive. An analysis was carried out of clinical records and other records kept by clinicians and staff at the centre. Outcome measures were numbers of days of retention in treatment and reasons for departure, categorized as completed treatment, planned or unplanned departure and expulsion from the programme. For patients who underwent in-house detoxification, a further outcome measure was whether or not detoxification was complete at discharge. Heroin was the main drug of abuse in 85% of admissions. Mean length of time for which individuals had been drug dependent was 8 years (range 1.3-20.1 years). The mean length of stay was 80.2 days (range 1-394, 95% confidence interval 61.8-98.6). Thirty-four individuals (25%) completed 90 days or more. No association was found between length of stay and age, sex, route of administration, polydrug use, length of time addicted or age of first addiction. Sixty-five per cent of those who received in-house detoxification completed the detoxification period. When patients were classified as 'successes' or 'failures' by reason for departure from the programme, 94 (68.1%) were classified as failures and 18 (13.0%) as successes. Data were unavailable for 26 patients. Success was not associated with any characteristic at entry apart from being drug free as opposed to requiring detoxification (P = 0.048, chi-square = 6.06, df = 2). This study shows overall low levels of programme completion and high levels of unplanned departure and eviction from the programme amongst these long-term drug users. On the other hand, the importance of abstinence for those who achieve it in residential rehabilitation should not be underestimated, nor should the possibility that long-term outcomes are influenced by the learning process involved in the intervention. It may be possible to operate better selection procedures in order to optimize outcomes.

Data Driven Order Selection for Projection Estimator of the Spectral Density of Time Series with Long Range Dependence

Fractional exponential (FEXP) models have been introduced by Robinson (1991) and Beran (1993) to model the spectral density of a covariance stationary long‐range dependent process. In this class of models, the spectral density f(x) of the process is decomposed as f(x) = |1 − exp(ix)|−2df*(x), where f*(x) accounts for the short‐memory component. In this contribution, FEXP models are used to construct semi‐parametric estimates of the fractional differencing coefficient and of the spectral density, by considering an infinite Fourier series expansion of log f*(x). A data‐driven order selection procedure, adapted from the Mallows' Cp procedure, is proposed to determine the order of truncation. The optimality of the data‐driven procedure is established, under mild assumptions on the short‐memory component f*(x). A limited Monte‐Carlo experiment is presented to support our claims.

The selection of the order and identification of nonzero elements in the polynomial matrices of vector autoregressive processes

In this paper we show how the residual white noise autoregressive order selection procedure can be used not only to effectively identify the order of Vector Autoregressive (VAR) processes, but also with the use of a seemingly-unrelated-type of estimation method to identify nonzero elements in the polynomial matrices of VAR models. Results from extensive simulation studies as well as from economic data are presented to demonstrate the performance of the proposed method.