Finite Model Parameters Research Articles

Parameter estimation for Gegenbaeur Arfisma processes with infinite variance innovations

. In this study, we consider the Gegenbauer ARFISMA process with α-stable innovations which belong to the class of infinite variance time series. This is a finite parameter model that exhibits long-range dependence, high variability, and Seasonal and /or Cyclical Long Memory (SCLM) variations. The Gegenbauer ARFISMA time series with α-stable innovations can be rewritten as linear processes (infinite order moving averages) with coefficients that decay slowly to zero and with innovations that are in the domain of attraction of a α-stable distribution with stability parameter ( 1 < α ≤ 2 ) . We assume that the coefficients of the linear process depend on an unknown parameter vector ξ which should be estimated from samples of length n. We prove that under some assumptions, a Whittle-type estimator ξ n for ξ is consistent (ξ n converges to the true value ξ 0 in probability as n ⟶ + ∞ ), and, we derive the limiting distribution of the resealed differences ( n / log ⁡ ( n ) ) 1 / α ( ξ n − ξ 0 ) . We perform some simulations to illustrate the consistency of the Whittle-type estimator ξ n for ξ.

Implicit correlations within phenomenological parametric models of the neutron star equation of state

The rapid increase in the number and precision of astrophysical probes of neutron stars in recent years allows for the inference of their equation of state. Observations target different macroscopic properties of neutron stars which vary from star to star, such as mass and radius, but the equation of state allows for a common description of all neutron stars. To connect these observations and infer the properties of dense matter and neutron stars simultaneously, models for the equation of state are introduced. Parametric models rely on carefully engineered functional forms that reproduce a large array of realistic equations of state. Such models benefit from their simplicity but are limited because any finite-parameter model cannot accurately approximate all possible equations of state. Nonparametric methods overcome this by increasing model freedom at the cost of increased complexity. In this study, we compare common parametric and nonparametric models, quantify the limitations of the former, and study the impact of modeling on our current understanding of high-density physics. We show that parametric models impose strongly model-dependent, and sometimes opaque, correlations between density scales. Such interdensity correlations result in tighter constraints that are unsupported by data and can lead to biased inference of the equation of state and of individual neutron star properties.

Characteristic Thermal Parameters in Electric Motors: Comparison Between Induction- and Permanent Magnet Excited Machine

The thermal modeling and design process of highly utilized electric machines is a complex task. The main heat paths within an electric drive are influenced by a variety of different thermal interfaces, that can mainly be described by thermal conduction and convection. The proper selection and estimation of these design parameters is challenging especially in the early design stage. This paper provides a systematic investigation evaluating inaccuracies and design influences of single thermal resistances, such as the convective heat transfer in the rotor-stator annulus, in the cooling jacket or interfaces between different machine components. Within the study, electromagnetic finite element models and thermal lumped parameter models of two traction drives are developed and validated using test bench measurements. The thermal design parameters are varied in a range resulting from intensive literature research and own laboratory experience. The influence of the design parameters in different operational points of the drives are studied in a sensitivity analysis.

Multi-Objective Optimization Design and Analysis of Double-Layer Winding Halbach Fault-Tolerant Motor

Double-layer winding halbach fault-tolerant motor (DLW-HFTM) combines the advantages of the permanent magnet motor and the fault-tolerant motor, which are beneficial to improve the characteristics of the joint robot. First, the structure of DLW-HFTM is proposed in view of the requirement of the fault tolerance of drive motor on the joint robot without degrading the other performances, such as the torque and the efficiency. Then, the working principle and initial design dimensions are depicted, and a finite element parameter model is established by Maxwell software. Furthermore, the design parameters are optimized by multi-objective sensitivity analysis. Finally, the electromagnetic performances before and after optimization are analyzed, including no-load back EMF, torque, loss, efficiency, etc. Meanwhile, the fault-tolerant performance of the motor is analyzed. The research results show that the DLW-HFTM can improve the fault-tolerance on the condition of meeting the design requirements.

Asymmetric, closed-form, finite-parameter models of multinomial choice

Class imbalance, where there are great differences between the number of observations associated with particular discrete outcomes, is common within transportation and other fields. In the statistics literature, one explanation for class imbalance that has been hypothesized is an asymmetric (rather than the typically symmetric) choice probability function. Unfortunately, few relatively simple models exist for testing this hypothesis in transportation settings—settings that are inherently multinomial. Our paper fills this gap.In particular, we address the following questions: “how can one construct asymmetric, closed-form, finite-parameter models of multinomial choice” and “how do such models compare against commonly used symmetric models?” Methodologically, we introduce (1) a new class of closed-form, finite-parameter, multinomial choice models, (2) a procedure for using these models to extend existing binary choice models to the multinomial setting, and (3) a procedure for creating new binary choice models (both symmetric and asymmetric). Together, our contributions allow us to create new asymmetric, closed-form, finite-parameter multinomial choice models. We demonstrate our methods by developing four new asymmetric, multinomial choice models. Empirically, most of our models strongly dominate the multinomial logit (MNL) model in terms of in-sample and out-of-sample log-likelihoods. Moreover, analyzing two policy applications, we find practical differences between the MNL and our new asymmetric models. Our results suggest that while asymmetric models may not always outperform symmetric ones, asymmetric choice models are worth testing because they might have better statistical performance and entail substantively different policy and financial implications when compared with traditional symmetric models, such as the MNL.

Quantitative Analysis and Classification of the Nasal Base Using a Parametric Model.

The nasal base view is often overlooked in rhinoplasty analysis and, unlike lateral and frontal views, lacks detailed quantitative analysis and descriptors. While shape-category analysis of the nasal base is well established, these descriptive methods remain subjective and do not facilitate quantitative analysis. To establish a simple and quantitative classification scheme using a multiple-parameter numerical model for analyzing and describing the shape of the nasal base. Deidentified photographs of the nasal base view were analyzed without knowledge of patients' pathology or medical history. Each nose was classified into 1 of 6 categories derived from literature (equilateral, narrow, flat, cloverleaf, boxy, and round). Finite parametric modeling was performed on each nose, and the correlations between the resulting parameters and the 6 categories were analyzed. Photographs for this study were acquired from the practice of a single facial plastic surgeon (B.J.F.W.) at a tertiary care academic medical center. One hundred twenty-one consecutive patients who had nasal base view photographs taken were included in the study. All of the 121 images were classified into 1 of the 6 categories by 1 reviewer (C.H.B.). The contour of each nasal base was curve fit to a 5-parameter numerical model. The 5 parameters controlled base size, deviation from the midline, projection-to-width ratio, degree of nasal alar recurvature, and anterior-posterior positioning of nasal base bulk. A numerical value for each nasal base shape type was predicted by the parametric model. In 121 patient photographs, the parametric model generated shapes that accurately matched the tracing of the actual nasal base contours with an average correlation coefficient of greater than 0.98. This finding indicates close approximation of the nasal base shape with the curve fit constructed by the PM. Parameters b (projection-to-width ratio) and e (roundedness) were shown to have significant differences among the groups (F statistic, 8.88; P < .001 and F statistic, 13.05; P < .001, respectively). These two curve-fit parameters alone could be used to classify nasal shape into 1 of the 6 clinically determined base geometries. A numerical approach to classify nasal base shape was developed using a 5-parameter model and tested against subjective analysis. This model may aid in the advancement of algorithm-driven objective nasal analysis techniques, preoperative modeling, intraoperative guidance, and surgical outcome measures beyond using Likert scales. NA.

Graphical LASSO based Model Selection for Time Series

We propose a novel graphical model selection scheme for high-dimensional stationary time series or discrete time processes. The method is based on a natural generalization of the graphical LASSO algorithm, introduced originally for the case of i.i.d. samples, and estimates the conditional independence graph of a time series from a finite length observation. The graphical LASSO for time series is defined as the solution of an l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -regularized maximum (approximate) likelihood problem. We solve this optimization problem using the alternating direction method of multipliers. Our approach is nonparametric as we do not assume a finite dimensional parametric model, but only require the process to be sufficiently smooth in the spectral domain. For Gaussian processes, we characterize the performance of our method theoretically by deriving an upper bound on the probability that our algorithm fails. Numerical experiments demonstrate the ability of our method to recover the correct conditional independence graph from a limited amount of samples.

Evaluation by FEM of the Influence of the Preheating and Post-Heating Treatments on Residual Stresses in Welding

During the last few years various experimental destructive and non-destructive methods were developed to evaluate residual stresses. However it is impossible to obtain a full residual stress distribution in welded structures by means of experimental methods. This disadvantage can be solved by means of computational analysis which allows to determine the whole stress and strain fields in complex structures. In this paper the temperature distribution and residual stresses were determined in a single-pass butt joint welded by GMAW (Gas Metal Arc Welding) process by finite element model (FEM). A 3D finite parametric element model has been carried out to analyze temperature distribution in butt weld joints and thermo-mechanical analyses were performed to evaluate resulting residual stresses. Temperature fields have been investigated by varying an initial preheating treatment. Moreover the technique of “element birth and death” was adopted to simulate the process of filler metal addition The high stresses were evaluated, with particular regard to fusion zone and heat affected zone. The influence of preheating and post-heating treatment on residual stresses was investigated. The residual stresses decrease when preheating temperature increases. The maximum value of longitudinal residual stresses without pre-heating can be reduced about 12% and 38% by using the preheating and post-heating process respectively.

Nonparametric Bayesian modeling of complex networks: an introduction

Modeling structure in complex networks using Bayesian nonparametrics makes it possible to specify flexible model structures and infer the adequate model complexity from the observed data. This article provides a gentle introduction to nonparametric Bayesian modeling of complex networks: Using an infinite mixture model as running example, we go through the steps of deriving the model as an infinite limit of a finite parametric model, inferring the model parameters by Markov chain Monte Carlo, and checking the model?s fit and predictive performance. We explain how advanced nonparametric models for complex networks can be derived and point out relevant literature.

Evaluating Statistical Hypotheses Using Weakly‐Identifiable Estimating Functions

Many statistical models arising in applications contain non- and weakly-identified parameters. Due to identifiability concerns, tests concerning the parameters of interest may not be able to use conventional theories and it may not be clear how to assess statistical significance. This paper extends the literature by developing a testing procedure that can be used to evaluate hypotheses under non- and weakly-identifiable semiparametric models. The test statistic is constructed from a general estimating function of a finite dimensional parameter model representing the population characteristics of interest, but other characteristics which may be described by infinite dimensional parameters, and viewed as nuisance, are left completely unspecified. We derive the limiting distribution of this statistic and propose theoretically justified resampling approaches to approximate its asymptotic distribution. The methodology's practical utility is illustrated in simulations and an analysis of quality-of-life outcomes from a longitudinal study on breast cancer.

Seasonal fractional ARIMA with stable innovations

We develop the theory of seasonally fractionally differenced ARIMA time series with stable infinite variance innovations establishing conditions for existence and invertibility. This is a finite parameter model which exhibits long range dependence, seasonality and high variability. We perform some simulations to illustrate the behavior of the model.

Finite Parameter Model for Doubly-Selective Channel Estimation in OFDM

To describe joint time-and frequency-selective (doubly-selective) channels in mobile broadband wireless communications, we propose to use the finite parameter model based on the same Bessel functions for each tap (Bessel model). An expression of channel estimation mean squared error (MSE) based on the finite parameter models in Orthogonal Frequency Division Multiplexing (OFDM) systems is derived. Then, our Bessel model is compared with commonly used finite parameter models in terms of the channel estimation MSE. Even if the channel taps have different channel correlations and some of the taps do not coincide with the Bessel function, the channel estimation MSE of the Bessel model is shown to be comparable or outperform existing models as validated by Monte-Carlo simulations over an ensemble of channels in typical urban and suburban environments.

Finite Parameter Model for Doubly-Selective Channel Estimation in OFDM

To describe joint time-and frequency-selective (doubly-selective) channels in mobile broadband wireless communications, we propose to use the finite parameter model based on the same Bessel functio...

Recursive Channel Estimation Based on Finite Parameter Model Using Reduced-Complexity Maximum Likelihood Equalizer for OFDM over Doubly-Selective Channels

To take intercarrier interference (ICI) attributed to time variations of the channel into consideration, the time- and frequency-selective (doubly-selective) channel is parameterized by a finite parameter model. By capitalizing on the finite parameter model to approximate the doubly-selective channel, a Kalman filter is developed for channel estimation. The ICI suppressing, reduced-complexity Viterbi-type Maximum Likelihood (RML) equalizer is incorporated into the Kalman filter for recursive channel tracking and equalization to improve the system performance. An enhancement in the channel tracking ability is validated by theoretical analysis, and a significant improvement in BER performance using the channel estimates obtained by the recursive channel estimation method is verified by Monte-Carlo simulations.

Broadband Semiparametric Estimation of the Memory Parameter of a Long‐Memory Time Series Using Fractional Exponential Models

We consider a fractional exponential, or FEXP estimator of the memory parameter of a stationary Gaussian long‐memory time series. The estimator is constructed by fitting a FEXP model of slowly increasing dimension to the log periodogram at all Fourier frequencies by ordinary least squares, and retaining the corresponding estimated memory parameter. We do not assume that the data were necessarily generated by a FEXP model, or by any other finite‐parameter model. We do, however, impose a global differentiability assumption on the spectral density except at the origin. Because of this, and its use of all Fourier frequencies, we refer to the FEXP estimator as a broadband semiparametric estimator. We demonstrate the consistency of the FEXP estimator, and obtain expressions for its asymptotic bias and variance. If the true spectral density is sufficiently smooth, the FEXP estimator can strongly outperform existing semiparametric estimators, such as the Geweke–Porter‐Hudak (GPH) and Gaussian semiparametric estimators (GSE), attaining an asymptotic mean squared error proportional to (log n)/n, where n is the sample size. In a simulation study, we demonstrate the merits of using a finite‐sample correction to the asymptotic variance, and we also explore the possibility of automatically selecting the dimension of the exponential model using Mallows’CL criterion.

Parameter estimation for infinite variance fractional ARIMA

Consider the fractional ARIMA time series with innovations that have infinite variance. This is a finite parameter model which exhibits both long-range dependence (long memory) and high variability. We prove the consistency of an estimator of the unknown parameters which is based on the periodogram and derive its asymptotic distribution. This shows that the results of Mikosch, Gadrich, Kluppelberg and Adler for ARMA time series remain valid for fractional ARIMA with long-range dependence. We also extend the limit theorem for sample autocovariances of infinite variance moving averages developed in Davis and Resnick to moving averages whose coefficients are not absolutely summable.

Efficiency. of infinite dimensional M‐ estimators

It is well‐known that maximum likelihood estimators are asymptotically normal with covariance equal to the inverse Fisher information in smooth, finite dimensional parametric models. Thus they are asymptotically efficient. A similar phenomenon has been observed for certain infinite dimensional parameter spaces. We give a simple proof of efficiency, starting from a theorem on asymptotic normality of infinite dimensional M‐estimators. The proof avoids the explicit calculation of the Fisher information. We also address Hadamard differentiability of the corresponding M‐functionals.

An asymptotic Wiener-Itô representation for the low frequency ordinates of the periodogram of a long memory time series

We consider a general long memory time series, assumed stationary and linear, but not necessarily Gaussian or generated by a finite-parameter model. For such a process, we derive the asymptotic joint distribution of the normalized periodogram at a fixed, finite collection of Fourier frequencies. The limiting distribution is represented in terms of Wiener-Itô integrals, and, for a single periodogram ordinate, it is an unequally weighted linear combination of independent χ 2 1 random variables. This result was previously known only in the Gaussian case. Our theorem may be useful for generalizing, beyond the Gaussian case, the applicability of a semiparametric method of estimating the long memory parameter based on log-periodogram regression.

Local asymptotic normality for multivariate linear processes

Local asymptotic normality is established for the likelihood ratios of multivariate linear processes generated by independent and identically distributed random vectors. The average Fisher informations for both infinite order AR and infinite order MA processes are derived and are presented in frequency domain. The frequency domain formulae for average Fisher information matrices of finite dimensional parameter models including finite order multivariate ARMA models are also presented.

ESTIMATION OF THE PREDICTION ERROR VARIANCE AND AN R2 MEASURE BY AUTOREGRESSIVE MODEL FITTING

Abstract. For predicting the future values of a stationary process {xt} (t= 0, pL 1, pL 2,…) on the basis of its past, two key parameters are the variance V (h), h≥ 1, of the h‐step prediction error and Z(h) ={R(0) ‐ V(h)}/R(0), the corresponding measure, in an R2 sense, of the predictability of the process from its past, where R(0) denotes the process variance. The estimation of V(h) and Z(h) from a realization of T consecutive observations of {xt} is considered, without requiring that the process follows a finite parameter model. Three different autoregressive estimators are examined and are shown to be asymptotically equivalent in the sense that as T∝ they have the same asymptotic normal distribution. The question of bias in estimating these parameters is also examined and a bias correction is proposed. Finite sample behaviour is investigated by a simulation study.