scholarly journals A nondegenerate Vuong test and post selection confidence intervals for semi/nonparametric models

2020 ◽  
Vol 11 (3) ◽  
pp. 983-1017
Author(s):  
Zhipeng Liao ◽  
Xiaoxia Shi
Keyword(s):  
Model Selection ◽  
Size Control ◽  
Parametric Models ◽  
Model Parameters ◽  
Local Alternatives ◽  
Finite Sample ◽  
Inference Procedure ◽  
Uniform Size ◽  
Nonparametric Models ◽  
Asymptotic Size

This paper proposes a new model selection test for the statistical comparison of semi/non‐parametric models based on a general quasi‐likelihood ratio criterion. An important feature of the new test is its uniformly exact asymptotic size in the overlapping nonnested case, as well as in the easier nested and strictly nonnested cases. The uniform size control is achieved without using pretesting, sample‐splitting, or simulated critical values. We also show that the test has nontrivial power against all n ‐local alternatives and against some local alternatives that converge to the null faster than n . Finally, we provide a framework for conducting uniformly valid post model selection inference for model parameters. The finite sample performance of the nondegenerate test and that of the post model selection inference procedure are illustrated in a mean‐regression example by Monte Carlo.

scholarly journals ECONOMETRIC ANALYSIS OF CONTINUOUS TIME MODELS: A SURVEY OF PETER PHILLIPS’S WORK AND SOME NEW RESULTS

2014 ◽  
Vol 30 (4) ◽  
pp. 737-774 ◽  
Author(s):  
Jun Yu
Keyword(s):  
Continuous Time ◽  
Econometric Analysis ◽  
Asymptotic Distributions ◽  
Parametric Models ◽  
Finite Sample ◽  
Nonparametric Models ◽  
Inference Problems ◽  
Long Span ◽  
Wide Range ◽  
Continuous Time Models

Econometric analysis of continuous time models has drawn the attention of Peter Phillips for 40 years, resulting in many important publications by him. In these publications he has dealt with a wide range of continuous time models and the associated econometric problems. He has investigated problems from univariate equations to systems of equations, from asymptotic theory to finite sample issues, from parametric models to nonparametric models, from identification problems to estimation and inference problems, and from stationary models to nonstationary and nearly nonstationary models. This paper provides an overview of Peter Phillips’ contributions in the continuous time econometrics literature. We review the problems that have been tackled by him, outline the main techniques suggested by him, and discuss the main results obtained by him. Based on his early work, we compare the performance of three asymptotic distributions in a simple setup. Results indicate that thein-fillasymptotics significantly outperforms thelong-spanasymptotics and thedoubleasymptotics.

NONPARAMETRIC TWO-STEP SIEVE M ESTIMATION AND INFERENCE

2018 ◽  
Vol 34 (6) ◽  
pp. 1281-1324 ◽  
Author(s):  
Jinyong Hahn ◽  
Zhipeng Liao ◽  
Geert Ridder
Keyword(s):  
Gaussian Approximation ◽  
Asymptotic Variance ◽  
Closed Form Expression ◽  
Second Step ◽  
Consistent Estimate ◽  
Finite Sample ◽  
Inference Procedure ◽  
Nonparametric Models ◽  
M Estimation ◽  
Nonparametric Estimates

This article studies two-step sieve M estimation of general semi/nonparametric models, where the second step involves sieve estimation of unknown functions that may use the nonparametric estimates from the first step as inputs, and the parameters of interest are functionals of unknown functions estimated in both steps. We establish the asymptotic normality of the plug-in two-step sieve M estimate of a functional that could be root-n estimable. The asymptotic variance may not have a closed form expression, but can be approximated by a sieve variance that characterizes the effect of the first-step estimation on the second-step estimates. We provide a simple consistent estimate of the sieve variance, thereby facilitating Wald type inferences based on the Gaussian approximation. The finite sample performance of the two-step estimator and the proposed inference procedure are investigated in a simulation study.

scholarly journals Analytical and Numerical Connections between Fractional Fickian and Intravoxel Incoherent Motion Models of Diffusion MRI

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1963
Author(s):  
Jingting Yao ◽  
Muhammad Ali Raza Anjum ◽  
Anshuman Swain ◽  
David A. Reiter
Keyword(s):  
Skeletal Muscle ◽  
Goodness Of Fit ◽  
Numerical Models ◽  
Tissue Perfusion ◽  
Parametric Models ◽  
Intravoxel Incoherent Motion ◽  
Fickian Diffusion ◽  
Model Parameters ◽  
Mathematical Framework ◽  
Stretched Exponential

Impaired tissue perfusion underlies many chronic disease states and aging. Diffusion-weighted imaging (DWI) is a noninvasive MRI technique that has been widely used to characterize tissue perfusion. Parametric models based on DWI measurements can characterize microvascular perfusion modulated by functional and microstructural alterations in the skeletal muscle. The intravoxel incoherent motion (IVIM) model uses a biexponential form to quantify the incoherent motion of water molecules in the microvasculature at low b-values of DWI measurements. The fractional Fickian diffusion (FFD) model is a parsimonious representation of anomalous superdiffusion that uses the stretched exponential form and can be used to quantify the microvascular volume of skeletal muscle. Both models are established measures of perfusion based on DWI, and the prognostic value of model parameters for identifying pathophysiological processes has been studied. Although the mathematical properties of individual models have been previously reported, quantitative connections between IVIM and FFD models have not been examined. This work provides a mathematical framework for obtaining a direct, one-way transformation of the parameters of the stretched exponential model to those of the biexponential model. Numerical simulations are implemented, and the results corroborate analytical results. Additionally, analysis of in vivo DWI measurements in skeletal muscle using both biexponential and stretched exponential models is shown and compared with analytical and numerical models. These results demonstrate the difficulty of model selection based on goodness of fit to experimental data. This analysis provides a framework for better interpreting and harmonizing perfusion parameters from experimental results using these two different models.

scholarly journals Assessing model mismatch and model selection in a Bayesian uncertainty quantification analysis of a fluid-dynamics model of pulmonary blood circulation

2020 ◽  
Vol 17 (173) ◽  
pp. 20200886
Author(s):  
L. Mihaela Paun ◽  
Mitchel J. Colebank ◽  
Mette S. Olufsen ◽  
Nicholas A. Hill ◽  
Dirk Husmeier
Keyword(s):  
Model Selection ◽  
Mean Squared Error ◽  
Formal Model ◽  
Circulation Model ◽  
Noise Model ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Imaging Data ◽  
Micro Computed Tomography ◽  
Model Mismatch

This study uses Bayesian inference to quantify the uncertainty of model parameters and haemodynamic predictions in a one-dimensional pulmonary circulation model based on an integration of mouse haemodynamic and micro-computed tomography imaging data. We emphasize an often neglected, though important source of uncertainty: in the mathematical model form due to the discrepancy between the model and the reality, and in the measurements due to the wrong noise model (jointly called ‘model mismatch’). We demonstrate that minimizing the mean squared error between the measured and the predicted data (the conventional method) in the presence of model mismatch leads to biased and overly confident parameter estimates and haemodynamic predictions. We show that our proposed method allowing for model mismatch, which we represent with Gaussian processes, corrects the bias. Additionally, we compare a linear and a nonlinear wall model, as well as models with different vessel stiffness relations. We use formal model selection analysis based on the Watanabe Akaike information criterion to select the model that best predicts the pulmonary haemodynamics. Results show that the nonlinear pressure–area relationship with stiffness dependent on the unstressed radius predicts best the data measured in a control mouse.

Near Observational Equivalence and Theoretical size Problems with Unit Root Tests

1996 ◽  
Vol 12 (4) ◽  
pp. 724-731 ◽  
Author(s):  
Jon Faust
Keyword(s):  
Unit Root ◽  
Sufficient Conditions ◽  
Unit Root Test ◽  
Asymptotic Distributions ◽  
Unit Root Tests ◽  
Finite Sample ◽  
Test Procedures ◽  
Asymptotic Size ◽  
Finite Sample Size ◽  
Topological Sense

Said and Dickey (1984,Biometrika71, 599–608) and Phillips and Perron (1988,Biometrika75, 335–346) have derived unit root tests that have asymptotic distributions free of nuisance parameters under very general maintained models. Under models as general as those assumed by these authors, the size of the unit root test procedures will converge to one, not the size under the asymptotic distribution. Solving this problem requires restricting attention to a model that is small, in a topological sense, relative to the original. Sufficient conditions for solving the asymptotic size problem yield some suggestions for improving finite-sample size performance of standard tests.

Combining Non-Parametric and Parametric Models for Stable and Computationally Efficient Battery Health Estimation

2020 ◽  
Author(s):  
Antti Aitio ◽  
David Howey
Keyword(s):  
Latent Variables ◽  
Linear Time ◽  
Full Range ◽  
Real Life ◽  
Internal Resistance ◽  
State Of Charge ◽  
Parametric Models ◽  
Model Parameters ◽  
Battery Management ◽  
Resistance Change

Abstract Equivalent circuit models for batteries are commonly used in electric vehicle battery management systems to estimate state of charge and other important latent variables. They are computationally inexpensive, but suffer from a loss of accuracy over the full range of conditions that may be experienced in real-life. One reason for this is that the model parameters, such as internal resistance, change over the lifetime of the battery due to degradation. However, estimating long term changes is challenging, because parameters also change with state of charge and other variables. To address this, we modelled the internal resistance parameter as a function of state of charge and degradation using a Gaussian process (GP). This was performed computationally efficiently using an algorithm [1] that interprets a GP to be the solution of a linear time-invariant stochastic differential equation. As a result, inference of the posterior distribution of the GP scales as 𝒪(n) and can be implemented recursively using a Kalman filter.

Parametric Models of Ultrasonic Piezoelectric Transducers over a Wide Temperature Range

2015 ◽  
Vol 2015 (HiTEN) ◽  
pp. 000266-000272 ◽  
Author(s):  
Steven A. Morris ◽  
Jeremy Townsend
Keyword(s):  
Dielectric Constant ◽  
Temperature Dependence ◽  
Coupling Coefficient ◽  
Thin Disk ◽  
Piezoelectric Transducers ◽  
Parametric Models ◽  
Model Parameters ◽  
Linear Temperature Dependence ◽  
Linear Temperature ◽  
Wide Range

Piezoelectric ultrasonic transducers are used extensively in well logging and logging-while-drilling applications for pulse-echo operation. We present a method of modeling the operation of ultrasonic thin-disk piezoelectric transducers over a wide range of temperatures. The model is based on using Redwood's version of Mason's model of thin-disk transducers. Laboratory measurements in the oven of non-backed transducers in air are used to extract the Mason model parameters as a function of temperature. Derived parameters are frequency-thickness constant, dielectric constant, and thickness mode coupling coefficient. A fourth parameter, bulk density, is measured independently and assumed constant over temperature. Temperature dependence of frequency thickness constant and coupling coefficient are modeled as linear temperature coefficients. Temperature dependence of the dielectric constant must be specified as a table because of the non-linear temperature dependence of that parameter.

scholarly journals Universal inference

2020 ◽  
Vol 117 (29) ◽  
pp. 16880-16890 ◽  
Author(s):  
Larry Wasserman ◽  
Aaditya Ramdas ◽  
Sivaraman Balakrishnan
Keyword(s):  
Maximum Likelihood ◽  
Likelihood Ratio ◽  
Likelihood Ratio Statistic ◽  
Model Misspecification ◽  
Null Distribution ◽  
Regularity Conditions ◽  
Ratio Test ◽  
Finite Sample ◽  
Confidence Sets ◽  
Nonparametric Models

We propose a general method for constructing confidence sets and hypothesis tests that have finite-sample guarantees without regularity conditions. We refer to such procedures as “universal.” The method is very simple and is based on a modified version of the usual likelihood-ratio statistic that we call “the split likelihood-ratio test” (split LRT) statistic. The (limiting) null distribution of the classical likelihood-ratio statistic is often intractable when used to test composite null hypotheses in irregular statistical models. Our method is especially appealing for statistical inference in these complex setups. The method we suggest works for any parametric model and also for some nonparametric models, as long as computing a maximum-likelihood estimator (MLE) is feasible under the null. Canonical examples arise in mixture modeling and shape-constrained inference, for which constructing tests and confidence sets has been notoriously difficult. We also develop various extensions of our basic methods. We show that in settings when computing the MLE is hard, for the purpose of constructing valid tests and intervals, it is sufficient to upper bound the maximum likelihood. We investigate some conditions under which our methods yield valid inferences under model misspecification. Further, the split LRT can be used with profile likelihoods to deal with nuisance parameters, and it can also be run sequentially to yield anytime-valid P values and confidence sequences. Finally, when combined with the method of sieves, it can be used to perform model selection with nested model classes.

scholarly journals FINITE-SAMPLE SIZE CONTROL OF IVX-BASED TESTS IN PREDICTIVE REGRESSIONS

2020 ◽  
pp. 1-25
Author(s):  
Mehdi Hosseinkouchack ◽  
Matei Demetrescu
Keyword(s):  
Size Control ◽  
Finite Sample ◽  
Limiting Distributions ◽  
Valid Inference ◽  
Tuning Parameters ◽  
Predictive Regressions ◽  
Chi Squared ◽  
Standard Normal ◽  
Finite Sample Size

Abstract In predictive regressions with variables of unknown persistence, the use of extended IV (IVX) instruments leads to asymptotically valid inference. Under highly persistent regressors, the standard normal or chi-squared limiting distributions for the usual t and Wald statistics may, however, differ markedly from the actual finite-sample distributions which exhibit in particular noncentrality. Convergence to the limiting distributions is shown to occur at a rate depending on the choice of the IVX tuning parameters and can be very slow in practice. A characterization of the leading higher-order terms of the t statistic is provided for the simple regression case, which motivates finite-sample corrections. Monte Carlo simulations confirm the usefulness of the proposed methods.

scholarly journals Model Selection Criteria on Beta Regression for Machine Learning

2019 ◽  
Vol 1 (1) ◽  
pp. 427-449
Author(s):  
Patrícia Espinheira ◽  
Luana da Silva ◽  
Alisson Silva ◽  
Raydonal Ospina
Keyword(s):  
Machine Learning ◽  
Model Selection ◽  
Selection Criteria ◽  
Real Data ◽  
Estimation Procedure ◽  
Computational Procedure ◽  
Information Criteria ◽  
Beta Regression ◽  
Finite Sample ◽  
Model Selection Criteria

Beta regression models are a class of supervised learning tools for regression problems with univariate and limited response. Current fitting procedures for beta regression require variable selection based on (potentially problematic) information criteria. We propose model selection criteria that take into account the leverage, residuals, and influence of the observations, both to systematic linear and nonlinear components. To that end, we propose a Predictive Residual Sum of Squares (PRESS)-like machine learning tool and a prediction coefficient, namely P 2 statistic, as a computational procedure. Monte Carlo simulation results on the finite sample behavior of prediction-based model selection criteria P 2 are provided. We also evaluated two versions of the R 2 criterion. Finally, applications to real data are presented. The new criterion proved to be crucial to choose models taking into account the robustness of the maximum likelihood estimation procedure in the presence of influential cases.

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