Local Maximum Likelihood Research Articles

Hypothesis Testing for Class-Conditional Noise Using Local Maximum Likelihood

In supervised learning, automatically assessing the quality of the labels before any learning takes place remains an open research question. In certain particular cases, hypothesis testing procedures have been proposed to assess whether a given instance-label dataset is contaminated with class-conditional label noise, as opposed to uniform label noise. The existing theory builds on the asymptotic properties of the Maximum Likelihood Estimate for parametric logistic regression. However, the parametric assumptions on top of which these approaches are constructed are often too strong and unrealistic in practice. To alleviate this problem, in this paper we propose an alternative path by showing how similar procedures can be followed when the underlying model is a product of Local Maximum Likelihood Estimation that leads to more flexible nonparametric logistic regression models, which in turn are less susceptible to model misspecification. This different view allows for wider applicability of the tests by offering users access to a richer model class. Similarly to existing works, we assume we have access to anchor points which are provided by the users. We introduce the necessary ingredients for the adaptation of the hypothesis tests to the case of nonparametric logistic regression and empirically compare against the parametric approach presenting both synthetic and real-world case studies and discussing the advantages and limitations of the proposed approach.

Estimating atmospheric motion winds from satellite image data using space‐time drift models

AbstractGeostationary weather satellites collect high‐resolution data comprising a series of images. The Derived Motion Winds (DMW) Algorithm is commonly used to process these data and estimate atmospheric winds by tracking features in the images. However, the wind estimates from the DMW Algorithm are often missing and do not come with uncertainty measures. Also, the DMW Algorithm estimates can only be half‐integers, since the algorithm requires the original and shifted data to be at the same locations, in order to calculate the displacement vector between them. This motivates us to statistically model wind motions as a spatial process drifting in time. Using a covariance function that depends on spatial and temporal lags and a drift parameter to capture the wind speed and wind direction, we estimate the parameters by local maximum likelihood. Our method allows us to compute standard errors of the local estimates, enabling spatial smoothing of the estimates using a Gaussian kernel weighted by the inverses of the estimated variances. We conduct extensive simulation studies to determine the situations where our method performs well. The proposed method is applied to the GOES‐15 brightness temperature data over Colorado and reduces prediction error of brightness temperature compared to the DMW Algorithm.

The t-Distribution Approach to the Second-Order Multiresponse Surface Model of Paracetamol Tablets Quality Characteristics

The normal distribution approach is often used in regression analysis at the Response Surface Methodology (RSM) modeling stage. Several studies have shown that the normal distribution approach has drawbacks compared to the more robust t-distribution approach. The t-distribution approach is found to control size much more successfully in small samples compared to existing methods in the presence of moderately heavy tails. In many RSM applications, there is more than one response (multiresponse), which is usually correlated with each other (multivariate). On the other hand, the actual response surface habitually indicates the curve by the optimal value, so the second-order model is used. This paper aims to develop the second-order multiresponse surface model using a multivariate t-distribution approach. This work also provides the parameter estimation procedure and hypothesis testing for the significance of the parameter. First, the parameter estimation is performed using the Maximum Likelihood Estimation (MLE), followed by the Expectation–Maximization algorithm as an iterative method to find (local) maximum likelihood. Next, the Likelihood Ratio Test (LRT) method is used to test the parameters simultaneously. The model obtained uses this approach to determine the conditions of input variables that optimize the Paracetamol tablets’ physical quality characteristics.

Temporally Local Maximum Likelihood with Application to SIS Model.

The parametric estimators applied by rolling are commonly used for the analysis of time series with nonlinear patterns, including time varying parameters and local trends. This paper examines the properties of rolling estimators in the class of temporally local maximum likelihood (TLML) estimators. We consider the TLML estimators of (a) constant parameters, (b) stochastic, stationary parameters and (c) parameters with the ultra-long run (ULR) dynamics bridging the gap between the constant and stochastic parameters. We show that the weights used in the TLML estimators have a strong impact on the inference. For illustration, we provide a simulation study of the epidemiological susceptible-infected-susceptible (SIS) model, which explores the finite sample performance of TLML estimators of a time varying contagion parameter.

Generalized varying-coefficient additive model for locally stationary time series

ABSTRACT Recently, the varying-coefficient additive model (VCAM) has received much attention due to its flexibility and interpretability. In this paper, we consider its generalized form, called a generalized varying-coefficient additive model (GVCAM), which can model discrete and continuous responses for locally stationary covariates. Specifically, the conditional mean function is specified via a link function g and a nonparametric part given by a VCAM. We develop a pilot-estimation-based local linear maximum likelihood estimator (PEB-LLE) to approximate the univariate component function. We also show the proposed estimators are oracle efficient and present the pointwise asymptotic distribution as well as simultaneous confidence bands. Simulation studies investigating the finite-sample performance of the proposed methodology are considered, and a real data application illustrating our method is also given.

Chinese physical fitness standard for campus football players: A pilot study of 765 children aged 9 to 11.

Objectives: In 2022, 55 million Chinese children participate in campus football; however, there is no physical fitness standard, making it a priority task to enhance the current national program. This study aimed to explore a pilot method for the development of a reliable physical fitness standard. Methods: This study examined 765 male football players aged 9 to 11 in 2020 and 2022. The anthropometric and physical fitness assessments were conducted in accordance with the Chinese Football Association’s field manuel. Physical fitness tests include sit and reach test, t test, 30 m run test, and vertical jump test. Physical fitness standard was modeled using the generalized additive models for location, scale, and shape (GAMLSS). Data were fitted with appropriate GAMLSS distributions and smoothing term. P-splines were applied to smooth the model’s parameters using the default local maximum likelihood method and link functions. Following diagnostics of fitted models, age-specific centile estimations were computed for physical fitness tests. In addition, players in each age group were categorized according to their body mass index as normal weight or overweight/obese. Welch’s t-test was utilized to compare the group differences in physical fitness testing. The significance level was chosen at p < 0.05. Results: Sit and reach test, t test, 30 m run test, and vertical jump test data were fitted with original Sinh-Arcsinh, Box-Cox power exponential, Box-Cox power exponential, and Box-Cox Cole and Green, respectively. Physical fitness standard for each age group is presented as tabulated centiles (1p, 3p, 5p, 15p, 25p, 50p, 75p, 85p, 95p, 97p, 99p). Overweight/obese campus football players did significantly worse (p < 0.05) on the t test, 30 m run test, and vertical jump test than their normal-weight peers of the same age. Conclusion: This study developed the first physical fitness standard for 9 to 11-year-old campus football players in China. We made three recommendations to Chinese policymakers on sample size, data management, and field procedure for the creation of a national physical fitness standard.

Global optimization for accurate and efficient parameter estimation in nanofiltration

One of the most well-established frameworks for modeling multicomponent transport in nanofiltration (NF) is the Donnan-Steric Pore Model with Dielectric Exclusion (DSPM-DE). Conventional DSPM-DE characterizes transport across NF membranes through four governing membrane parameters: (1) pore radius; (2) effective membrane thickness; (3) membrane charge density; and (4) the dielectric constant inside the membrane pores. The process for quantifying these parameters is typically sequential. First, neutral solute experiments are performed to determine pore radius and effective membrane thickness. Next, charged species experiments are conducted, and the data is used to regress out the remaining parameters. The resulting regressions are often performed using local search algorithms that can struggle to provide low residuals with robust fits. In addition, this two-step approach tends to: (1) require a substantial number of charged and uncharged solute experiments; and (2) introduce assumed relationships between pore size and water flux, such as the Hagen-Poiseuille equation, which may not be representative of transport through complex pore networks. To address these issues, we propose the use of metaheuristic global optimization techniques supplemented with gradient-free local search and maximum likelihood estimation to simultaneously regress all four membrane parameters directly from charged species experiments. We validate our approach against eight independent datasets across diverse input salinities, compositions, and membranes.

A new method for estimating Sharpe ratio function via local maximum likelihood

The Sharpe ratio function is a commonly used risk/return measure in financial econometrics. To estimate this function, most existing methods take a two-step procedure that first estimates the mean and volatility functions separately and then applies the plug-in method. In this paper, we propose a direct method via local maximum likelihood to simultaneously estimate the Sharpe ratio function and the negative log-volatility function as well as their derivatives. We establish the joint limiting distribution of the proposed estimators, and moreover extend the proposed method to estimate the multivariate Sharpe ratio function. We also evaluate the numerical performance of the proposed estimators through simulation studies, and compare them with existing methods. Finally, we apply the proposed method to the three-month US Treasury bill data and that captures a well-known covariate-dependent effect on the Sharpe ratio.

Regression Discontinuity for Binary Response and Local Maximum Likelihood Estimator to Extrapolate Treatment.

Regression discontinuity is popular in finding treatment/policy effects when the treatment is determined by a continuous variable crossing a cutoff. Typically, a local linear regression (LLR) estimator is used to find the effects. For binary response, however, LLR is not suitable in extrapolating the treatment, as in doubling/tripling the treatment dose/intensity. The reason is that doubling/tripling the LLR estimate can give a number out of the bound , despite that the effect should be a change in probability. We propose local maximum likelihood estimators which overcome these shortcomings, while giving almost the same estimates as the LLR estimator does for the original treatment. A simulation study and an empirical analysis for effects of an income subsidy program on religion demonstrate these points.

Semiparametric estimation of spatial autoregressive smooth-coefficient panel stochastic frontier models

This paper considers the estimation of a spatial autoregressive stochastic frontier model, where the production frontier coefficients, as well as the spatial parameter, are allowed to depend on a set of observed environmental factors. The inefficiency term is multiplicatively separable into a scaling function of either the same or totally different set of environmental factors and a standard half-normal random variable. A two-step semiparametric procedure is developed using a combination of local GMM and maximum likelihood approaches. We also derive the estimators of direct and indirect average partial effects and predictors of technical efficiency. We work out the asymptotic theory for the proposed second step estimator and propose a test of the relevance of the environmental factors. A special case of the model where the spatial parameter is a non-zero constant is also considered. The finite sample behavior of the proposed estimator and test are examined using Monte Carlo simulations. An empirical application to the Chinese chemical industry is included to illustrate the usefulness of our proposed models and methods.

Semiparametric Averaging of Nonlinear Marginal Logistic Regressions and Forecasting for Time Series Classification

Binary classification is an important issue in many applications but mostly studied for independent data in the literature. A binary time series classification is investigated by proposing a semiparametric procedure named “Model Averaging nonlinear MArginal LOgistic Regressions” (MAMaLoR) for binary time series data based on the time series information of predictor variables. The procedure involves approximating the logistic multivariate conditional regression function by combining low-dimensional non-parametric nonlinear marginal logistic regressions, in the sense of Kullback-Leibler distance. A time series conditional likelihood method is suggested for estimating the optimal averaging weights together with local maximum likelihood estimations of the nonparametric marginal time series logistic (auto)regressions. The asymptotic properties of the procedure are established under mild conditions on the time series observations that are of β-mixing property. The procedure is less computationally demanding and can avoid the “curse of dimensionality” for, and be easily applied to, high dimensional lagged information based nonlinear time series classification forecasting. The performances of the procedure are further confirmed both by Monte-Carlo simulation and an empirical study for market moving direction forecasting of the financial FTSE 100 index data.

Phylogenomic analysis for Campylobacter fetus ocurring in Argentina.

Background and Aim:Campylobacter fetus is one of the most important pathogens that severely affects livestock industry worldwide. C. fetus mediated bovine genital campylobacteriosis infection in cattle has been associated with significant economic losses in livestock production in the Pampas region, the most productive area of Argentina. The present study aimed to establish the genomic relationships between C. fetus strains, isolated from the Pampas region, at local and global levels. The study also explored the utility of multi-locus sequence typing (MLST) as a typing technique for C. fetus.Materials and Methods:For pangenome and phylogenetic analysis, whole genome sequences for 34 C. fetus strains, isolated from cattle in Argentina were downloaded from GenBank. A local maximum likelihood (ML) tree was constructed and linked to a Microreact project. In silico analysis based on MLST was used to obtain information regarding sequence type (ST) for each strain. For global phylogenetic analysis, a core genome ML-tree was constructed using genomic dataset for 265 C. fetus strains, isolated from various sources obtained from 20 countries.Results:The local core genome phylogenetic tree analysis described the presence of two major clusters (A and B) and one minor cluster (C). The occurrence of 82% of the strains in these three clusters suggested a clonal population structure for C. fetus. The MLST analysis for the local strains revealed that 31 strains were ST4 type and one strain was ST5 type. In addition, a new variant was identified that was assigned a novel ST, ST70. In the present case, ST4 was homogenously distributed across all the regions and clusters. The global analysis showed that most of the local strains clustered in the phylogenetic groups that comprised exclusively of the strains isolated from Argentina. Interestingly, three strains showed a close genetic relationship with bovine strains obtained from Uruguay and Brazil. The ST5 strain grouped in a distant cluster, with strains obtained from different sources from various geographic locations worldwide. Two local strains clustered in a phylogenetic group comprising intercontinental Campylobacter fetus venerealis strains.Conclusion:The results of the study suggested active movement of animals, probably due to economic trade between different regions of the country as well as with neighboring countries. MLST results were partially concordant with phylogenetic analysis. Thus, this method did not qualify as a reliable subtyping method to assess C. fetus diversity in Argentina. The present study provided a basic platform to conduct future research on C. fetus, both at local and international levels.

Modeling nonstationary extremes of storm severity: Comparing parametric and semiparametric inference

AbstractThis article compares the modeling of nonstationary extreme events using parametric models with local parametric and semiparametric approaches also motivated by extreme value theory. Specifically, three estimators are compared based on (a) (local) semiparametric moment estimation, (b) (local) maximum likelihood estimation, and (c) spline‐based maximum likelihood estimation. Inference is performed in a sequential manner, highlighting the synergies between the different approaches to estimating extreme quantiles, including the T‐year level and right endpoint when finite. We present a novel heuristic to estimate nonstationary extreme value threshold with exceedances varying on a circular domain, and hypothesis‐testing procedures for identifying max‐domain of attraction in the nonstationary setting. Bootstrapping is used to estimate nonstationary confidence bounds throughout. We provide step‐by‐step guides for estimation, and explore the different inference strategies in application to directional modeling of hindcast storm peak significant wave heights recorded in the North Sea.

A Local Search Maximum Likelihood Parameter Estimator of Chirp Signal

A local search Maximum Likelihood (ML) parameter estimator for mono-component chirp signal in low Signal-to-Noise Ratio (SNR) conditions is proposed in this paper. The approach combines a deep learning denoising method with a two-step parameter estimator. The denoiser utilizes residual learning assisted Denoising Convolutional Neural Network (DnCNN) to recover the structured signal component, which is used to denoise the original observations. Following the denoising step, we employ a coarse parameter estimator, which is based on the Time-Frequency (TF) distribution, to the denoised signal for approximate estimation of parameters. Then around the coarse results, we do a local search by using the ML technique to achieve fine estimation. Numerical results show that the proposed approach outperforms several methods in terms of parameter estimation accuracy and efficiency.

Estimation of nonparametric ordinal logistic regression model using local maximum likelihood estimation

Ordinal logistic regression is a statistical method used to analyze the ordinal response variable with three or more categories and predictor variables that are categorical or continuous. The parametric models for ordinal response variable assume that the predictor is given by a linear form of covariates. In this study, the parametric models are extended to include smooth components based on nonparametric approach. The covariates are modeled as unspecified but smooth functions. Estimation is based on local maximum likelihood estimation (LMLE).

Semiparametric quantile regression using family of quantile-based asymmetric densities

Quantile regression is an important tool in data analysis. Linear regression, or more generally, parametric quantile regression imposes often too restrictive assumptions. Nonparametric regression avoids making distributional assumptions, but might have the disadvantage of not exploiting distributional modelling elements that might be brought in. A semiparametric approach towards estimating conditional quantile curves is proposed. It is based on a recently studied large family of asymmetric densities of which the location parameter is a quantile (and not a mean). Passing to conditional densities and exploiting local likelihood techniques in a multiparameter functional setting then leads to a semiparametric estimation procedure. For the local maximum likelihood estimators the asymptotic distributional properties are established, and it is discussed how to assess finite sample bias and variance. Due to the appealing semiparametric framework, one can discuss in detail the bandwidth selection issue, and provide several practical bandwidth selectors. The practical use of the semiparametric method is illustrated in the analysis of maximum winds speeds of hurricanes in the North Atlantic region, and of bone density data. A simulation study includes a comparison with nonparametric local linear quantile regression as well as an investigation of robustness against miss-specifying the parametric model part.

Estimation of semi- and nonparametric stochastic frontier models with endogenous regressors

This paper considers the problem of estimating a nonparametric stochastic frontier model with shape restrictions and when some or all regressors are endogenous. We discuss three estimation strategies based on constructing a likelihood with unknown components. One approach is a three-step constrained semiparametric limited information maximum likelihood, where the first two steps provide local polynomial estimators of the reduced form and frontier equation. This approach imposes the shape restrictions on the frontier equation explicitly. As an alternative, we consider a local limited information maximum likelihood, where we replace the constrained estimation from the first approach with a kernel-based method. This means the shape constraints are satisfied locally by construction. Finally, we consider a smooth-coefficient stochastic frontier model, for which we propose a two-step estimation procedure based on local GMM and MLE. Our Monte Carlo simulations demonstrate attractive finite sample properties of all the proposed estimators. An empirical application to the US banking sector illustrates empirical relevance of these methods.

Estimation of general time-varying single particle tracking linear models using local likelihood.

In this work, we study a general approach to the estimation of single particle tracking models with time-varying parameters. The main idea is to use local Maximum Likelihood (ML), applying a sliding window over the data and estimating the model parameters in each window. We combine local ML with Expectation Maximization to iteratively find the ML estimate in each window, an approach that is amenable to generalization to nonlinear models. Results using controlled-experimental data generated in our lab show that our proposed algorithm is able to track changes in the parameters as they evolve during a trajectory under real-world experimental conditions, outperforming other algorithms of similar nature.

A local maximum likelihood model of crop yield distributions

AbstractIn this note, we propose a local maximum likelihood estimator for spatially‐dependent distributions. Our estimator adopts the Poisson regression approach for density ratio models and incorporates spatial smoothing via local regression. We also present a method of smoothing parameter selection. We illustrate this easy‐to‐implement estimator with an application to the estimation of corn yield distributions of Iowa counties. The usefulness of the approach is further demonstrated via an application to the estimation of crop insurance premium.

Beam Acquisition and Training in Millimeter Wave Networks With Narrowband Pilots

This paper studies initial beam acquisition in a millimeter wave network consisting of multiple access points (APs) and mobile devices. A training protocol for joint estimation of transmit and receive beams is presented with a general frame structure consisting of an initial access sub-frame followed by data transmission sub-frames. During the initial subframe, APs and mobiles sweep through a set of beams and determine the best transmit and receive beams via a handshake. All pilot signals are narrowband (tones), and the mobiles are distinguished by their assigned pilot frequencies. Both non-coherent and coherent beam estimation methods based on, respectively, power detection and maximum likelihood (ML) are presented. To avoid exchanging information about beamforming vectors between APs and mobiles, a local maximum likelihood (LML) algorithm is also presented. An efficient fast Fourier transform implementation is proposed for ML and LML to achieve high-resolution. A system-level optimization is performed in which the frame length, training time, and training bandwidth are selected to maximize a rate objective taking into account blockage and mobility. Simulation results based on a realistic network topology are presented to compare the performance of different estimation methods and training codebooks, and demonstrate the effectiveness of the proposed protocol.