Minimum Distance Estimator Research Articles

Standard Errors for Calibrated Parameters

Abstract Calibration, the practice of choosing the parameters of a structural model to match certain empirical moments, can be viewed as minimum distance estimation. Existing standard error formulas for such estimators require a consistent estimate of the correlation structure of the empirical moments, which is often unavailable in practice. Instead, the variances of the individual empirical moments are usually readily estimable. Using only these variances, we derive conservative standard errors and confidence intervals for the structural parameters that are valid even under the worst-case correlation structure. In the over-identified case, we show that the moment weighting scheme that minimizes the worst-case estimator variance amounts to a moment selection problem with a simple solution. Finally, we develop tests of over-identifying or parameter restrictions. We apply our methods empirically to a model of menu cost pricing for multi-product firms and to a heterogeneous agent New Keynesian model.

Multi-line laser 3D reconstruction method based on spatial quadric surface and geometric estimation

The traditional multi-line laser 3D reconstruction is based on binocular epipolar constraints and the equation of the laser optical plane. Firstly, matching points are identified based on the epipolar constraints. Then, the correct matching points are selected based on the optical plane equation of the multi-line laser. Finally, 3D reconstruction is performed using the selected matching points. In actual production processes involving multi-line lasers, noticeable distortion occurs due to the projection of Diffractive Optical Elements (DOE) at a large angle. This results in curved laser light planes and curved reflections on the measured objects. Under such circumstances, efficiently screening matching points using the traditional method based on the laser plane equation becomes challenging. Additionally, inherent noise in multi-line laser systems introduces errors in extracted laser center coordinates, making it impossible to directly obtain high-precision 3D data. To address these issues, this paper proposes a method that utilizes spatial quadric surfaces and geometric estimation for completing multi-line laser 3D reconstructions. By analyzing the distortion principle of DOE and the positional relationship after optical diffraction, the multi-line laser manifests as a quadric surface on the optical output plane. Consequently, by calibrating the equations of the quadric surface and applying binocular polar constraints, suitable matching points for the multi-line laser can be chosen. Once an accurate matching point is identified, a minimum geometric distance estimation can be established based on the distance constraint between the point and its corresponding epipolar line. This distance represents the separation between the left and right camera’s laser center points and their respective epipolar lines. Utilizing this estimate of the minimum geometric distance, a refined calculation can be performed to better satisfy epipolar constraints and obtain new matching points. Ultimately, utilizing these new matching points enables the completion of 3D reconstruction for multi-line lasers. In comparison with methods relying on spatial plane and epipolar constraints, our algorithm exhibits a superior degree of matchability and accuracy.According to multiple groups of test data, the average error before optimization is 0.3126 mm, and can be increased to 0.0336 mm after optimization.

Minimum profile Hellinger distance estimation for single-index models

Single-index models are the most commonly used covariate models and are widely used in statistical applications. Such models include linear models and generalised linear models as special cases. This article investigates efficient and robust estimates for single-index models. For this purpose, we employ the minimum distance approach which in general is automatically robust with respect to the stability of the quantity being estimated. In particular, the minimum Hellinger distance approach introduced by Beran [(1977), ‘Minimum Hellinger Distance Estimators for Parametric Models’, Annals of Statistics, 5, 445–463] produces estimators that are asymptotically efficient at the model density and simultaneously possess excellent robustness properties. In this paper, we construct a minimum profile Hellinger distance estimator (MPHDE) for single-index models. We prove the consistency of the proposed MPHDE and examine its finite-sample performance and robustness properties via Monte Carlo simulation studies and real data analysis.

Minimum Profile Hellinger Distance Estimation of General Covariate Models

Covariate models, such as polynomial regression models, generalized linear models, and heteroscedastic models, are widely used in statistical applications. The importance of such models in statistical analysis is abundantly clear by the ever-increasing rate at which articles on covariate models are appearing in the statistical literature. Because of their flexibility, covariate models are increasingly being exploited as a convenient way to model data that consist of both a response variable and one or more covariate variables that affect the outcome of the response variable. Efficient and robust estimates for broadly defined semiparametric covariate models are investigated, and for this purpose the minimum distance approach is employed. In general, minimum distance estimators are automatically robust with respect to the stability of the quantity being estimated. In particular, minimum Hellinger distance estimation for parametric models produces estimators that are asymptotically efficient at the model density and simultaneously possess excellent robustness properties. For semiparametric covariate models, the minimum Hellinger distance method is extended and a minimum profile Hellinger distance estimator is proposed. Its asymptotic properties such as consistency are studied, and its finite-sample performance and robustness are examined by using Monte Carlo simulations and three real data analyses. Additionally, a computing algorithm is developed to ease the computation of the estimator.

Estimating separable matching models

SummaryMost recent empirical applications of matching with transferable utility have imposed a natural restriction: that the joint surplus be separable in the sources of unobserved heterogeneity. We propose here two simple methods to estimate models in this class. The first method is a minimum distance estimator that relies on the generalized entropy of matching. The second applies to the more special but popular Choo and Siow model, which reformulates as a generalized linear model with two‐way fixed effects. Neither method requires solving for the stable matching. Both methods are easy to apply and perform very well.

Predicting lodging severity in dry peas using UAS-mounted RGB, LIDAR, and multispectral sensors

This study investigated the feasibility of using data collected by sensors mounted onto unmanned aerial systems (UASs) and traditional classification methods (Maximum Likelihood, Mahalanobis Distance, Minimum Distance, and Adaptive Coherence Estimator) and four machine learning models (Random Forest [RF], Support Vector Machine [SVM], K-Nearest Neighbor [KNN], and Extreme Gradient Boosting [XGBOOST]) to predict the severity of dry pea lodging. Data were collected in two environments in North Dakota during the 2022 crop season, where lodging was visually estimated at the plot level using a lodging scale range of 0 to 9. Aerial images were collected using two UASs (DJI Matrice 200 and 300) during early, mid, and late stages of growth. Synthetic Minority Oversampling Technique combined with Edited Nearest Neighbors (SMOTE-ENN) was used to balance the imbalanced dataset. Different feature selection models (recursive feature elimination, lasso regression, principal component analysis, and correlation-based methods) were used and compared to identify the most important features in the dataset. Our study found that similar channels can be used interchangeably for analyzing lodging without compromising accuracy, simplifying data acquisition, and saving time and resources. The maximum plant height values obtained from LiDAR and RGB sensors showed a strong correlation with actual values. Recursive feature elimination was the most effective feature selection method for handling high-dimensional datasets. The XGBOOST model outperformed all traditional and machine learning classification models, with the lowest variation in precision values. RF showed the most pronounced overfitting among the machine learning models, while Mahalanobis distance showed the least overfitting among all traditional classification models. Overall, the study demonstrated the potential of UAS and machine learning models for predicting lodging severity in dry peas, with XGBOOST being the best-performing model.

A Discrete Odd Lindley Half-Logistic Distribution with Applications

In the reality, the most of lifetime data is discrete in nature, despite it is known that this data is continuous. As a consequence, the tendency to convert the continuous lifetime distributions to its discrete counterpart has raised. The nature of the most lifetime data in real life is discrete, thus, many of researchers interested to convert. This article aims to introduce a new one-parameter discrete distribution, namely Discrete Odd Lindley Half-Logistic (DOLiHL) distribution. The DOLiHL distribution is derived by discretizing the analogue continuous distribution, using a survival discretization technique. An intensive study of this distribution is provided, including characteristic functions and statistical properties. Moreover, the unknown parameter is estimated using different methods of estimation namely, the maximum likelihood method, method of moments, least squares method and Cramer-von Mises minimum distance estimation method. A simulation study is conducted to examine the distribution’s behavior and compare between the estimation methods at different sample sizes. To evaluate the efficiency of this distribution against other competitive distributions, an implementation on real data in different fields is performed. In conclude, the DOLiHL distribution has assured its efficiency of fitting in lifetime and count data from various fields in real life.

Identification and estimation of sequential games of incomplete information with multiple equilibria

This paper discusses the identification and estimation of game-theoretic models, mainly focusing on sequential games of incomplete information. In most empirical games, researchers cannot observe the exact order of actions played in the game and rely on the assumption of simultaneous actions. My structural modeling generalizes an empirical game to encompass simultaneous and sequential actions as special cases. I specify a sequential game allowing for multiple players in each stage and multiple Perfect Bayesian Nash Equilibria, showing that the structural parameters, including the payoff function parameters, the order of actions, and the equilibrium selection mechanism, are separately identified. The various exclusion restrictions in the finite mixture literature help attain point identification of structural parameters and provide a testable method to verify identification conditions. Next, I consider a Sieve Minimum Distance (SMD) estimator of Ai and Chen (2003) for the structural parameters and verify its asymptotic properties. The Monte Carlo simulations evaluate the performance of the proposed estimator and provide numerical evidence of potential bias under the misspecified order of actions. The empirical application of Walmart and Kmart’s entry game demonstrates that retailers compete sequentially in a significant portion of markets.

An identification and testing strategy for proxy-SVARs with weak proxies

When proxies (external instruments) used to identify target structural shocks are weak, inference in proxy-SVARs (SVAR-IVs) is nonstandard and the construction of asymptotically valid confidence sets for the impulse responses of interest requires weak-instrument robust methods. In the presence of multiple target shocks, test inversion techniques require extra restrictions on the proxy-SVAR parameters other than those implied by the proxies that may be difficult to interpret and test. We show that frequentist asymptotic inference in these situations can be conducted through Minimum Distance estimation and standard asymptotic methods if the proxy-SVAR can be identified by using ‘strong’ instruments for the non-target shocks; i.e., the shocks which are not of primary interest in the analysis. The suggested identification strategy hinges on a novel pre-test for the null of instrument relevance, based on bootstrap resampling, which is not subject to pre-testing issues. Specifically, the validity of post-test asymptotic inferences remains unaffected by the test outcomes due to an asymptotic independence result between the bootstrap and non-bootstrap statistics. The test is robust to conditionally heteroskedastic and/or zero-censored proxies, is computationally straightforward and applicable regardless of the number of shocks being instrumented. Some illustrative examples show the empirical usefulness of the suggested identification and testing strategy.

Permanent and transitory earnings dynamics and lifetime income inequality in Sweden

This paper studies the role of permanent- and transitory earnings variability for lifetime income inequality in Sweden. We fit a permanent–transitory error component model to the autocovariance structure of earnings using administrative data for 2002–2015 and minimum distance estimation. We find that permanent earnings inequality increased during the first decade and that the financial crisis of 2008 temporarily heightened earnings volatility. Using this model, we simulate pension entitlements and study lifetime income inequality conditional on the pre- and post-1990s pension system. We find that permanent earnings differences generally contribute the most to lifetime income inequality. We conclude that the Swedish pension system provides some insurance against earnings risk, but accentuates the role of permanent earnings differences in explaining lifetime inequality.

A confirmatory factor analysis approach for addressing the errors-in-variables problem with colored output noise

Over the years, errors-in-variables (EIV) system identification has attracted considerable research interest. Among the many proposed approaches for identifying EIV models is confirmatory factor analysis (CFA), here referred to as EIV-CFA. This study extends previous research by presenting a EIV-CFA modeling framework that allows for colored output noise. Considerable attention is paid to the theoretical aspects of the minimum distance (MD) estimator. The finite sample performance of the MD estimator is briefly evaluated using simulation. The results suggest that model parameters are well estimated.

Inverse Unit Teissier Distribution: Theory and Practical Examples

In this paper, we emphasize a new one-parameter distribution with support as [1,+∞). It is constructed from the inverse method applied to an understudied one-parameter unit distribution, the unit Teissier distribution. Some properties are investigated, such as the mode, quantiles, stochastic dominance, heavy-tailed nature, moments, etc. Among the strengths of the distribution are the following: (i) the closed-form expressions and flexibility of the main functions, and in particular, the probability density function is unimodal and the hazard rate function is increasing or unimodal; (ii) the manageability of the moments; and, more importantly, (iii) it provides a real alternative to the famous Pareto distribution, also with support as [1,+∞). Indeed, the proposed distribution has different functionalities but also benefits from the heavy-right-tailed nature, which is demanded in many applied fields (finance, the actuarial field, quality control, medicine, etc.). Furthermore, it can be used quite efficiently in a statistical setting. To support this claim, the maximum likelihood, Anderson–Darling, right-tailed Anderson–Darling, left-tailed Anderson–Darling, Cramér–Von Mises, least squares, weighted least-squares, maximum product of spacing, minimum spacing absolute distance, and minimum spacing absolute-log distance estimation methods are examined to estimate the unknown unique parameter. A Monte Carlo simulation is used to compare the performance of the obtained estimates. Additionally, the Bayesian estimation method using an informative gamma prior distribution under the squared error loss function is discussed. Data on the COVID mortality rate and the timing of pain relief after receiving an analgesic are considered to illustrate the applicability of the proposed distribution. Favorable results are highlighted, supporting the importance of the findings.

A queueing model of visual search

Understanding how attentional resources are deployed in visual processing is a fundamental and highly debated topic. As an alternative to theoretical models of visual search that propose sequences of separate serial or parallel stages of processing, we suggest a queueing processing structure that entails a serial transition between parallel processing stages. We develop a continuous-time queueing model for standard visual search tasks to formalize and implement this notion. Specified as a finite-time, single-line, multiserver queueing system, the model accounts for both accuracy and response time (RT) data in visual search on a distributional level. It assumes two stages of processing. Visual stimuli first go through a massively parallel preattentive stage of feature encoding. They wait if necessary and then enter a limited-capacity attentive stage serially where multiple processing channels (“servers”) integrate features of several stimuli in parallel. A core feature of our model is the serial transition from the unlimited-capacity preattentive processing stage to the limited-capacity attentive processing stage. It enables asynchronous attentive processing of multiple stimuli in parallel and is more efficient than a simple chain of two successive, strictly parallel processing stages. The model accounts for response errors by means of two underlying mechanisms, namely, imperfect processing of the servers and, in addition, incomplete search adopted by the observer to maximize search efficiency under an accuracy constraint. For statistical inference, we develop a Monte-Carlo-based parameter estimation procedure, using maximum likelihood (ML) estimation for accuracy-related parameters and minimum distance (MD) estimation for RT-related parameters. We fit the model to two large empirical data sets from two types of visual search tasks. The model captures the accuracy rates almost perfectly and the observed RT distributions quite well, indicating a high explanatory power. The number of independent parallel processing channels that explain both data sets best was five. We also perform a Monte-Carlo model uncertainty analysis and show that the model with the correct number of parallel channels is selected for more than 90% of the simulated samples.

Efficient estimation of a triangular system of equations for quantile regression

This paper proposes a one-step sieve estimator of the parameter in the semiparametric triangular model for quantile regression of Lee (2007). The proposed estimator is a penalized sieve minimum distance (PSMD) estimator developed by Chen and Pouzo (2009). We develop the asymptotic theory for the PSMD estimator under a set of low-level conditions. The PSMD estimator is shown to be semiparametrically efficient, and the validity of a weighted bootstrap is established. A small Monte Carlo simulation study shows that our estimator performs well in finite samples.

Integrative analysis of individual-level data and high-dimensional summary statistics.

Researchers usually conduct statistical analyses based on models built on raw data collected from individual participants (individual-level data). There is a growing interest in enhancing inference efficiency by incorporating aggregated summary information from other sources, such as summary statistics on genetic markers' marginal associations with a given trait generated from genome-wide association studies. However, combining high-dimensional summary data with individual-level data using existing integrative procedures can be challenging due to various numeric issues in optimizing an objective function over a large number of unknown parameters. We develop a procedure to improve the fitting of a targeted statistical model by leveraging external summary data for more efficient statistical inference (both effect estimation and hypothesis testing). To make this procedure scalable to high-dimensional summary data, we propose a divide-and-conquer strategy by breaking the task into easier parallel jobs, each fitting the targeted model by integrating the individual-level data with a small proportion of summary data. We obtain the final estimates of model parameters by pooling results from multiple fitted models through the minimum distance estimation procedure. We improve the procedure for a general class of additive models commonly encountered in genetic studies. We further expand these two approaches to integrate individual-level and high-dimensional summary data from different study populations. We demonstrate the advantage of the proposed methods through simulations and an application to the study of the effect on pancreatic cancer risk by the polygenic risk score defined by BMI-associated genetic markers. R package is available at https://github.com/fushengstat/MetaGIM.

On Fitting the Lomax Distribution: A Comparison between Minimum Distance Estimators and Other Estimation Techniques

In this paper, we investigate the performance of a variety of frequentist estimation techniques for the scale and shape parameters of the Lomax distribution. These methods include traditional methods such as the maximum likelihood estimator and the method of moments estimator. A version of the maximum likelihood estimator adjusted for bias is included as well. Furthermore, an alternative moment-based estimation technique, the L-moment estimator, is included, along with three different minimum distance estimators. The finite sample performances of each of these estimators are compared in an extensive Monte Carlo study. We find that no single estimator outperforms its competitors uniformly. We recommend one of the minimum distance estimators for use with smaller samples, while a bias-reduced version of maximum likelihood estimation is recommended for use with larger samples. In addition, the desirable asymptotic properties of traditional maximum likelihood estimators make them appealing for larger samples. We include a practical application demonstrating the use of the described techniques on observed data.

An autocovariance-based learning framework for high-dimensional functional time series

Many scientific and economic applications involve the statistical learning of high-dimensional functional time series, where the number of functional variables is comparable to, or even greater than, the number of serially dependent functional observations. In this paper, we model observed functional time series, which are subject to errors in the sense that each functional datum arises as the sum of two uncorrelated components, one dynamic and one white noise. Motivated from the fact that the autocovariance function of observed functional time series automatically filters out the noise term, we propose a three-step framework by first performing autocovariance-based dimension reduction, then formulating a novel autocovariance-based block regularized minimum distance estimation to produce block sparse estimates, and based on which obtaining the final functional sparse estimates. We investigate theoretical properties of the proposed estimators, and illustrate the proposed estimation procedure with the corresponding convergence analysis via three sparse high-dimensional functional time series models. We demonstrate via both simulated and real datasets that our proposed estimators significantly outperform their competitors.

Usage of LDPC Codes in a Gilbert Channel

Although low-density parity-check (LDPC) codes in modern communication standards have been extensively studied over a memoryless channel, their burst error correction capacity in channels with memory has yet to be thoroughly analyzed. The conventional approach to transmission in channels with memory uses interleaving within a buffer of several codewords. However, such an approach reduces the efficiency of the redundancy embedded by the error-correcting code. It is known from information theory that considering channel memory during decoding allows the transmission rate to be increased. An evaluation of the decoding error probability of different types of low-density parity-check codes in channels with memory is presented along with estimates of minimum distance and burst error correction capability for the considered codes. The decoding error probability is estimated for conventional decoding with deinterleaving and decoding taking channel memory into account. The decoding error probability is estimated for several parameters of a channel with memory and different buffer lengths. The obtained results reveal the absence of the unique decoding approach for all parameters of the channel with memory. The best decoding error probability is determined by the degree of channel memory correlation.

Railways and urban expansion: how does rail transport affect urban expansion in metropolitan areas? (Warsaw and Copenhagen case)

ABSTRACT Railway transportation plays a key role in the formation of the spatial structure of metropolitan areas. The metropolitan areas with coherent and regular railways seem to have more disciplined spatial development. The present study aims to express the relationship between the railways and the discipline of spatial structure using a developmental-applied approach. To this end, two metropolitan areas with railway coverage are selected as case studies, and four methods of minimum-distance estimation, spatial regression, fractal geometry, and cellular automata are used to analyze the data. The results indicate that the railway plays a direct role in urban expansion so that, in Copenhagen with an orderly railway network, urban development is channelized around the railway but in Warsaw with a more complicated railway network, urban expansion is more dispersed and located around rail intersections.

A Faster Procedure for Estimating SEMs Applying Minimum Distance Estimators With a Fixed Weight Matrix

This study presents a separable nonlinear least squares (SNLLS) implementation of the minimum distance (MD) estimator employing a fixed-weight matrix for estimating structural equation models (SEMs). In contrast to the standard implementation of the MD estimator, in which the complete set of parameters is estimated using nonlinear optimization, the SNLLS implementation allows a subset of parameters to be estimated using (linear) least squares (LS). The SNLLS implementation possesses a number of benefits, such as faster convergence, better performance in ill-conditioned estimation problems, and fewer required starting values. The present work demonstrates that SNLLS, when applied to SEM estimation problems, significantly reduces the estimation time. Reduced estimation time makes SNLLS particularly useful in applications involving some form of resampling, such as simulation and bootstrapping.