Minimum distance estimation in a finite mixture regression model

Simulated minimum Hellinger distance estimation of stochastic volatility models

Maximum likelihood estimation of fixed effects dynamic panel data models covering short time periods

Attribute-Level Heterogeneity

A minimum Hellinger distance estimator for stochastic differential equations: An application to statistical inference for continuous time interest rate models

This paper presents a comprehensive comparative study of twelve estimation methods for the exponential logarithmic distribution. The methods investigated include maximum likelihood estimator, moments estimator, modified moments estimator, least squares estimator, weighted least squares estimator, percentiles estimator, maximum product spacings estimator, minimum spacing absolute distance estimator, minimum spacing absolute-log distance estimator, Cramér-von Mises estimator, Anderson-Darling estimator, and the right tail Anderson-Darling estimator. Through simulation studies, we assess the efficiency of each estimator based on the mean relative estimate, mean squared error, D abs , and D max criteria, with preference given to estimators exhibiting a mean relative estimate close to one and smaller values of mean squared error, D abs , and D max . Additionally, the practical applicability of these methods is demonstrated through the analysis of three real datasets, showcasing their effectiveness in various scenarios.

Summary Certain repeated cross-sectional data sets, such as the Current Population Survey (CPS), use special sampling designs by which samples from different times periods are partially matched. This paper proposes a correction to the optimal weighting matrix in minimum distance (MD) estimation of pseudo-panel models to account for such partially matched samples. This partially matched sample correction may be needed if the sample matching rate is nontrivial and, at the same time, there is a fixed effect, a serially correlated idiosyncratic error, or both in the underlying linear panel data model data generating process, all of which lead to a block diagonal structure of the optimal weighting matrix. Using the correction can result in considerable efficiency gains both in finite sample and asymptotically. Furthermore, it is shown that this correction is needed, not only for the optimal MD estimator, but for any MD estimator to make the inference right. As an illustration, the correction is applied to the classical question of estimating the monetary return to education using the yearly Merged Outgoing Rotation Group files from CPS.

This paper contributes to the interface literature of new methodological foundation of analyzing historical data with space and spatio-temporal phenomena. In particular, I consider estimating the spatial panel autoregressive model using the minimum distance estimator. Spatial autoregression has important implications for economic system that typifies correlatedness across many spatial locations and which could evolve over long span of time. To overcome computational difficulties, I suggest a two-stage estimation procedure based on minimum distance estimators. A striking feature of the proposed model is that minimum distance estimates are derived under common slopes and complete equality of parameters across spatial units. Assumption of common slopes across spatial units is an empirical and theoretical plausibility as many spatial units are observed to share common trend and typology of changes occurring to the individual system under which equality of parameters are possibilities. The estimation strategy allows various restrictions on time-varying vector parameters. Moreover, those restrictions can easily be tested. I apply this procedure to the residential demand for water of 115 French municipalities over the biannual period 1988–1993. The primary contribution of the paper is to the methodological side of cliometrics while the empirical application (with shorter time period) has been presented for illustrative purpose although, it can nonetheless be readily applied to historical data with long-time horizon allowing for restrictions such as spatio-temporal common vector and structural break in parameter estimates.

A numerical method for minimum distance estimation problems

Efficiency and robustness are two essential concerns on statistical estimation. Unfortunately, it was widely accepted that there existed a contradiction between achieving efficiency and robustness simultaneously. For parametric models with complete data, the minimum Hellinger distance estimation introduced by Beran (Ann Stat 5:445–463, 1977) has been shown that it can reconcile this contradiction. Because data in biostatistics, actuarial science or economics are often subject to censoring and even involve a fraction of long-term survivors, our study aims to extend the minimum Hellinger distance estimation to a two-sample semiparametric cure rate model with right-censored survival data. The asymptotic properties such as consistency, efficiency, normality, and robustness of the proposed estimator have been considered and its performances are examined via simulation studies in comparison with those of the maximum semiparametric conditional likelihood estimator introduced by Shen et al. (J Am Stat Assoc 102:1235–1244, 2007). Finally, our method is illustrated by analyzing a real data set: Bone Marrow Transplant Data.

Abstract. This paper considers a minimumα‐divergence estimation for a class of ARCH(p) models. For these models with unknown volatility parameters, the exact form of the innovation density is supposed to be unknown in detail but is thought to be close to members of some parametric family. To approximate such a density, we first construct an estimator for the unknown volatility parameters using the conditional least squares estimator given by Tjøstheim [Stochastic processes and their applications (1986) Vol. 21, pp. 251–273]. Then, a nonparametric kernel density estimator is constructed for the innovation density based on the estimated residuals. Using techniques of the minimum Hellinger distance estimation for stochastic models and residual empirical process from an ARCH(p) model given by Beran [Annals of Statistics (1977) Vol. 5, pp. 445–463] and Lee and Taniguchi [Statistica Sinica (2005) Vol. 15, pp. 215–234] respectively, it is shown that the proposed estimator is consistent and asymptotically normal. Moreover, a robustness measure for the score of the estimator is introduced. The asymptotic efficiency and robustness of the estimator are illustrated by simulations. The proposed estimator is also applied to daily stock returns of Dell Corporation.

The paper presents construction of a highly robust estimator for block-error ratio in the binomial transmission model under heavy additional noise or disturbances. The estimator is based on the empirical probability generating function computed at single point in the transform domain. Such construction leads to explicit expressions for influence function and asymptotic variance. The influence analysis explains why the estimator is notably useful when estimating small error probabilities and how to tune its performance in presence of gross outliers. While robustness comes often at the expense of increased bias, variance and/or computational effort, the proposed estimator is nearly unbiased, possibly very efficient, and easy to compute without processing the data or any optimization procedure. The last feature makes it attractive for automated real-time and online applications. The asymptotic arguments are validated in simulations for small and moderate sample sizes. Advantages over the sample median, the maximum likelihood estimator and the minimum Hellinger distance estimator in context of this application are discussed.

A family of minimum quantile distance estimators, based on a subset of the sample quantiles, is proposed for the parameters of the three-parameter Weibull distribution. The estimation procedure is applicable to either complete or censored samples and, through use of the associated distance measure, provides a goodness-of-fit test for the Weibull model. The proposed estimators are both consistent and asymptotically normal and, in a particular instance, are optimal over the class of all estimators based on the same quantile subset. The problem of optimal quantile selection is also considered.

Given the modelYi=m(χi)+ɛi,whereE(ɛi) =0,Xi≠Ci=1, ...,n, andC is ap-dimensional compact set, we have designed a new method for testing the hypothesis that the regression function follows a general linear model,m(·) ∈ {mθ(·) =At(·)θ}θ∈Θ⊂ℛq, withA a function fromℜp toℜq. The statistic, denoted ΔASE, used fortesting the given hypothesis is defined to be the difference between the average squared errors (ASE) associated with the non-parametric estimator\(\hat m\) ofm and the minimum distance parametric estimator\(m_{\hat \theta } \) ofm. The asymptotic normality of both ΔASE and the minimum distance estimators is proved under general conditions. Alternative bootstrap versions of ΔASE are also considered.

On the basis of the segment of observations X1,…, Xn from a ∅-mixing sequence of random variables, a minimum distance estimate \( {{\hat{P}}_{n}} \) of the probability measure P,governing the process, is constructed. Under suitable regularity conditions, it is shown that \( {{\hat{P}}_{n}} \) is weakly uniformly consistent, within the class P of assumed probability measures, at the same rate as in the independent identically distributed case. Strengthening of the underlying assumptions provides for strong consistency.

This paper presents a numerically more efficient implementation of the quadratic form minimum distance (MD) estimator with a fixed weight matrix for confirmatory factor analysis (CFA) models. In structural equation modeling (SEM) computer software, such as EQS, lavaan, LISREL and Mplus, various MD estimators are available to the user. Standard procedures for implementing MD estimators involve a one-step approach applying non-linear optimization techniques. Our implementation differs from the standard approach by utilizing a two-step estimation procedure. In the first step, only a subset of the parameters are estimated using non-linear optimization. In the second step, the remaining parameters are obtained using numerically efficient linear least squares (LLS) methods. Through examples, it is demonstrated that the proposed implementation of MD estimators may be considerably faster than what the standard implementation offer. The proposed procedure will be of particular interest in computationally intensive applications such as simulation, bootstrapping, and other procedures involving re-sampling.