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Modern machine learning models often exhibit the benign overfitting phenomenon, which has recently been characterized using the double descent curves. In addition to the classical U-shaped learning curve, the learning risk undergoes another descent as we increase the number of parameters beyond a certain threshold. In this article, we examine the conditions under which benign overfitting occurs in the random feature (RF) models, that is, in a two-layer neural network with fixed first layer weights. Adopting a novel view of random features, we show that benign overfitting emerges because of the noise residing in such features. The noise may already exist in the data and propagates to the features, or it may be added by the user to the features directly. Such noise plays an implicit yet crucial regularization role in the phenomenon. In addition, we derive the explicit tradeoff between the number of parameters and the prediction accuracy, and for the first time demonstrate that overparameterized model can achieve the optimal learning rate in the minimax sense. Finally, our results indicate that the learning risk for overparameterized models has multiple, instead of double descent behavior, which is empirically verified in recent works. for this article are available online. [ABSTRACT FROM AUTHOR]

Banks have always played an ambivalent role in financial markets. On the one hand, they provide essential services for the market; on the other hand, problems in the banking sector can send shock waves through the entire economy. Given this prominent role, it is not surprising that Pereira and Rua [2018. "Asset Pricing with a Bank Risk Factor." Journal of Money, Credit and Banking 50(5): 993–1032. doi:] found that the health of the banking sector exerts an influence on stock returns in the US. Understanding the relationship between banks and their impact on the asset prices of non-financials is essential to evaluate the risk emanating from an unhealthy banking sector and should be considered in new regulatory requirements. The aim of this study is to determine if the health of European banks is of such importance for the European stock market so that spillover effects are visible. Our results show that none of our banking-health variables have explanatory power on the cross-section of European stock returns. These findings contrast those for the US. The reasons may be manifold, from an unimportant liquidity provisioning channel over reduced room for actions due to regulatory requirements up to a moral hazard situation in Europe, where investors strongly rely on the governmental bailouts of distressed banks. [ABSTRACT FROM AUTHOR]

This paper investigates the parameter estimation of errors-in-variables Wiener (EIV-W) nonlinear systems. In such nonlinear systems, both input and output contain interference noises, and some intermediate processes are also interfered by noises. The hierarchical technology is applied to decompose the whole system into two subsystems firstly. For the linear subsystem, in order to obtain unbiased estimates of model parameters, a bias compensation method is introduced. Then, the bias-compensated least squares (BLS) algorithm is proposed. For the nonlinear subsystem, on the basis of particle swarm optimisation (PSO), the fuzzy control technology is added to improve the ability of jumping out of the local optimum. Thus, a bias-compensated least squares and fuzzy PSO based hierarchical (BLS-FPSO-H) method is derived at last. In simulation, a numerical example and a case study about the carbon fibre stretching process are implemented. Results indicate that the BLS-FPSO-H algorithm can effectively identify EIV-W nonlinear systems, the convergence speed and identification accuracy are greatly improved than the basic PSO method and some other PSO variants. [ABSTRACT FROM AUTHOR]

Measurement errors and missing data are often arise in practice. Under this circumstance, we focus on using jackknife empirical likelihood (JEL) and adjust jackknife empirical likelihood (AJEL) methods to construct confidence intervals for the error variance in linear models. Based on residuals of the models, the biased-corrected inverse probability weighted estimator of the error variance is introduced. Furthermore, we propose the jackknife estimator, jackknife and adjust jackknife empirical log-likelihood ratios of the error variance and establish their asymptotic distributions. Simulation studies in terms of coverage probability and average length of confidence intervals are conducted to evaluate the proposed method. A real data set is used to illustrate the proposed JEL and AJEL methods. [ABSTRACT FROM AUTHOR]

In this paper, we consider least squares estimation and empirical likelihood inference for partial functional linear models when the covariates in the non-functional linear component are measured with additive error and the responses are missing at random. Asymptotic properties of the proposed estimators for the parametric and nonparametric components are established. A class of empirical log-likelihood ratio functions of the parametric component and response mean are developed, and the corresponding maximum empirical likelihood estimators are constructed. We also prove that the empirical log-likelihood ratio functions are asymptotic standard chi-squared distribution. The results can be used to construct confidence intervals for the parametric component and response mean. The asymptotic distributions of the corresponding maximum empirical likelihood estimators are also established. Meanwhile, a simulation study is conducted to demonstrate the finite sample performance of the proposed procedure. A real data analysis is also used to illustrate our methods. [ABSTRACT FROM AUTHOR]

This paper studies how to estimate and test the symmetry of a continuous variable under the additive distortion measurement errors setting. The unobservable variable is distorted in a additive fashion by an observed confounding variable. Firstly, a direct plug-in estimation procedure is proposed to calibrate the unobserved variable. Next, we propose four test statistics for testing whether the unobserved variable is symmetric or not. The asymptotic properties of the proposed estimators and test statistics are investigated. We conduct Monte Carlo simulation experiments to examine the performance of the proposed estimators and test statistics. These methods are applied to analyze a real dataset for an illustration. [ABSTRACT FROM AUTHOR]

In this paper, we consider the statistical inference for the partially linear panel data models with fixed effects. We focus on the case where some covariates are measured with additive errors. We propose a modified profile least squares estimator of the regression parameter and the nonparametric components. The asymptotic normality for the parametric component and the rate of convergence for the nonparametric component are established. Consistent estimations of the error variance are also developed. We conduct simulation studies to demonstrate the finite sample performance of our proposed method and we also present an illustrative empirical application. [ABSTRACT FROM AUTHOR]

In the paper, we derive Procrustes-based closed-form solutions to the point-wise weighted rigid-body transformation under different adjustment scenarios. We treat both asymmetric and symmetric cases. By asymmetric (or Gauss–Markov) models we mean those in which either a source system or a target system is subject to random errors. On the other hand, by the symmetric model (Gauss-Helmert or errors-in-variables) we mean the one in which points of both coordinate systems are considered erroneous. The solutions are universal in the sense that they fit both 2D and 3D transformation cases without modifications of computational algorithms. Presented results are also attractive because the solutions require neither linearisation nor iteration. [ABSTRACT FROM AUTHOR]

A logarithmic calibration estimation procedure is proposed for nonparametric regression models under the multiplicative distortion measurement errors setting. The unobservable response variable and covariates are both distorted in a multiplicative fashion by an observed confounding variable. By using the logarithmic calibration estimation procedure for unobserved variables, we consider to study the estimates of nonparametric mean function and its first derivative, the variance function, the Sharpe ratio function and correlation curve. We obtain asymptotic normality results for the proposed nonparametric estimators. Monte Carlo simulation experiments are conducted to examine the performance of the proposed estimators. The proposed estimators are applied to analyse a real dataset for an illustration. [ABSTRACT FROM AUTHOR]

We discuss an algorithm for the autoregression (AR) model as a typical time-series model. By analyzing the structure of the AR model, we highlight the shortcomings of traditional algorithms for model parameter estimation and propose an approach to overcome the shortcomings of traditional solutions for the AR model. The errors-in-variables (EIV) model is used to solve an existing problem. There is an obvious difference between the AR model and a traditional model. For the AR model, one observation datum appears repeatedly; hence, the residual of one observation datum is not unique. Furthermore, in theory, the optimal estimation of model parameters cannot be obtained by current solutions. Based on an analysis of the AR model, we focus on how to obtain the optimal estimation when the observation data of the AR model are contaminated by outliers. The median function is used to establish a modified solution for the AR model based on the institute of geodesy & geophysics, Chinese academy of sciences (IGG) weight function by comparison with current algorithms for the robust estimation of the EIV model. We propose an iterative algorithm based on median function. Finally, we apply two numerical instances to compare the proposed algorithm with traditional algorithms and draw conclusions from results of the instances. [ABSTRACT FROM AUTHOR]

The purpose of this paper is twofold. First, we investigate estimations in varying-coefficient partially linear errors-in-variables models with covariates missing at random. However, the estimators are often biased due to the existence of measurement errors, the bias-corrected profile least-squares estimator and local liner estimators for unknown parametric and coefficient functions are obtained based on inverse probability weighted method. The asymptotic properties of the proposed estimators both for the parameter and nonparametric parts are established. Second, we study asymptotic distributions of an empirical log-likelihood ratio statistic and maximum empirical likelihood estimator for the unknown parameter. Based on this, more accurate confidence regions of the unknown parameter can be constructed. The methods are examined through simulation studies and illustrated by a real data analysis. [ABSTRACT FROM AUTHOR]

Semi-functional linear regression models are important in practice. In this paper, their estimation is discussed when function-valued and real-valued random variables are all measured with additive error. By means of functional principal component analysis and kernel smoothing techniques, the estimators of the slope function and the non parametric component are obtained. To account for errors in variables, deconvolution is involved in the construction of a new class of kernel estimators. The convergence rates of the estimators of the unknown slope function and non parametric component are established under suitable norm and conditions. Simulation studies are conducted to illustrate the finite sample performance of our method. [ABSTRACT FROM AUTHOR]

A correlation curve measures the strength of the association between two variables locally at different values of covariate. This paper studies how to estimate the correlation curve under the multiplicative distortion measurement errors setting. The unobservable variables are both distorted in a multiplicative fashion by an observed confounding variable. We obtain asymptotic normality results for the estimated correlation curve. We conduct Monte Carlo simulation experiments to examine the performance of the proposed estimator. The estimated correlation curve is applied to analyze a real dataset for an illustration. [ABSTRACT FROM AUTHOR]

Growth value model (GVM) considers stock intrinsic value as the synergy of book value and return on equity (ROE), which contains two parameters, value factor and growth factor. This study addresses the problem of independent variables having measurement errors by utilizing errors-in-variables regression to estimate accurate model parameters. Research findings show the following: (1) The regression curve derived by traditional regression analysis exhibits severe bias. Errors-in-variables regression is capable of correcting the bias. (2) Large-scale firms exhibit lower value factor and higher growth factor, which indicates that large-scale firms possess better profit persistence. [ABSTRACT FROM AUTHOR]

In this paper, we propose an empirical likelihood based diagnostic technique for heteroscedasticity in the semiparametric varying-coefficient partially linear errors-in-variables models. Under mild conditions, a nonparametric version of Wilk’s theorem is derived. Simulation results reveal that our test performs well in both size and power. [ABSTRACT FROM AUTHOR]

In most practical applications, the quality of count data is often compromised due to errors-in-variables (EIVs). In this paper, we apply Bayesian approach to reduce bias in estimating the parameters of count data regression models that have mismeasured independent variables. Furthermore, the exposure model is misspecified with a flexible distribution, hence our approach remains robust against any departures from normality in its true underlying exposure distribution. The proposed method is also useful in realistic situations as the variance of EIVs is estimated instead of assumed as known, in contrast with other methods of correcting bias especially in count data EIVs regression models. We conduct simulation studies on synthetic data sets using Markov chain Monte Carlo simulation techniques to investigate the performance of our approach. Our findings show that the flexible Bayesian approach is able to estimate the values of the true regression parameters consistently and accurately. [ABSTRACT FROM AUTHOR]

We study partial linear single-index models (PLSiMs) when the response and the covariates in the parametric part are measured with additive distortion measurement errors. These distortions are modeled by unknown functions of a commonly observable confounding variable. We use the semiparametric profile least-squares method to estimate the parameters in the PLSiMs based on the residuals obtained from the distorted variables and confounding variable. We also employ the smoothly clipped absolute deviation penalty (SCAD) to select the relevant variables in the PLSiMs. We show that the resulting SCAD estimators are consistent and possess the oracle property. For the non parametric link function, we construct the simultaneous confidence bands and obtain the asymptotic distribution of the maximum absolute deviation between the estimated link function and the true link function. A simulation study is conducted to evaluate the performance of the proposed methods and a real dataset is analyzed for illustration. [ABSTRACT FROM PUBLISHER]

This paper studies the estimation of correlation coefficient between unobserved variables of interest. These unobservable variables are distorted in a additive fashion by an observed confounding variable. Two estimators, a direct-plug-in estimator and a residual-based estimator, are proposed. Their asymptotical results are obtained, and the residual-based estimator is shown asymptotically efficient. Moreover, we suggest an asymptotic normal approximation and an empirical likelihood-based statistic to construct the confidence interval. The empirical likelihood statistic is shown to be asymptotically chi-squared. Simulation studies are conducted to examine the performance of the proposed estimators. These methods are applied to analyse the Boston housing price data for an illustration. [ABSTRACT FROM PUBLISHER]

A linearerrors-in-variables(EIV) model that contains measurement errors in the input and output data is considered.Weakly dependent(α- and ϕ-mixing) errors, not necessarily stationary nor identically distributed, are taken into account within the EIV model. Parameters of the EIV model are estimated by thetotal least squaresapproach, which provideshighly non linearestimates. Because of this, many statistical procedures for constructing confidence intervals and testing hypotheses cannot be applied. One possible solution to this dilemma is ablock bootstrap. An appropriate moving block bootstrap procedure is provided and its correctness proved. The results are illustrated through a simulation study and applied on real data as well. [ABSTRACT FROM PUBLISHER]

This paper considers statistical inference for the partially linear additive models, which are useful extensions of additive models and partially linear models. We focus on the case where some covariates are measured with additive errors, and the response variable is sometimes missing. We propose a profile least-squares estimator for the parametric component and show that the resulting estimator is asymptotically normal. To construct a confidence region for the parametric component, we also propose an empirical-likelihood-based statistic, which is shown to have a chi-squared distribution asymptotically. Furthermore, a simulation study is conducted to illustrate the performance of the proposed methods. [ABSTRACT FROM PUBLISHER]

Instrumental variable (IV) regression provides a number of statistical challenges due to the shape of the likelihood. We review the main Bayesian literature on instrumental variables and highlight these pathologies. We discuss Jeffreys priors, the connection to the errors-in-the-variables problems and more general error distributions. We propose, as an alternative to the inverted Wishart prior, a new Cholesky-based prior for the covariance matrix of the errors in IV regressions. We argue that this prior is more flexible and more robust thanthe inverted Wishart prior since it is not based on only one tightness parameter and therefore can be more informative about certain components of the covariance matrix and less informative about others. We show how prior-posterior inference can be formulated in a Gibbs sampler and compare its performance in the weak instruments case for synthetic as well as two illustrations based on well-known real data. [ABSTRACT FROM PUBLISHER]

Empirical likelihood-based inference for the nonparametric components in additive partially linear models is investigated. An empirical likelihood approach to construct the confidence intervals of the nonparametric components is proposed when the linear covariate is measured with and without errors. We show that the proposed empirical log-likelihood ratio is asymptotically standard chi-squared without requiring the undersmoothing of the nonparametric components. Then, it can be directly used to construct the confidence intervals for the nonparametric functions. A simulation study indicates that, compared with a normal approximation-based approach, the proposed method works better in terms of coverage probabilities and widths of the pointwise confidence intervals. [ABSTRACT FROM AUTHOR]

The solution to the errors-in-variables problem computed through total least squares is highly nonlinear. Because of this, many statistical procedures for constructing confidence intervals and testing hypotheses cannot be applied. One possible solution to this dilemma is bootstrapping. A nonparametric bootstrap technique could fail. Here, the proper nonparametric bootstrap procedure is provided and its correctness is proved. On the other hand, a residual bootstrap is not valid and suitable in this case. The results are illustrated through a simulation study. An application of this approach to calibration data is presented. [ABSTRACT FROM AUTHOR]

As a compromise between parametric regression and nonparametric regression, partially linear models are frequently used in statistical modelling. This article considers statistical inference for this semiparametric model when the linear covariate is measured with additive error and some additional linear restrictions on the parametric component are assumed to hold. We propose a restricted corrected profile least-squares estimator for the parametric component, and study the asymptotic normality of the estimator. To test hypothesis on the parametric component, we construct a Wald test statistic and obtain its limiting distribution. Some simulation studies are conducted to illustrate our approaches. [ABSTRACT FROM AUTHOR]

Virtually all methods aimed at correcting for covariate measurement error in regressions rely on some form of additional information (e.g., validation data, known error distributions, repeated measurements, or instruments). In contrast, we establish that the fully nonparametric classical errors-in-variables model is identifiable from data on the regressor and the dependent variable alone, unless the model takes a very specific parametric form. This parametric family includes (but is not limited to) the linear specification with normally distributed variables as a well-known special case. This result relies on standard primitive regularity conditions taking the form of smoothness constraints and nonvanishing characteristic functions’ assumptions. Our approach can handle both monotone and nonmonotone specifications, provided the latter oscillate a finite number of times. Given that the very specific unidentified parametric functional form is arguably the exception rather than the rule, this identification result should have a wide applicability. It leads to a new perspective on handling measurement error in nonlinear and nonparametric models, opening the way to a novel and practical approach to correct for measurement error in datasets where it was previously considered impossible (due to the lack of additional information regarding the measurement error). We suggest an estimator based on non/semiparametric maximum likelihood, derive its asymptotic properties, and illustrate the effectiveness of the method with a simulation study and an application to the relationship between firm investment behavior and market value, the latter being notoriously mismeasured. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

Algorithms for the recursive/semi-recursive estimation of the system parameters as well as the measurement noise variances for linear single-input single-output errors-in-variables systems are considered. Approaches based on three offline techniques are presented: namely, the bias eliminating least squares, the Frisch scheme and the extended bias compensating the least squares method. Whilst the underlying equations used within these approaches are identical under certain design choices, the performances of the recursive/semi-recursive algorithms are investigated via simulation, in order to determine the most suitable technique for practical applications. [ABSTRACT FROM PUBLISHER]

This article shows that the first autocorrelation of basketball shot results is a highly biased and inconsistent estimator of the first autocorrelation of the ex ante probabilities with which the shots are made. Shot result autocorrelation is close to zero even when shot probability autocorrelation is close to one. The bias is caused by what is equivalent to a severe measurement error problem. The results imply that the widespread belief among players and fans in the hot hand is not necessarily a cognitive fallacy. [ABSTRACT FROM AUTHOR]

A well-known approach to linear least squares regression is that which involves minimizing the sum of squared orthogonal projections of data points onto the best fit line. This form of regression is known as orthogonal regression, and the linear model that it yields is known as the major axis. A similar method, reduced major axis regression, is predicated on minimizing the total sum of triangular areas formed between data points and the best fit line. Either of these methods is appropriately applied when both x and y are measured, a typical case in the natural sciences. In comparison to classical linear regression, equation derivation for the slope of the major axis and reduced major axis lines is a nontrivial process. For this reason, derivations are presented herein drawing from previous literature with as few steps as possible to enable an easily accessible understanding. Application to eruption data for Old Faithful geyser, Yellowstone National Park, Wyoming and Montana, USA enables a teaching opportunity for choice of model. [ABSTRACT FROM AUTHOR]

This paper proposes a wavelet (spectral) approach to estimate the parameters of a linear regression model where the regressand and the regressors are persistent processes and contain a measurement error. We propose a wavelet filtering approach which does not require instruments and yields unbiased estimates for the intercept and the slope parameters. Our Monte Carlo results also show that the wavelet approach is particularly effective when measurement errors for the regressand and the regressor are serially correlated. With this paper, we hope to bring a fresh perspective and stimulate further theoretical research in this area. [ABSTRACT FROM PUBLISHER]

This article considers a class of partially linear single-index models when some linear covariates are not observed, but their ancillary variables are available. This model can avoid the 'curse of dimensionality' in multivariate nonparametric regressions, and it contains many existing statistical models such as the partially linear model (Engle, R.F., Granger, W. J., Rice, J., and Weiss, A. (1986), 'Semiparametric Estimates of the Relation Between Weather and Electricity Sales', Journal of The American Statistical Association, 80, 310-319), the single-index model (Hardle, W., Hall, P., and Ichimura, H. (1993), 'Optimal Smoothing in Single-Index Models', The Annals of Statistics, 21, 157-178), the partially linear errors-in-variables model (Liang, H., Hardle, W., and Carroll, R.J. (1999), 'Estimation in a Semi-parametric Partially Linear Errors-in-Variables Model', The Annals of Statistics, 27, 1519-1535), the partially linear single-index measurement error model (Liang, H., and Wang, N. (2005), 'Partially Linear Single-Index Measurement Error Models', Statistica Sinica, 15, 99-116), and so on as special examples. In this article, an estimation procedure for the unknowns of the proposed models is proposed, and asymptotic properties of the corresponding estimators are derived. Finite sample performance of the proposed methodology is assessed by Monte Carlo simulation studies. A real example is also given to illustrate the proposed procedures. [ABSTRACT FROM AUTHOR]

In this article, we consider empirical likelihood inference for the parameter in the additive partially linear models when the linear covariate is measured with error. By correcting for attenuation, a corrected-attenuation empirical log-likelihood ratio statistic for the unknown parameter β, which is of primary interest, is suggested. We show that the proposed statistic is asymptotically standard chi-square distribution without requiring the undersmoothing of the nonparametric components, and hence it can be directly used to construct the confidence region for the parameter β. Some simulations indicate that, in terms of comparison between coverage probabilities and average lengths of the confidence intervals, the proposed method performs better than the profile-based least-squares method. We also give the maximum empirical likelihood estimator (MELE) for the unknown parameter β, and prove the MELE is asymptotically normal under some mild conditions. [ABSTRACT FROM AUTHOR]

In a lot of situations, variables are measured with errors. While this problem has been previously studied in the context of kernel regression, no work has been done in quantile regression. To estimate this function, we use deconvolution kernel estimators. We obtain asymptotic results (MSE and normality) for two estimators of conditional quantiles and analyse their finite sample performances via a large simulation study. [ABSTRACT FROM AUTHOR]

In this paper, empirical likelihood inferences for semiparametric varying-coefficient partially linear error-in-variables models with longitudinal data are investigated. By correcting the attenuation, we propose a corrected empirical likelihood ratio function for the parametric components and a residual-adjusted empirical likelihood ratio function for the nonparametric components. Wilks' phenomenon is proved and the confidence regions for parametric components and nonparametric components are constructed. A simulation study is undertaken to assess the finite sample performance of the proposed confidence regions. [ABSTRACT FROM AUTHOR]

Predicting the value of a variable Y corresponding to a future value of an explanatory variable X, based on a sample of previously observed independent data pairs (X1, Y1),..., (X1, Y1) distributed like (X, Y), is very important in statistics. In the error-free case, where Xis observed accurately, this problem is strongly related to that of standard regression estimation, since prediction of Y can be achieved via estimation of the regression curve E(YIX). When the observed X,s and the future observation of X are measured with error, prediction is of a quite different nature. Here, if T denotes the future (contaminated) available version of X, prediction of Y can be achieved via estimation of E(YIT). In practice, estimating E(YIT) can be quite challenging, as data may be collected under different conditions, making the measurement errors on X and X nonidentically distributed. We take up this problem in the nonparametric setting and introduce estimators which allow a highly adaptive approach to smoothing. Reflecting the complexity of the problem, optimal rates of convergence of estimators can vary from the semiparametric n-1/2 rate to much slower rates that are characteristic of nonparametric problems. Nevertheless, we are able to develop highly adaptive, data-driven methods that achieve very good performance in practice. This article has the supplementary materials online. [ABSTRACT FROM AUTHOR]

This article considers the problem of estimating linear model parameters from noisy measurements. The starting point is the classical approach by Koopmans for linear regression analysis. It is known that concerning the direct application of those early results for process identification, neither the original Koopmans algorithm nor its updated forms called Koopmans-Levin algorithms exhibit maximum-likelihood (ML) parameter estimation. In this article, a new, numerically advanced method is developed to ensure ML property for the parameter estimation, assuming noisy inputs and outputs, respectively. [ABSTRACT FROM AUTHOR]

In the classical errors-in-variables problem, the goal is to estimate a regression curve from data in which the explanatory variable is measured with error. In this context, nonparametric methods have been proposed that rely on the assumption that the measurement errors are identically distributed. Although there are many situations in which this assumption is too restrictive, nonparametric estimators in the more realistic setting of heteroscedastic errors have not been studied in the literature. We propose an estimator of the regression function in such a setting and show that it is optimal. We give estimators in cases in which the error distributions are unknown and replicated observations are available. Practical methods, including an adaptive bandwidth selector for the errors-in-variables regression problem, are suggested, and their finite-sample performance is illustrated through simulated and real data examples. [ABSTRACT FROM AUTHOR]

Regression methods for the analysis of paired measurements produced by two fallible assay methods are described and their advantages and pitfalls discussed. The difficulties for the analysis, as in any errors-in-variables problem lies in the lack of identifiability of the model and the need to introduce questionable and often naïve assumptions in order to gain identifiability. Although not a panacea, the use of instrumental variables and associated instrumental variable (IV) regression methods in this area of application has great potential to improve the situation. Large samples are frequently needed and two-phase sampling methods are introduced to improve the efficiency of the IV estimators. [ABSTRACT FROM AUTHOR]

This note deals with the problem of estimating the support of a distribution function when the empirical data are contaminated. An easily computable estimation method based on moment estimation is introduced. Unlike earlier approaches, these estimators also cover situations in which the sharpness of the target distribution at the support boundaries is arbitrarily low and in which the distribution is discontinuous at several points within the support. General consistency results for the estimators are achieved and rates of convergence are studied in the case of normal measurement error. The practical performance of the estimation procedure is studied in a simulation section. [ABSTRACT FROM AUTHOR]

The linear model with classical measurement error is an alternative to the standard regression model, in which it is assumed that the independent variables are subject to error. This assumption can cause statistical inferences and parameter estimators to differ dramatically from those obtained by the standard regression model. However, in some cases, inferences remain unchanged even though the independent variables are assumed to be subject to error. This article investigates the invariance property of score tests for assessing heteroscedasticity, first-order autoregressive disturbance, and the need for a Box-Cox power transformation. Under specific constraints, we show that the score tests for measurement error models are identical to the corresponding well-established tests derived from standard regression models. Hence practitioners can assess assumptions of constant variance and independent errors, as well as the need for a Box-Cox transformation, irrespective of whether or not the variables are measured with error. We also discuss some possible generalizations. [ABSTRACT FROM AUTHOR]

In many situations, variables are measured with errors. Though this problem has been studied previously in the context of kernel regression, the results have been applied to the case where only the covariates are contaminated. This article addresses the problem where both (covariates and response variables) are contaminated. We estimate the conditional mode function. To estimate this function, we use deconvoluting kernel estimators. The asymptotic behavior of these estimators depends on the smoothness of the noise distribution. Asymptotic normality is established for strongly mixing stochastic processes, when the error distribution is smooth. [ABSTRACT FROM AUTHOR]

In this article, we consider the Bayesian estimation of Engel curves specified as the Working-Lesser form with the measurement errors on both the left and the right sides. It is noteworthy that in the Bayesian approach no additional variation data (i.e., instrumental variables) are required in contrast with the non-Bayesian approach. We present the Bayesian estimation procedure in both models without an instrumental variable and with an instrumental variable. We also compare our results with the generalized method of moments estimates proposed by Lewbel. [ABSTRACT FROM AUTHOR]

The estimator holding the central place in the theory of the multivariate "errors-in-the-variables" (EV) model results from performing orthogonal regression on variables rescaled according to the covariance matrix of the errors. Our simulations on the univariate model essentially relegate this estimator to use only in large samples on data with no trace of outlier contamination. A modification requiring a robust preliminary slope is proposed that essentially sets out the generalization to EV of the robust w-estimator in regression. It is demonstrated that the modification is robust to outlier contamination even in small samples, given a sufficiently good preliminary estimator. Candidates for a preliminary slope estimator based on the data are discussed and the performance of one under simulation is examined. [ABSTRACT FROM AUTHOR]

We consider several grouping tests for regression misspecification, with reference to housing-demand function estimation. We compare three existing test procedures, demonstrate modifications necessary in most applications, and propose a fourth test to distinguish between two categories of potential specification error. The test procedures are evaluated in artificial simulations of alternative errors. Finally, we apply the tests to FHA home purchase data. We reject the hypothesis that household and grouped regressions differ only by sampling error or random mismeasurement of household income or price. Our results have implications for choices among test procedures and interpretations of previous housing-demand analysis. [ABSTRACT FROM AUTHOR]