Estimation of dynamic panel data models with both individual and time-specific effects

This paper proposes a generalized least squares and a generalized method of moment estimators for dynamic panel data models with both individual-specific and time-specific effects. We also demonstrate that the common estimators ignoring the presence of time-specific effects are inconsistent when N→∞$N\to \infty$ but T is finite if the time-specific effects are indeed present. Monte Carlo studies are also conducted to investigate the finite sample properties of various estimators. It is found that the generalized least squares estimator has the smallest bias and root mean square error, and also has nominal size close to the empirical size. It is also found that even when there is no presence of time-specific effects, there is hardly any efficiency loss of the generalized least squares estimator assuming its presence compared to the generalized least squares estimator allowing only the presence of individual-specific effects.     

Minimax Linear Smoothers

We consider the problem of estimating the mean of a multivariate distribution. As a general alternative to penalized least squares estimators, we consider minimax estimators for squared error over a restricted parameter space where the restriction is determined by the penalization term. For a quadratic penalty term, the minimax estimator among linear estimators can be found explicitly. It is shown that all symmetric linear smoothers with eigenvalues in the unit interval can be characterized as minimax linear estimators over a certain parameter space where the bias is bounded. The minimax linear estimator depends on smoothing parameters that must be estimated in practice. Using results in Kneip (1994), this can be done using Mallows' C _L -statistic and the resulting adaptive estimator is now asymptotically minimax linear. The minimax estimator is compared to the penalized least squares estimator both in finite samples and asymptotically.     

Small sample properties of a ridge regression estimator when there exist omitted variables

In this paper, we derive the exact formulae for moments of the ridge regression estimator proposed by Huang (Econ Lett 62:261–264, 1999), when there exist omitted variables. We show the conditions under which the ridge regression estimator has smaller mean squared error (MSE) than the ordinary least squares estimator. Based on the exact formulae for moments, we compare the bias and MSE performances of both estimators by numerical evaluations.     

A new estimator combining the ridge regression and the restricted least squares methods of estimation

It is well-known in the literature on multicollinearity that one of the major consequences of multicollinearity on the ordinary least squares estimator is that the estimator produces large sampling variances, which in turn might inappropriately lead to exclusion of otherwise significant coefficients from the model. To circumvent this problem, two accepted estimation procedures which are often suggested are the restricted least squares method and the ridge regression method. While the former leads to a reduction in the sampling variance of the estimator, the later ensures a smaller mean square error value for the estimator. In this paper we have proposed a new estimator which is based on a criterion that combines the ideas underlying these two estimators. The standard properties of this new estimator have been studied in the paper. It has also been shown that this estimator is superior to both the restricted least squares as well as the ordinary ridge regression estimators by the criterion of mean sauare error of the estimator of the regression coefficients when the restrictions are indeed correct. The conditions for superiority of this estimator over the other two have also been derived for the situation when the restrictions are not correct.     

Estimating Percentiles of Time-to-Failure Distribution Obtained from a Linear Degradation Model Using Kernel Density Method

In this article, we propose a nonparametric estimator for percentiles of the time-to-failure distribution obtained from a linear degradation model using the kernel density method. The properties of the proposed kernel estimator are investigated and compared with well-known maximum likelihood and ordinary least squares estimators via a simulation technique. The mean squared error and the length of the bootstrap confidence interval are used as the basis criteria of the comparisons. The simulation study shows that the performance of the kernel estimator is acceptable as a general estimator. When the distribution of the data is assumed to be known, the maximum likelihood and ordinary least squares estimators perform better than the kernel estimator, while the kernel estimator is superior when the assumption of our knowledge of the data distribution is violated. A comparison among different estimators is achieved using a real data set.     

Estimation of a Change Point in a Hazard Function Based on Censored Data

The hazard function plays an important role in reliability or survival studies since it describes the instantaneous risk of failure of items at a time point, given that they have not failed before. In some real life applications, abrupt changes in the hazard function are observed due to overhauls, major operations or specific maintenance activities. In such situations it is of interest to detect the location where such a change occurs and estimate the size of the change. In this paper we consider the problem of estimating a single change point in a piecewise constant hazard function when the observed variables are subject to random censoring. We suggest an estimation procedure that is based on certain structural properties and on least squares ideas. A simulation study is carried out to compare the performance of this estimator with two estimators available in the literature: an estimator based on a functional of the Nelson-Aalen estimator and a maximum likelihood estimator. The proposed least squares estimator tums out to be less biased than the other two estimators, but has a larger variance. We illustrate the estimation method on some real data sets.     

A simulation study of least squares and ridge estimaors for normal and nonnormal autocorrelated disturbances

The purpose of this paper is to examine the small sample properties of various ridge estimators along with least squares, in some special settings.Specifically, we consider a first order autoregressive structuure for normal and nonnormal disturbances, and report on a Monte Carlo study the small sample behavior of these estimators according to the criteria of bias and dispersion.The results suggest that under all the examined settings and for all the criteria used the HKB estimator exhibited a superior performance compared to the other estimators, while the LS and LW estimators gave consistently poor results.Also if the error term is only moderately autocorrelated the performance of the ridge estimators that do not account for autocorrelation outperform their counterparts as well as least squares that account for autocorrelation.     

Heteroskedasticity-consistent covariance matrix estimation:white's estimator and the bootstrap ∗

This paper considers the issue of estimating the covariance matrix of ordinary least squares estimates in a linear regression model when heteroskedasticity is suspected. We perform Monte Carlo simulation on the White estimator, which is commonly used in.

empirical research, and also on some alternatives based on different bootstrapping schemes. Our results reveal that the White estimator can be considerably biased when the sample size is not very large, that bias correction via bootstrap does not work well, and that the weighted bootstrap estimators tend to display smaller biases than the White estimator and its variants, under both homoskedasticity and heteroskedasticity. Our results also reveal that the presence of (potentially) influential observations in the design matrix plays an important role in the finite-sample performance of the heteroskedasticity-consistent estimators.     

Estimation of a population size through capture-mark-recapture method: a comparison of various point and interval estimators

This article deals with the estimation of a fixed population size through capture-mark-recapture method that gives rise to hypergeometric distribution. There are a few well-known and popular point estimators available in the literature, but no good comprehensive comparison is available about their merits. Apart from the available estimators, an empirical Bayes (EB) estimator of the population size is proposed. We compare all the point estimators in terms of relative bias and relative mean squared error. Next, two new interval estimators – (a) an EB highest posterior distribution interval and (b) a frequentist interval estimator based on a parametric bootstrap method, are proposed. The comparison is then carried among the two proposed interval estimators and interval estimators derived from the currently available estimators in terms of coverage probability and average length (AL). Based on comprehensive numerical results, we rank and recommend the point estimators as well as interval estimators for practical use. Finally, a real-life data set for a green treefrog population is used as a demonstration for all the methods discussed.     

An approximation for analyzing a broad class of implicitly and explicitly defined estimators

An approximation is presented that can be used to gain insight into the characteristics – such as outlier sensitivity, bias, and variability – of a wide class of estimators, including maximum likelihood and least squares. The approximation relies on a convenient form for an arbitrary order Taylor expansion in a multivariate setting. The implicit function theorem can be used to construct the expansion when the estimator is not defined in closed form. We present several finite-sample and asymptotic properties of such Taylor expansions, which are useful in characterizing the difference between the estimator and the expansion.     

Wavelet estimation in time-varying coefficient time series models with measurement errors

The article studies a time-varying coefficient time series model in which some of the covariates are measured with additive errors. In order to overcome the bias of estimator of the coefficient functions when measurement errors are ignored, we propose a modified least squares estimator based on wavelet procedures. The advantage of the wavelet method is to avoid the restrictive smoothness requirement for varying-coefficient functions of the traditional smoothing approaches, such as kernel and local polynomial methods. The asymptotic properties of the proposed wavelet estimators are established under the α-mixing conditions and without specifying the error distribution. These results can be used to make asymptotically valid statistical inference.     

A note on the greenwood variance estimator in cohort life tables: Isolating the effect of one source of bias

A modification of the Greenwood variance estimator is defined and shown to be free of bias whenever its constitu­ent interval estimators are conditionally unbiased, given the sample size at the start of the interval. Using the modified estimator as a standard of comparison, the original Greenwood estimator is seen to have an intrinsic positive bias.Under­estimation of variances through the use of Greenwood's formula must be due to bias in the constituent interval estimators and/or, with fixed interval bounds, due to disregarding the random character of the total number of life table intervals to exhaustion of ttje sample. Some easy to prove properties of the modified and the original Greenwood estimators are stated that apply in the absence of censoring. A suggest­ion is made for reducing the bias of the interval variance estimators.     

Some finite sample properties of generalized ridge regression estimators

In this paper we study the mean square error properties of the generalized ridge estimator. We obtain the exact and the approximate bias and the mean square error of the operational generalized ridge estimator in terms of G( ) functions. We show, among other things, that the operational generalized ridge estimator does not dominate the ordinary least squares estimator up to a certain order of approximation. Finally, we note that the iterative procedures to obtain coverging ridge estimators should be used with caution.     

Impacts of auxiliary information on outliers in regression

Iheil and Goldberger (1961) and Theil (1963) founded the mixed regression approach, Their mixed regression estimator is essentially a large class of estimators that includes ridge, generalized ridge and shrinkage estimators, Properties of these estimators when data contain outliers have not been examined extensively. The present investigation shows that the mixed regression estimator, when observationsare subject to shift in means and variances, is uniformly superior, in terms of squared bias and variance, to the least squares estimator.     

Moment properties of estimators for a type 1 extreme-value regression model

A regression model is considered in which the response variable has a type 1 extreme-value distribution for smallest values. Bias approximations for the maximum likelihood estimators are pivm and a bias reduction estimator for the scale parameter is proposed. The small sample moment properties of the maximum likelihood estimators are compared with the properties of the ordinary least squares estimators and the best linear unbiased estimators based on order statistics for grouped data.     

Boundary and Bias Correction in Kernel Hazard Estimation

A new class of local linear hazard estimators based on weighted least square kernel estimation is considered. The class includes the kernel hazard estimator of Ramlau-Hansen (1983), which has the same boundary correction property as the local linear regression estimator (see Fan & Gijbels, 1996). It is shown that all the local linear estimators in the class have the same pointwise asymptotic properties. We derive the multiplicative bias correction of the local linear estimator. In addition we propose a new bias correction technique based on bootstrap estimation of additive bias. This latter method has excellent theoretical properties. Based on an extensive simulation study where we compare the performance of competing estimators, we also recommend the use of the additive bias correction in applied work.     

Nonparametric density estimation for multivariate bounded data

We propose a new nonparametric estimator for the density function of multivariate bounded data. As frequently observed in practice, the variables may be partially bounded (e.g. nonnegative) or completely bounded (e.g. in the unit interval). In addition, the variables may have a point mass. We reduce the conditions on the underlying density to a minimum by proposing a nonparametric approach. By using a gamma, a beta, or a local linear kernel (also called boundary kernels), in a product kernel, the suggested estimator becomes simple in implementation and robust to the well known boundary bias problem. We investigate the mean integrated squared error properties, including the rate of convergence, uniform strong consistency and asymptotic normality. We establish consistency of the least squares cross-validation method to select optimal bandwidth parameters. A detailed simulation study investigates the performance of the estimators. Applications using lottery and corporate finance data are provided.     

Moments of the function of non-normal random vector with applications to econometric estimators and test statistics

In this paper we have provided a general result on the moments of a function of nonnormal random vector. The results for the normal case follow as a special case of this result. It is also indicated that the moments of a large class of econometric estimators and test statistics can be obtained by using our general result. This includes least squares estimator in the dynamic model, unit root tests, and the two step semiparametric estimators, among others.     

Robust Sparse Regression with High-Breakdown Value

Penalized least squares estimators are sensitive to the influence of outliers like the ordinary least squares estimator. We propose a sparse regression estimator for robust variable selection and estimation based on a robust initial estimator. It is proven that our estimator has at least the same breakdown value as the initial estimator. Numerical examples are presented to illustrate our method.     

Moments of the function of non-normal random vector with applications to econometric estimators and test statistics 1

In this paper we have provided a general result on the moments of a function of nonnormal random vector. The results for the normal case follow as a special case of this result. It is also indicated that the moments of a large class of econometric estimators and test statistics can be obtained by using our general result. This includes least squares estimator in the dynamic model, unit root tests, and the two step semiparametric estimators, among others.