System GMM estimation with a small sample

Properties of GMM estimators for panel data, which have become very popular in the empirical economic growth literature, are not well known when the number of individuals is small. This paper analyses through Monte Carlo simulations the properties of various GMM and other estimators when the number of individuals is the one typically available in country growth studies. It is found that, provided that some persistency is present in the series, the system GMM estimator has a lower bias and higher efficiency than all the other estimators analysed, including the standard first-differences GMM estimator.

Swain: Stata module to correct the SEM chi-square overidentification test in small sample sizes or complex models. Statistical Software Components S457617, Boston College Department of Economics.

Swain corrects the chi-square overidentification test (i.e., likelihood ratio test of fit) for structural equation models whethr with or without latent variables. The chi-square statistic is asymptotically correct; however, it does not behave as expected in small samples and/or when the model is complex (cf. Herzog, Boomsma, & Reinecke, 2007). Thus, particularly in situations where the ratio of sample size (n) to the number of parameters estimated (p) is relatively small (i.e., the p to n ratio is large), the chi-square test will tend to overreject correctly specified models. To obtain a closer approximation to the distribution of the chi-square statistic, Swain (1975) developed a correction; this scaling factor, which converges to 1 asymptotically, is multiplied with the chi-square statistic. The correction better approximates the chi-square distribution resulting in more appropriate Type 1 reject error rates (see Herzog & Boomsma, 2009; Herzog, et al., 2007).

Nonlinear models and small sample performance of the generalized method of moments

In this paper I explore the issue of nonlinearity (both in the datageneration process and in the functional form that establishes therelationship between the parameters and the data) regarding the poorperformance of the Generalized Method of Moments (GMM) in small samples.To this purpose I build a sequence of models starting with a simple linearmodel and enlarging it progressively until I approximate a standard (nonlinear)neoclassical growth model. I then use simulation techniques to find the smallsample distribution of the GMM estimators in each of the models.

Small-Sample Corrections for Score Tests in Birnbaum-Saunders Regressions

In this article, we deal with the issue of performing accurate small-sample inference in the Birnbaum-Saunders regression model, which can be useful for modeling lifetime or reliability data. We derive a Bartlett-type correction for the score test and numerically compare the corrected test with the usual score test and some other competitors.

Accuracy in the measurement of fertility changes with only small sample data

Includes bibliography

Accuracy in the measurement of fertility changes with only small sample data

Includes bibliography

Improving IRT parameter estimates with small sample sizes: Evaluating the efficacy of a new data augmentation technique

The 3PL model is a flexible and widely used tool in assessment. However, it suffers from limitations due to its need for large sample sizes. This study introduces and evaluates the efficacy of a new sample size augmentation technique called Duplicate, Erase, and Replace (DupER) Augmentation through a simulation study. Data are augmented using several variations of DupER Augmentation (based on different imputation methodologies, deletion rates, and duplication rates), analyzed in BILOG-MG 3, and results are compared to those obtained from analyzing the raw data. Additional manipulated variables include test length and sample size. Estimates are compared using seven different evaluative criteria. Results are mixed and inconclusive. DupER augmented data tend to result in larger root mean squared errors (RMSEs) and lower correlations between estimates and parameters for both item and ability parameters. However, some DupER variations produce estimates that are much less biased than those obtained from the raw data alone. For one DupER variation, it was found that DupER produced better results for low-ability simulees and worse results for those with high abilities. Findings, limitations, and recommendations for future studies are discussed. Specific recommendations for future studies include the application of Duper Augmentation (1) to empirical data, (2) with additional IRT models, and (3) the analysis of the efficacy of the procedure for different item and ability parameter distributions.

Consequences of small sample 0-D data collection in the transportation planning process /

Mode of access: Internet.

Tables describing small-sample properties of the mean, median, standard deviation, and other statistics in sampling from various distributions /

Mode of access: Internet.

Estimation of IRT Parameters over a Small Sample. Bootstrapping of the Item Responses

2000 Mathematics Subject Classification: 97C40.

Small sample confidence intervals for the mean of a positively skewed distribution

This thesis proposes some confidence intervals for the mean of a positively skewed distribution. The following confidence intervals are considered: Student-t, Johnson-t, median-t, mad-t, bootstrap-t, BCA, T1 , T3 and six new confidence intervals, the median bootstrap-t, mad bootstrap-t, median T1, mad T1 , median T3 and the mad T3. A simulation study has been conducted and average widths, coefficient of variation of widths, and coverage probabilities were recorded and compared across confidence intervals. To compare confidence intervals, the width and coverage probabilities were compared so that smaller widths indicated a better confidence interval when coverage probabilities were the same. Results showed that the median T1 and median T3 outperformed other confidence intervals in terms of coverage probability and the mad bootstrap-t, mad-t, and mad T3 outperformed others in terms of width. Some real life data are considered to illustrate the findings of the thesis.

Moderating effects of management control systems and innovation on performance. Simple methods for correcting the effects of measurement error for interaction effects in small samples

In the accounting literature, interaction or moderating effects are usually assessed by means of OLS regression and summated rating scales are constructed to reduce measurement error bias. Structural equation models and two-stage least squares regression could be used to completely eliminate this bias, but large samples are needed. Partial Least Squares are appropriate for small samples but do not correct measurement error bias. In this article, disattenuated regression is discussed as a small sample alternative and is illustrated on data of Bisbe and Otley (in press) that examine the interaction effect of innovation and style of use of budgets on performance. Sizeable differences emerge between OLS and disattenuated regression

Bringing game theory to hypothesis testing: Establishing finite sample bounds on inference

Small sample properties are of fundamental interest when only limited data is avail-able. Exact inference is limited by constraints imposed by speci.c nonrandomizedtests and of course also by lack of more data. These e¤ects can be separated as we propose to evaluate a test by comparing its type II error to the minimal type II error among all tests for the given sample. Game theory is used to establish this minimal type II error, the associated randomized test is characterized as part of a Nash equilibrium of a .ctitious game against nature.We use this method to investigate sequential tests for the di¤erence between twomeans when outcomes are constrained to belong to a given bounded set. Tests ofinequality and of noninferiority are included. We .nd that inference in terms oftype II error based on a balanced sample cannot be improved by sequential sampling or even by observing counter factual evidence providing there is a reasonable gap between the hypotheses.