Testing for covariate balance using quantile regression and resampling methods

Consistency of propensity score matching estimators hinges on the propensity score's ability to balance the distributions of covariates in the pools of treated and non-treated units. Conventional balance tests merely check for differences in covariates’ means, but cannot account for differences in higher moments. For this reason, this paper proposes balance tests which test for differences in the entire distributions of continuous covariates based on quantile regression (to derive Kolmogorov–Smirnov and Cramer–von-Mises–Smirnov-type test statistics) and resampling methods (for inference). Simulations suggest that these methods are very powerful and capture imbalances related to higher moments when conventional balance tests fail to do so.     

Testing for Equivalence of Means under Heteroskedasticity by an Approximate Solution of a Partial Differential Equation of Infinite Order

Abstract. A test for two‐sided equivalence of means has been developed under the assumption of normally distributed populations with heterogeneous variances. Its rejection region is limited by functions ± h that depend on the empirical variances. h is stated implicitly by a partial differential equation, an exact solution of which would provide a test that is exactly similar at the boundary of the null hypothesis of non‐equivalence. h is approximated by Taylor series up to third powers in the reciprocal number of degrees of freedom. This suffices to obtain error probabilities of the first kind that are very close to a nominal level of α = 0 . 05 at the boundary of the null hypothesis. For more than 10 data points in each group, they range between 0.04995 and 0.05005, and are thus much more precise than those obtained by other authors.     

Non‐parametric interval estimation for the partial area under the ROC curve

Accurate diagnosis of disease is a critical part of health care. New diagnostic and screening tests must be evaluated based on their abilities to discriminate diseased conditions from non‐diseased conditions. For a continuous‐scale diagnostic test, a popular summary index of the receiver operating characteristic (ROC) curve is the area under the curve (AUC). However, when our focus is on a certain region of false positive rates, we often use the partial AUC instead. In this paper we have derived the asymptotic normal distribution for the non‐parametric estimator of the partial AUC with an explicit variance formula. The empirical likelihood (EL) ratio for the partial AUC is defined and it is shown that its limiting distribution is a scaled chi‐square distribution. Hybrid bootstrap and EL confidence intervals for the partial AUC are proposed by using the newly developed EL theory. We also conduct extensive simulation studies to compare the relative performance of the proposed intervals and existing intervals for the partial AUC. A real example is used to illustrate the application of the recommended intervals. The Canadian Journal of Statistics 39: 17–33; 2011 © 2011 Statistical Society of Canada     

Goodness of fit tests with misclassified data

The most popular goodness of fit test for a multinomial distribution is the chi-square test. But this test is generally biased if observations are subject to misclassification, In this paper we shall discuss how to define a new test procedure when we have double sample data obtained from the true and fallible devices. An adjusted chi-square test based on the imputation method and the likelihood ratio test are considered, Asymptotically, these two procedures are equivalent. However, an example and simulation results show that the former procedure is not only computationally simpler but also more powerful under finite sample situations.     

Testing for normally in censored regressions

This paper derives a Lagrange Multiplier test for normality in censored regressions. The test is derived against the generalized log-gamma distribution, in which normal is a special case. The resulting test statistic coincides to some extent with previously suggested score and conditional moment tests. Estimation of the variance is performed by using the matrix of second order derivatives in order to get an easy to use test statistic. Small sample performance of the test is studied and compared to other tests by Monte Carlo experiments.     

Inference for Variance Components in a Mixed Model for Unbalanced Split Plot Design

Abstract

We consider the unbalanced split-plot design with the whole plot and the subplot effect from nonnormal universes. The three estimators for the whole plot effect variance component are obtained. An approximate test for significance of the whole plot effect variance component is presented.     

Testing Heterogeneity for Frailty Distribution in Shared Frailty Model

Abstract

The frailties, representing extra variations due to unobserved measurements, are often assumed to be iid in shared frailty models. In medical applications, however, a speculation can arise that a data set might violate the iid assumption. In this paper we investigate this conjecture through an analysis of the kidney infection data in McGilchrist and Aisbett (McGilchrist, C. A., Aisbett, C. W. (1991). Regression with frailty in survival analysis. Biometrics 47:461–466). As a test procedure, we consider the cusum of squares test which is frequently used for monitoring a variance change in statistical models. Our result strongly sustains the heterogeneity of the frailty distribution.     

A Locally Most Mean Powerful Based Score Test for ARCH and GARCH Regression Disturbances

This article considers the twin problems of testing for autoregressive conditional heteroscedasticity (ARCH) and generalized ARCH disturbances in the linear regression model. A feature of these testing problems, ignored by the standard Lagrange multiplier test, is that they are onesided in nature. A test that exploits this one-sided aspect is constructed based on the sum of the scores. The small-sample-size and power properties of two versions of this test under both normal and leptokurtic disturbances are investigated via a Monte Carlo experiment. The results indicate that both versions of the new test typically have superior power to two versions of the Lagrange multiplier test and possibly also more accurate asymptotic critical values.     

Smooth Tests of Copula Specifications

We present a family of smooth tests for the goodness of fit of semiparametric multivariate copula models. The proposed tests are distribution free and can be easily implemented. They are diagnostic and constructive in the sense that when a null distribution is rejected, the test provides useful pointers to alternative copula distributions. We then propose a method of copula density construction, which can be viewed as a multivariate extension of Efron and Tibshirani. We further generalize our methods to the semiparametric copula-based multivariate dynamic models. We report extensive Monte Carlo simulations and three empirical examples to illustrate the effectiveness and usefulness of our method.     

Seasonality Tests

This article modifies and extends the test against nonstationary stochastic seasonality proposed by Canova and Hansen. A simplified form of the test statistic in which the nonparametric correction for serial correlation is based on estimates of the spectrum at the seasonal frequencies is considered and shown to have the same asymptotic distribution as the original formulation. Under the null hypothesis, the distribution of the seasonality test statistics is not affected by the inclusion of trends, even when modified to allow for structural breaks, or by the inclusion of regressors with nonseasonal unit roots. A parametric version of the test is proposed, and its performance is compared with that of the nonparametric test using Monte Carlo experiments. A test that allows for breaks in the seasonal pattern is then derived. It is shown that its asymptotic distribution is independent of the break point, and its use is illustrated with a series on U.K. marriages. A general test against any form of permanent seasonality, deterministic or stochastic, is suggested and compared with a Wald test for the significance of fixed seasonal dummies. It is noted that tests constructed in a similar way can be used to detect trading-day effects. An appealing feature of the proposed test statistics is that under the null hypothesis, they all have asymptotic distributions belonging to the Cramér–von Mises family.