Unbiased F Tests for Factorial Experiments for Correlated Data

This paper finds a general form of the correlation matrix that may be used to provide unbiased F tests in a.k-way factorial experiment.     

A class of distribution-free tests for the two-sample slippage problem

A class of distribution-free tests for the two-sample slippage problem, when the random variables take only nonnegative values, is proposed. These tests are consistent and unbiased against the general slippage alternative. Recurrence relations for generating small sample significance points are given. The tests have been compared with the Savage test, the Wilcoxon test and the appropriate locally most powerful rank test by considering Pitman asymptotic relative efficiencies for several alternative hypotheses. Some of these tests exhibit considerable robustness in terms of efficiency for the various alternative hypotheses which are considered.     

Unbiased goodness-of-fit tests

Familiar distribution-free goodness-of-fit tests like the Kolmogorov–Smirnov test are all biased tests. In this paper, we show how to compute the bias of any distribution-free goodness-of-fit test that corresponds to a distribution-free confidence band for the cumulative distribution function (CDF). The bias of the Kolmogorov–Smirnov test turns out to be smaller than the biases of other distribution-free goodness-of-fit tests. We also develop a method for obtaining unbiased goodness-of-fit tests, which can then be inverted to obtain unbiased confidence bands for the CDF. Interestingly, only a discrete set of levels are available for the unbiased tests. Our power comparisons show that while removing bias improves the power of a test at some alternatives, it does not improve the overall power properties of the test.     

Finite sample power of Cliff–Ord-type tests for spatial disturbance correlation in linear regression

The paper considers tests against autocorrelation among the disturbances in linear regression models that can be expressed as ratios of quadratic forms. It shows that such tests are, in general, not unbiased and that power can even drop to zero for certain regressors and spatial weight matrices. Whether or not this can happen is however easily diagnosed for given regressors and for given spatial weights.     

The approximation of an unbiased test with a small level for the bioequivalence problem

In the bioequivalence problem. Brown. Hwang and Munk (1997) constructed an unbiased level a test and other tests which are uniformly more powerful than the two one-sided tests procedures when a iscomparatively larger. In this paper, for a small level, an unbiased test is shown to be approxirnately constructeQ lor tnis prooiem oy using tneir Metnog. ine numerical construction is also given.     

Corrected f-tests in the general linear model

The theory of corrected F-tests in the general linear modeL with correlated errors is studied in this paper. Strictly unbiased F-tests are constructed in the presence of a large class of known non-identity correlation structures. These are generalized likelihood ratio tests which are easily computed. Critical points from the standard F-tables can be used to provide an exact test of desired size.     

Partial Round-Robin Comparisons with Perfect Rankings

In teaching the development of uniformly most powerful unbiased (UMPU) tests, one rarely discusses the performance of alternative biased tests. It is shown, through the comparison of two independent Bernoulli proportions, that a biased test (the Z test) can be more powerful than the UMPU test (Fisher's exact test—randomized) in a large region of the alternative parameter space. A more general example is also given.     

Robust inference for bivariate point processes

In the analysis of recurrent events where the primary interest lies in studying covariate effects on the expected number of events occurring over a period of time, it is appealing to base models on the cumulative mean function (CMF) of the processes (Lawless & Nadeau 1995). In many chronic diseases, however, more than one type of event is manifested. Here we develop a robust inference procedure for joint regression models for the CMFs arising from a bivariate point process. Consistent parameter estimates with robust variance estimates are obtained via unbiased estimating functions for the CMFs. In most situations, the covariance structure of the bivariate point processes is difficult to specify correctly, but when it is known, an optimal estimating function for the CMFs can be obtained. As a convenient model for more general settings, we suggest the use of the estimating functions arising from bivariate mixed Poisson processes. Simulation studies demonstrate that the estimators based on this working model are practically unbiased with robust variance estimates. Furthermore, hypothesis tests may be based on the generalized Wald or generalized score tests. Data from a trial of patients with bronchial asthma are analyzed to illustrate the estimation and inference procedures.     

Lessons from TGN1412 and TARGET: implications for observational studies and meta-analysis

Two very different studies are examined: the first, a very large trial in osteoarthritis (the so-called TARGET study) and the second a very small 'first-in-man' study of the monoclonal antibody TGN1412. In each trial the unbiased estimate of the treatment effect is not efficient and in con sequence the efficient estimate is not unbiased. In the case of the large trial it seems reasonable that unbiased estimation is desirable but in the case of the small trial it leads to absurd conclusions. These two cases are examined in detail and some general lessons for the analysis of clinical trials and observational studies and collections of studies are drawn.     

Exact tests for matched pairs:studies with covariates

In prospective or retrospective studies with matched pairs one often wishes to control for covariates other than those used in the matching process.Large sample procedures assuming a logistic model are available for this problem.The present paper presents some exact permutation tests which are uniformly most powerful unbiased within a large class of tests.     

Linear hypothesis testing for weighted functional data with applications

In socioeconomic areas, functional observations may be collected with weights, called weighted functional data. In this paper, we deal with a general linear hypothesis testing (GLHT) problem in the framework of functional analysis of variance with weighted functional data. With weights taken into account, we obtain unbiased and consistent estimators of the group mean and covariance functions. For the GLHT problem, we obtain a pointwise F-test statistic and build two global tests, respectively, via integrating the pointwise F-test statistic or taking its supremum over an interval of interest. The asymptotic distributions of test statistics under the null and some local alternatives are derived. Methods for approximating their null distributions are discussed. An application of the proposed methods to density function data is also presented. Intensive simulation studies and two real data examples show that the proposed tests outperform the existing competitors substantially in terms of size control and power.     

Comparing Equal-Tail Probability and Unbiased Confidence Intervals for the Intraclass Correlation Coefficient

The conventional confidence interval for the intraclass correlation coefficient assumes equal-tail probabilities. In general, the equal-tail probability interval is biased and other interval procedures should be considered. Unbiased confidence intervals for the intraclass correlation coefficient are readily available. The equal-tail probability and unbiased intervals have exact coverage as they are constructed using the pivotal quantity method. In this article, confidence intervals for the intraclass correlation coefficient are built using balanced and unbalanced one-way random effects models. The expected length of confidence intervals serves as a tool to compare the two procedures. The unbiased confidence interval outperforms the equal-tail probability interval if the intraclass correlation coefficient is small and the equal-tail probability interval outperforms the unbiased interval if the intraclass correlation coefficient is large.     

Locally optimal test for simultaneously testing the mean and variance of a normal distribution

A generalization of the locally most powerful unbiased (LMPU) test for the single parameter case to the k-parameter case was proposed by SenGupta and Vermeire (1986). In particular we defined a locally most mean power unbiased (LMMPU) test based on the mean curvature of the power hypersurface. Compared to the type C tests of Neyman and Pearson and the type D tests (Isaacson, 1951), LMMPU tests possess better theoretical properties and enjoy ease of construction of critical regions. In this paper we present an interesting example of a two-parameter univariate normal population for which Isaacson (1951, p. 233) was unsuccessful in finding a type D test. For the case of one observation, we prove that no Type D region exists but the LMMPU test is obtained - it is an example of a test with singular Hessian matrix for its power but is nevertheless a strictly locally unbiased (LU) test.     

Unbiased Estimation of the Distribution Function of an Exponential Population Using Order Statistics with Application in Ranked Set Sampling

In this paper we consider the problem of unbiased estimation of the distribution function of an exponential population using order statistics based on a random sample. We present a (unique) unbiased estimator based on a single, say ith, order statistic and study some properties of the estimator for i = 2. We also indicate how this estimator can be utilized to obtain unbiased estimators when a few selected order statistics are available as well as when the sample is selected following an alternative sampling procedure known as ranked set sampling. It is further proved that for a ranked set sample of size two, the proposed estimator is uniformly better than the conventional nonparametric unbiased estimator, further, for a general sample size, a modified ranked set sampling procedure provides an unbiased estimator uniformly better than the conventional nonparametric unbiased estimator based on the usual ranked set sampling procedure.     

A class of exact UMP unbiased tests for conditional symmetry in small-sample square contingency tables

Testing conditional symmetry against various alternative diagonals-parameter symmetry models often provides a point of departure in studies of square contingency tables with ordered categories. Typically, chi-square or likelihood-ratio tests are used for such purposes. Since these tests depend on the validity of asymptotic approximation, they may be inappropriate in small-sample situations where exact tests are required. In this paper, we apply the theory of UMP unbiased tests to develop a class of exact tests for conditional symmetry in small samples. Oesophageal cancer and longitudinal income data are used to illustrate the approach.     

Choice of Parametric Accelerated Life and Proportional Hazards Models for Survival Data: Asymptotic Results

We discuss the impact of misspecifying fully parametric proportional hazards and accelerated life models. For the uncensored case, misspecified accelerated life models give asymptotically unbiased estimates of covariate effect, but the shape and scale parameters depend on the misspecification. The covariate, shape and scale parameters differ in the censored case. Parametric proportional hazards models do not have a sound justification for general use: estimates from misspecified models can be very biased, and misleading results for the shape of the hazard function can arise. Misspecified survival functions are more biased at the extremes than the centre. Asymptotic and first order results are compared. If a model is misspecified, the size of Wald tests will be underestimated. Use of the sandwich estimator of standard error gives tests of the correct size, but misspecification leads to a loss of power. Accelerated life models are more robust to misspecification because of their log-linear form. In preliminary data analysis, practitioners should investigate proportional hazards and accelerated life models; software is readily available for several such models.     

On equality of ordinary least squares estimator,best linear unbiased estimator and best linear unbiased predictor in the general linear model

The equality of ordinary least squares estimator (OLSE), best linear unbiased estimator (BLUE) and best linear unbiased predictor (BLUP) in the general linear model with new observations is investigated through matrix rank method, some new necessary and sufficient conditions are given.     

A Test for Slope Heterogeneity in Fixed Effects Models

Typical panel data models make use of the assumption that the regression parameters are the same for each individual cross-sectional unit. We propose tests for slope heterogeneity in panel data models. Our tests are based on the conditional Gaussian likelihood function in order to avoid the incidental parameters problem induced by the inclusion of individual fixed effects for each cross-sectional unit. We derive the Conditional Lagrange Multiplier test that is valid in cases where N → ∞ and T is fixed. The test applies to both balanced and unbalanced panels. We expand the test to account for general heteroskedasticity where each cross-sectional unit has its own form of heteroskedasticity. The modification is possible if T is large enough to estimate regression coefficients for each cross-sectional unit by using the MINQUE unbiased estimator for regression variances under heteroskedasticity. All versions of the test have a standard Normal distribution under general assumptions on the error distribution as N → ∞. A Monte Carlo experiment shows that the test has very good size properties under all specifications considered, including heteroskedastic errors. In addition, power of our test is very good relative to existing tests, particularly when T is not large.     

Simple least squares estimation versus best linear unbiased prediction

Necessary and sufficient conditions are developed for the simple least squares estimator to coincide with the best linear unbiased predictor. The conditions obtained are valid for a general linear model and are generalizations of the condition given by Watson (1972). Also, as a preliminary result, a new representation of the best linear unbiased predictor is established.     

Uniformly most powerful unbiased test in univariate linear calibration

In this paper, we deal with the hypothesis testing problems for the univariate linear calibration, where a normally distributed response variable and an explanatory variable are involved, and the observations of the response variable corresponding to known values of the explanatory variable are used for making inferences concerning a single unknown value of the explanatory variable. The uniformly most powerful unbiased tests for both one-sided and two-sided hypotheses are constructed and verified. The power behaviour of the proposed tests is numerically compared with that of the existing method, and simulations show that the proposed tests make the powers improved.