Nonparametric multivariate rank tests and their unbiasedness

Although unbiasedness is a basic property of a good test, many tests on vector parameters or scalar parameters against two-sided alternatives are not finite-sample unbiased. This was already noticed by Sugiura [Ann. Inst. Statist. Math. 17 (1965) 261--263]; he found an alternative against which the Wilcoxon test is not unbiased. The problem is even more serious in multivariate models. When testing the hypothesis against an alternative which fits well with the experiment, it should be verified whether the power of the test under this alternative cannot be smaller than the significance level. Surprisingly, this serious problem is not frequently considered in the literature. The present paper considers the two-sample multivariate testing problem. We construct several rank tests which are finite-sample unbiased against a broad class of location/scale alternatives and are finite-sample distribution-free under the hypothesis and alternatives. Each of them is locally most powerful against a specific alternative of the Lehmann type. Their powers against some alternatives are numerically compared with each other and with other rank and classical tests. The question of affine invariance of two-sample multivariate tests is also discussed.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ326 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Testing the Rational Expectations Hypothesis on the Retail Trade Sector Using Survey Data from Malaysia

The rational expectations hypothesis states that when people are expecting things to happen, using the available information, the predicted outcomes usually occur. This study utilized survey data provided by the Business Expectations Survey of Limited Companies to test whether forecasts of the Malaysian retail sector, based on gross revenue and capital expenditures, are rational. The empirical evidence illustrates that the decision-makers expectations in the retail sector are biased and too optimistic in forecasting gross revenue and capital expenditures.REH, Unbiasedness, Non-serial Correlation, Weak-form Efficiency

The Accuracy and Efficiency of the Consensus Forecasts: A Further Application and Extension of the Pooled Approach

In this paper we analyze the macroeconomic forecasts of the Consensus Forecasts for 12 countries over the period from 1996 to 2006 regarding bias and information efficiency. A pooled approach is employed which permits the evaluation of all forecasts for each target variable over 24 horizons simultaneously. It is shown how the pooled approach needs to be adjusted in order to accommodate the forecasting scheme of the Consensus Forecasts. Furthermore, the pooled approach is extended by a sequential test with the purpose of detecting the critical horizon after which the forecast should be regarded as biased. Moreover, heteroscedasticity in the form of year-specific variances of macroeconomic shocks is taken into account. The results show that in the analyzed period which was characterized by pronounced macroeconomic shocks, several countries show biased forecasts, especially with forecasts covering more than 12 months. In addition, information efficiency has to be rejected in almost all cases. --business cycle forecasting,forecast evaluation,Consensus Forecasts

Unbiased Instrumental Variables Estimation Under Known First-Stage Sign

We derive mean-unbiased estimators for the structural parameter in instrumental variables models with a single endogenous regressor where the sign of one or more first stage coefficients is known. In the case with a single instrument, there is a unique non-randomized unbiased estimator based on the reduced-form and first-stage regression estimates. For cases with multiple instruments we propose a class of unbiased estimators and show that an estimator within this class is efficient when the instruments are strong. We show numerically that unbiasedness does not come at a cost of increased dispersion in models with a single instrument: in this case the unbiased estimator is less dispersed than the 2SLS estimator. Our finite-sample results apply to normal models with known variance for the reduced-form errors, and imply analogous results under weak instrument asymptotics with an unknown error distribution

Optimal testing of equivalence hypotheses

In this paper we consider the construction of optimal tests of equivalence hypotheses. Specifically, assume X_1,..., X_n are i.i.d. with distribution P_{\theta}, with \theta \in R^k. Let g(\theta) be some real-valued parameter of interest. The null hypothesis asserts g(\theta)\notin (a,b) versus the alternative g(\theta)\in (a,b). For example, such hypotheses occur in bioequivalence studies where one may wish to show two drugs, a brand name and a proposed generic version, have the same therapeutic effect. Little optimal theory is available for such testing problems, and it is the purpose of this paper to provide an asymptotic optimality theory. Thus, we provide asymptotic upper bounds for what is achievable, as well as asymptotically uniformly most powerful test constructions that attain the bounds. The asymptotic theory is based on Le Cam's notion of asymptotically normal experiments. In order to approximate a general problem by a limiting normal problem, a UMP equivalence test is obtained for testing the mean of a multivariate normal mean.Comment: Published at http://dx.doi.org/10.1214/009053605000000048 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Accuracy, Unbiasedness and Efficiency of Professional Macroeconomic Forecasts: An empirical Comparison for the G7

In this paper, we use survey data to analyze the accuracy, unbiasedness, and the efficiency of professional macroeconomic forecasts. We analyze a large panel of individual forecasts that has not been analyzed in the literature so far. We provide evidence on the properties of forecasts for all G7 counties and for four diffierent macroeconomic variables. Our results show a high degree of dispersion of forecast accuracy across forecasters. We also find that there are large diffierences in the performance of forecasters not only across countries but also across diffierent macroeconomic variables. In general, forecasts tend to be biased in situations where forecasters have to respond to large structural shocks or gradual changes in the trend of a variable. Furthermore, while a sizable fraction of forecasters seem to smooth their GDP forecasts significantly, this does not apply to forecasts made for other macroeconomic variables.Evaluating forecasts, Macroeconomic Forecasting, Rationality, Survey Data, Fixed-Event Forecasts

Are Errors in Official U.S. Budget Receipts Forecasts Just Noise?

Existing evidence suggests that U.S. Government budget receipts forecasts are unbiased and efficient. Our study is an attempt to examine the veracity of these findings. The time series framework employed in this study is distinguished from previous work in three ways. First, we build a model that explicitly admits serial correlation in the residuals by allowing for autoregressive, moving-average, serial correlation. Second, we employ the nonparametric Monte-Carlo bootstrap to free ourselves from reliance on asymptotic distribution theory which is suspect given the short data series available for this study. Third, we control for errors in the macroeconomic and financial assumptions used to produce the U.S. Government's budget forecasts. We find that the U.S. Government's annual, one-year ahead, budget receipts forecasts for fiscal years 1963 through 2003 are biased and inefficient. In addition, we find that these forecasts exhibit serial correlation in their errors and thus do not efficiently exploit all available information. Finally, we find evidence that is consistent with strategic bias that may reflect the political goals of the Administration in power. Working Paper 07-2

Testing Distributional Inequalities and Asymptotic Bias

When Barret and Donald (2003) in Econometrica proposed a consistent test of stochastic dominance, they were silent about the asymptotic unbiasedness of their tests against √n-converging Pitman local alternatives. This paper shows that when we focus on first-order stochastic dominance, there exists a wide class of √n-converging Pitman local alternatives against which their test is asymptotically biased, i.e., having the local asymptotic power strictly below the asymptotic size. This phenomenon more generally applies to one-sided nonparametric tests which have a sup norm of a shifted standard Brownian bridge as their limit under √n-converging Pitman local alternatives. Among other examples are tests of independence or conditional independence. We provide an intuitive explanation behind this phenomenon, and illustrate the implications using the simulation studies.Asymptotic Bias, One-sided Tests, Stochastic Dominance, Conditional Independence, Pitman Local Alternatives, Brownian Bridge Processes