Empirical Power Study Research Articles

Goodness-of-fit tests for the one-sided Lévy distribution based on quantile conditional moments

In this paper we introduce a novel statistical framework based on the first two quantile conditional moments that facilitates effective goodness-of-fit testing for one-sided Lévy distributions. The scale-ratio framework introduced in this paper extends our previous results in which we have shown how to extract unique distribution features using conditional variance ratio for the generic class of α-stable distributions. We show that the conditional moment-based goodness-of-fit statistics are a good alternative to other methods introduced in the literature tailored to the one-sided Lévy distributions. The usefulness of our approach is verified using an empirical test power study. For completeness, we also derive the asymptotic distributions of the test statistics and show how to apply our framework to real data.

Power and leadership in small Russian monotowns

ABSTRACT This article presents the outcomes of an empirical study of power and leadership in three small Russian monotowns, conducted in 2011–2015 and 2018–2020. The study demonstrates the variability of power relations in Russian towns, despite the policy of centralization and the strengthening of authoritarian tendencies in Russian politics. The political process in monotowns retains its specificity due to the presence of town-forming enterprises, which largely determine the life of urban communities. Town-forming enterprises retain a high potential for influence in the political space of small towns, especially those enterprises that have solid economic resources and are successfully developing; their presence creates additional opportunities for the formation of an urban regime. The role of these enterprises in local politics varies significantly—from active participation to actual withdrawal. The differences largely depend on their economic potential and development prospects, as well as on a personal factor—the position of enterprise owners and the readiness of the leaders of municipal authorities and enterprises to cooperate.

New characterization-based exponentiality tests for randomly censored data

Recently, the characterization-based approach for the construction of goodness of fit tests has become popular. Most of the proposed tests have been designed for complete i.i.d. samples. Here, we present the adaptation of the recently proposed exponentiality tests based on equidistribution-type characterizations for the case of randomly censored data. Their asymptotic properties are provided. Besides, we present the results of wide empirical power study including the powers of several recent competitors. This study can be used as a benchmark for future tests proposed for this kind of data.

Does Power Corrupt? An Empirical Study of Power, Accountability, and Performance Triangle in Public Administration

ABSTRACTFoundational work in public administration has considered the relationship between administrative power, accountability, and performance in public organizations. Even with the vast literature addressing power, accountability, and performance, scholars are still theorizing on how they influence one another. This study proposes and empirically tests a theoretical model of the relationships between each of these three constructs. Data are analyzed from an original survey of a national sample of US local government public administrators—city managers. Using structural equation modeling, results show that there are positive relationships between power and accountability, power and performance, and accountability and performance. The article discusses theoretical and practical implications of these findings.

Representative body of local government: effects and costs of business presence

The article examines effects that presence of business in deputy corps and use of deputy (political) status in business activity have on potential of representative body of local government. The article is based on an empirical study of power in two Russian small towns - Kushva, Sverdlovsk region and Kungur, Perm region. Motives of entrepreneurs elected as deputies are presented. It is shown how the specificity of their interests affects the agenda of the representative body of public authority. The research specifies peculiarities of functioning of local government bodies in which local business is widely represented. It is shown how this type of representative bodies promotes rise of informal practices of authority and business interaction in the space of a town. It is proved that representative bodies of local government could act as coordinating and communicative platforms or lobbying platforms for local politicians and entrepreneurs. Conclusion is made about limited possibilities of realizing political potential of representative bodies of local government that are mainly comprised of local business

A wide review on exponentiality tests and two competitive proposals with application on reliability

ABSTRACTIn this paper, two new statistics based on comparison of the theoretical and empirical distribution functions are proposed to test exponentiality. Critical values are determined by means of Monte Carlo simulations for various sample sizes and different significance levels. Through an extensive simulation study, 50 selected exponentiality tests are studied for a wide collection of alternative distributions. From the empirical power study, it is concluded that, firstly, one of our proposals is preferable for IFR (increasing failure rate) and UFR (unimodal failure rate) alternatives, whereas the other one is preferable for DFR (decreasing failure rate) and BFR (bathtub failure rate) alternatives and, secondly, the new tests can be considered serious and powerful competitors to other existing proposals, since they have the same (or higher) level of performance than the best tests in the statistical literature.

Direction-Projection-Permutation for High-Dimensional Hypothesis Tests

High-dimensional low sample size (HDLSS) data are becoming increasingly common in statistical applications. When the data can be partitioned into two classes, a basic task is to construct a classifier that can assign objects to the correct class. Binary linear classifiers have been shown to be especially useful in HDLSS settings and preferable to more complicated classifiers because of their ease of interpretability. We propose a computational tool called direction-projection-permutation (DiProPerm), which rigorously assesses whether a binary linear classifier is detecting statistically significant differences between two high-dimensional distributions. The basic idea behind DiProPerm involves working directly with the one-dimensional projections of the data induced by binary linear classifier. Theoretical properties of DiProPerm are studied under the HDLSS asymptotic regime whereby dimension diverges to infinity while sample size remains fixed. We show that certain variations of DiProPerm are consistent and that consistency is a nontrivial property of tests in the HDLSS asymptotic regime. The practical utility of DiProPerm is demonstrated on HDLSS gene expression microarray datasets. Finally, an empirical power study is conducted comparing DiProPerm to several alternative two-sample HDLSS tests to understand the advantages and disadvantages of each method.

A Jonckheere–Terpstra-type test for perfect ranking in balanced ranked set sampling

Many methods based on ranked set sampling (RSS) assume perfect ranking of the samples. Here, by using the data measured by a balanced RSS scheme, we propose a nonparametric test for the assumption of perfect ranking. The test statistic that we use formally corresponds to the Jonckheere–Terpstra-type test statistic. We show formal relations of the proposed test for perfect ranking to other methods proposed recently in the literature. Through an empirical power study, we demonstrate that the proposed method performs favorably compared to many of its competitors.

A directional test of exponentiality based on maximum correlations

In Fortiana and Grane (J Stat Plann Infer 108:85–97), we study a scale-free statistic, based on Hoeffding’s maximum correlation, for testing exponentiality. This statistic admits an expansion along a countable set of orthogonal axes, originating a sequence of statistics. Linear combinations of a given number p of terms in this sequence can be written as a quotient of L-statistics. In this paper, we propose a scale-free adaptive statistic for testing exponentiality with optimal power against a specific alternative and obtain its exact distribution. An empirical power study shows that the test based on this new statistic has the same level of performance than the best tests in the statistical literature.

Testing Exponentiality Versus Pareto Distribution via Likelihood Ratio

We consider the problem of maximum likelihood estimation of the parameters of the Pareto Type II (Lomax) distribution. We show that in certain parametrization and after modification of the parameter space to include exponential distribution as a special case, the MLEs of parameters always exist. Moreover, the MLEs have a non standard asymptotic distribution in the exponential case due to the lack of regularity. Further, we develop a likelihood ratio test for exponentiality versus Pareto II distribution. We emphasize that this problem is non standard, and the limiting null distribution of the deviance statistic in not chi-square. We derive relevant asymptotic theory as well as a convenient computational formula for the critical values for the test. An empirical power study and power comparisons with other tests are also provided. A problem from climatology involving precipitation data from hundreds of meteorological stations across North America provides a motivation for and an illustration of the new test.

Testing Equality of Order Constrained Inverse Gaussian Means

The inverse Gaussian family of non negative, skewed random variables is analytically simple, and its inference theory is well known to be analogous to the normal theory in numerous ways. Hence, it is widely used for modeling non negative positively skewed data. In this note, we consider the problem of testing homogeneity of order restricted means of several inverse Gaussian populations with a common unknown scale parameter using an approach based on the classical methods, such as Fisher's, for combining independent tests. Unlike the likelihood approach which can only be readily applied to a limited number of restrictions and the settings of equal sample sizes, this approach is applicable to problems involving a broad variety of order restrictions and arbitrary sample size settings, and most importantly, no new null distributions are needed. An empirical power study shows that, in case of the simple order, the test based on Fisher's combination method compares reasonably with the corresponding likelihood ratio procedure.

Two-sample median test for order restricted randomized designs

A two-sample Mood median test, along with an associated confidence interval, is developed for the contrast parameter of the treatment and control medians, under an order restricted randomization. The exact and asymptotic null distributions of the test statistic are derived. It is shown that the proposed test is superior to the corresponding procedures based on completely randomized and ranked set sampling designs both in asymptotic relative efficiency and in empirical power study.

Goodness-of-Fit to the Exponential Distribution, Focused on Weibull Alternatives

ABSTRACT The goodness-of-fit technique based on the use of transformed empirical processes (TEPs) is applied to the construction of a test of exponentiality, focused on Weibull alternatives. The resulting procedure shares some desirable properties with other existing applications of the same technique: (a) the tests are consistent against fixed alternatives, (b) local alternatives belonging to the Weibull family are detected with an asymptotic power that does not differ significantly from the power of a two-sided (non consistent) likely ratio test (LRT), and (c) this asymptotic power is the same already encountered when a quadratic Cramér–von Mises–Watson type test statistic is used to test the fit to a single probability distribution, or to a parametric model with estimation of parameters–-In that sense, it is distribution free. In addition, an empirical power study shows that our test has the same level of performance than the best tests in the statistical literature.

New Tests for Multivariate Ordered Alternatives

We consider testing the equality of vector means against a multivariate ordered alternative. An extension of the Abelson and Tukey test is first derived under the assumption that the covariance matrix is known. The asymptotic distribution is obtained when the covariance is estimated. We also extend Schaafsma and Smid's somewhere most powerful test to multivariate normal settings, under the assumption that the covariance matrix is known. An empirical power study shows that these tests perform better than their multi-sided χ2 test counterparts.

Testing exponentiality by comparing the empirical distribution function of the normalized spacings with that of the original data

We introduce new goodness of fit tests for exponentiality by using a characterization based on normalized spacings. We provide relevant asymptotic theory for these tests and study their efficiency. An empirical power study and comparisons are also provided.

Measuring Duopoly Power in the British Electricity Spot Market

This article presents an empirical study of market power in the British electricity industry. Estimates of price-cost markups are derived using direct measures of marginal cost and several approaches that do not rely on cost data. Since two suppliers facing inelastic demand dominate the industry, most oligopoly models predict prices substantially above marginal costs. All estimates indicate that prices, while higher than marginal costs, are not nearly as high as most theoretical models predict. Regulatory constraints, the threat of entry, and financial contracts between the suppliers and their customers are considered as possible explanations for the observed price levels. (JEL L13, L94)

A Multivariate MultiSample Quantile Test for Ordered Alternatives

We propose and study a multivariate c-sample rank test for order-restricted alternatives when the underlying distributions have a contaminated component. An example concerning lens opacity in adults is presented. The asymptotic distributions are obtained under local mixture alternatives, and Pitman efficiencies are calculated. An empirical power study is also included.

A note on voting

A framework is presented in which to analyze the power of players in a cooperative game in which only certain coalitions are allowed. The allowable coalitions are characterized by a closure operator that combinatorially abstracts the notion of convexity. The Shapley-Shubik index is extended to this situation, allowing a computation of the power of each player. One example of this framework, voting on a one-dimensional spectrum, is analyzed and it is shown that the powerful players are mid-way between the middle and the extremes. This framework is also applied to an empirical study of power of the Supreme Court. Implications and generalizations are also discussed.

Nonparametric tests for orderedcsample contaminated distributions

In this paper, we propose and study a csample rank test for ordered alternatives when the underlying distributions have a contaminated component We obtain the asymptotic distributions under local mixture alternatives. Pitman efficiencies arc calculated and an empirical power study helps compare tests. Bahadur efficiency calculations are presented for the two sample case.

An Empirical Power Comparison of Three Tests of Exponentiality Under Mixture‐ and Outlier‐Models

AbstractWe present the results of an empirical power study of three prominent goodness‐of‐fit tests for exponentiality due to Shapiro and Wilk (1972), Durbin (1975), and Tiku (1980) by considering the mixture‐ and the outlier‐ exponential models as alternatives. This study is on similar lines as those of Dyer and Harbin (1981) and Balakrishnan (1983). We show that Tiku's test is on the whole considerably more powerful than the other two tests.