Optimal Test Statistic Research Articles

Ordering for Reduced Transmission Energy Detection in Sensor Networks Testing a Shift in the Mean of a Gaussian Graphical Model

Detection of a shift in the mean of a vector following a decomposable Gaussian graphical model (DGGM) is considered, where each component of the vector is measured at a different sensor in a network. We provide a new method eliminating transmissions normally needed in an optimum clustering approach by using ordered transmissions while achieving the same Bayes risk as the optimum clustering approach. In the new approach, the Bayes optimum test statistic is represented as a sum of local test statistics, where each local test statistic depends only on the observations made at one clique in a generalization of the ordered transmission approach previously suggested for statistically independent observations. Hence, we propose to organize the sensors into clusters based on the clique of the DGGM they belong to, and each cluster selects one sensor to be its cluster head (CH). After collecting and summarizing the observed data at each cluster, the ordered transmission approach is employed over the CHs in an attempt to reduce the number of communications from the CHs to the fusion center where the decision is made. It is shown that the developed approach can guarantee a lower bound on the average number of transmissions saved from the ordered transmission approach for any given DGGM which approaches approximately half the number of cliques when the norm of the mean-shift vector in each clique becomes sufficiently large. In all the cases considered, numerical results imply that a significant portion of the transmissions can be saved, and the developed lower bound is obeyed. The development of the appropriate local processing and the proof of savings are highly nontrivial generalizations of ordering for statistically independent observations and this paper represents the first justification of an ordering approach for cases with statistically dependent observations.

On the statistical power of Baarda’s outlier test and some alternative

Abstract Baarda’s outlier test is one of the best established theories in geodetic practice. The optimal test statistic of the local model test for a single outlier is known as the normalized residual. Also other model disturbances can be detected and identified with this test. It enjoys the property of being a uniformly most powerful invariant (UMPI) test, but is not a uniformly most powerful (UMP) test. In this contribution we will prove that in the class of test statistics following a common central or non-central χ2 distribution, Baarda’s solution is also uniformly most powerful, i.e. UMPχ2 for short. It turns out that UMPχ2 is identical to UMPI, such that this proof can be seen as another proof of the UMPI property of the test. We demonstrate by an example that by means of the Monte Carlo method it is even possible to construct test statistics, which are regionally more powerful than Baarda’s solution. They follow a so-called generalized χ2 distribution. Due to high computational costs we do not yet propose this as a ”new outlier detection method”, but only as a proof that it is in principle possible to outperform the statistical power of Baarda’s test.

Comparing family-based rare variant association tests for dichotomous phenotypes.

BackgroundIt has been repeatedly stressed that family-based samples suffer less from genetic heterogeneity and that association analyses with family-based samples are expected to be powerful for detecting susceptibility loci for rare disease. Various approaches for rare-variant analysis with family-based samples have been proposed.MethodsIn this report, performances of the existing methods were compared with the simulated data set provided as part of Genetic Analysis Workshop 19 (GAW19). We considered the rare variant transmission disequilibrium test (RV-TDT), generalized estimating equations-based kernel association (GEE-KM) test, an extended combined multivariate and collapsing test for pedigree data (known as Pedigree Combined Multivariate and Collapsing [PedCMC]), gene-level kernel and burden association tests with disease status for pedigree data (PedGene), and the family-based rare variant association test (FARVAT).ResultsThe results show that PedGene and FARVAT are usually the most efficient, and the optimal test statistic provided by FARVAT is robust under different disease models. Furthermore, FARVAT was implemented with C++, which is more computationally faster than other methods.ConclusionsConsidering both statistical and computational efficiency, we conclude that FARVAT is a good choice for rare-variant analysis with extended families.

A note on a family of criteria for evaluating test statistics

ABSTRACTIn noting that the usual criteria for choosing an optimal test, Uniform Power and Local Power are at opposite ends of a spectrum of dominance criteria, a complete “Power Dominance” family of criteria for classifying and choosing optimal tests on the basis of their power characteristics is identified, wherein successive orders of dominance attach increasing weight to power close to the null hypothesis. Indices of the extent to which a preferred test has superior power characteristics over other members in its class, and an index of the proximity of a test to the envelope function of alternative tests are also provided. The ideas are exemplified using various optimal test statistics for Normal and Laplace population distributions.

Optimal Test Statistics for Minimising not Cured Proportion in Adaptive Clinical Trial

In last several decades adaptive sequential binary design has been used with a goal to increase performance in estimation, testing of parameters and to reduce expected number of non-cured patients in the context of clinical trials.The procedures have been studied theoretically and also using simulation techniques in many papers. As for example play the winner rule, randomised play the winner rule, adaptive randomised play the winner rule have been studied extensively. Rosenberger et al. (Biometrics 57, 3, 909–913, 2001) considered different types of difference function of \( \hat {p_{A}}\) and \(\hat {p_{B}}\) as the test statistic in adaptive sequential design for the purpose of better inference along with decreasing number of non-cured patients. In this paper we considered how to choose the optimal function to achieve the goals with better performance. Using extensive simulation studies we have supported our claim and have shown that our methods perform better than existing methods. Also in the methods given by us we have a choice on the proportion of non-cured patients which we can vary with the inferential goal in mind. This is a new approach in adaptive sequential design.

On the Choice of Test Statistic for Conditional Moment Inequalities

This paper derives asymptotic approximations to the power of Cramer-von Mises (CvM) style tests for inference on a finite dimensional parameter defined by conditional moment inequalities in the case where the parameter is set identified. Combined with power results for Kolmogorov-Smirnov (KS) tests, these results can be used to choose the optimal test statistic, weighting function and, for tests based on kernel estimates, kernel bandwidth. The results show that, in the setting considered here, KS tests are preferred to CvM tests, and that a truncated variance weighting is preferred to bounded weightings.

Cooperative Spectrum Sensing in the Presence of Correlated and Malicious Cognitive Radios

While cooperative spectrum sensing improves sensing reliability when secondary users (SUs) have independent measurements, these gains are limited in the presence of correlated or malicious SUs. In this paper, we propose algorithms to improve spectrum sensing performance when the system contains both honest and malicious SUs all of whom may be experiencing correlated fading channels. We show that, when the SUs’ reports at each time slot are independent and identically distributed, it is impossible to distinguish between malicious collaboration, i.e., collusion, and correlations caused by the environment. Thus, the optimal test statistic for cooperative spectrum sensing depends on the correlations in the SU reports but not on the source of these correlations. We propose two algorithms: one to identify SUs whose reports are correlated and another to infer the spectrum occupancy by using the learned structure of correlations. Groups of SUs whose reports are correlated are identified by learning the structure of the underlying Bayesian network model. This structure is implemented as a factor graph to infer the spectrum occupancy using a loopy belief propagation algorithm. We derive an upper bound of the error probability of the proposed structure learning algorithm and prove convergence of our loopy belief propagation algorithm.

A Hybrid Mutation Chemical Reaction Optimization Algorithm for Global Numerical Optimization

This paper proposes a hybrid metaheuristic approach that improves global numerical optimization by increasing optimal quality and accelerating convergence. This algorithm involves a recently developed process for chemical reaction optimization and two adjustment operators (turning and mutation operators). Three types of mutation operators (uniform, nonuniform, and polynomial) were combined with chemical reaction optimization and turning operator to find the most appropriate framework. The best solution among these three options was selected to be a hybrid mutation chemical reaction optimization algorithm for global numerical optimization. The optimal quality, convergence speed, and statistical hypothesis testing of our algorithm are superior to those previous high performance algorithms such as RCCRO, HP-CRO2, and OCRO.

Stochastic Resonance with Colored Noise for Neural Signal Detection

We analyze signal detection with nonlinear test statistics in the presence of colored noise. In the limits of small signal and weak noise correlation, the optimal test statistic and its performance are derived under general conditions, especially concerning the type of noise. We also analyze, for a threshold nonlinearity–a key component of a neural model, the conditions for noise-enhanced performance, establishing that colored noise is superior to white noise for detection. For a parallel array of nonlinear elements, approximating neurons, we demonstrate even broader conditions allowing noise-enhanced detection, via a form of suprathreshold stochastic resonance.

Constructing Locally Best Invariant Tests of the Linear Regression Model Using the Density Function of a Maximal Invariant

In the context of the linear regression model in which som e regression coefficients are of interest and others are purely nuisance parameters, we derive the density function of a maximal invariant statistic after eliminating the nuisance parameters by the principle of invariance argu ment. This allows the construction of a range of optimal test statistics including the locally best invariant (LBI) test wh ich is equivalent to the well-known one-sided t-test. The resultant LBI test is also found to be uniformly most powerfu l invariant (UMPI).

DANPOS: Dynamic analysis of nucleosome position and occupancy by sequencing

Recent developments in next-generation sequencing have enabled whole-genome profiling of nucleosome organizations. Although several algorithms for inferring nucleosome position from a single experimental condition have been available, it remains a challenge to accurately define dynamic nucleosomes associated with environmental changes. Here, we report a comprehensive bioinformatics pipeline, DANPOS, explicitly designed for dynamic nucleosome analysis at single-nucleotide resolution. Using both simulated and real nucleosome data, we demonstrated that bias correction in preliminary data processing and optimal statistical testing significantly enhances the functional interpretation of dynamic nucleosomes. The single-nucleotide resolution analysis of DANPOS allows us to detect all three categories of nucleosome dynamics, such as position shift, fuzziness change, and occupancy change, using a uniform statistical framework. Pathway analysis indicates that each category is involved in distinct biological functions. We also analyzed the influence of sequencing depth and suggest that even 200-fold coverage is probably not enough to identify all the dynamic nucleosomes. Finally, based on nucleosome data from the human hematopoietic stem cells (HSCs) and mouse embryonic stem cells (ESCs), we demonstrated that DANPOS is also robust in defining functional dynamic nucleosomes, not only in promoters, but also in distal regulatory regions in the mammalian genome.

A simple and efficient test for the Pareto law

This note presents a simple and locally optimal test statistic for the Pareto law. The test is based on the Lagrange multiplier principle and can be computed easily once the maximum likelihood estimator of the scale parameter of the Pareto density has been obtained. A Monte Carlo exercise shows the good small sample properties of the test under the null of the Pareto law and also its power against some sensible and interesting alternatives. In addition, the proposed test is compared to a goodness of fit test which is powerful against more or less all alternatives. Eventually, a simple application to urban economics is performed.

A selection scheme for optimum number of cooperative secondary users in spectrum sensing

An optimization scheme for choosing the optimum number of secondary users in cooperative spectrum sensing based on the cyclostationary feature detection with Neyman-Pearson criterion is proposed in this paper. The optimal soft combination test statistic for the cooperative spectrum sensing based on cyclostationary feature detection is derived according to the generalized likelihood ratio test and its corresponding detection performance is deduced. A target function, considering two important parameters as the resource use efficiency and the number of samples employed by each cooperative secondary user in the system design, is constructed to obtain the optimum number of cooperative secondary users. It can be found that the selection scheme is to make a tradeoff between the system complexity of the cognitive radio network and the global sensing performance of the cooperative spectrum sensing.

A Powerful and Robust Test Statistic for Randomization Inference in Group‐Randomized Trials with Matched Pairs of Groups

For group-randomized trials, randomization inference based on rank statistics provides robust, exact inference against nonnormal distributions. However, in a matched-pair design, the currently available rank-based statistics lose significant power compared to normal linear mixed model (LMM) test statistics when the LMM is true. In this article, we investigate and develop an optimal test statistic over all statistics in the form of the weighted sum of signed Mann-Whitney-Wilcoxon statistics under certain assumptions. This test is almost as powerful as the LMM even when the LMM is true, but it is much more powerful for heavy tailed distributions. A simulation study is conducted to examine the power.

Ranking analysis for identifying differentially expressed genes

Microarrays allow researchers to examine the expression of thousands of genes simultaneously. However, identification of genes differentially expressed in microarray experiments is challenging. With an optimal test statistic, we rank genes and estimate a threshold above which genes are considered to be differentially expressed genes (DE). This overcomes the embarrassing shortcoming of many statistical methods to determine the cut-off values in ranking analysis. Experiments demonstrate that our method is a good performance and avoids the problems with graphical examination and multiple hypotheses testing that affect alternative approaches. Comparing to those well known methods, our method is more sensitive to data sets with small differentially expressed values and not biased in favor of data sets based on certain distribution models.

Designing clinical trials to test disease-modifying agents: application to the treatment trials of Alzheimer’s disease

Therapeutic trials of disease-modifying agents on Alzheimer's disease (AD) require novel designs and analyses involving switch of treatments for at least a portion of subjects enrolled. Randomized start and randomized withdrawal designs are two examples of such designs. Crucial design parameters such as sample size and the time of treatment switch are important to understand in designing such clinical trials. The purpose of this article is to provide methods to determine sample sizes and time of treatment switch as well as optimum statistical tests of treatment efficacy for clinical trials of disease-modifying agents on AD. A general linear mixed effects model is proposed to test the disease-modifying efficacy of novel therapeutic agents on AD. This model links the longitudinal growth from both the placebo arm and the treatment arm at the time of treatment switch for these in the delayed treatment arm or early withdrawal arm and incorporates the potential correlation on the rate of cognitive change before and after the treatment switch. Sample sizes and the optimum time for treatment switch of such trials as well as optimum test statistic for the treatment efficacy are determined according to the model. Assuming an evenly spaced longitudinal design over a fixed duration, the optimum treatment switching time in a randomized start or a randomized withdrawal trial is half way through the trial. With the optimum test statistic for the treatment efficacy and over a wide spectrum of model parameters, the optimum sample size allocations are fairly close to the simplest design with a sample size ratio of 1:1:1 among the treatment arm, the delayed treatment or early withdrawal arm, and the placebo arm. The application of the proposed methodology to AD provides evidence that much larger sample sizes are required to adequately power disease-modifying trials when compared with those for symptomatic agents, even when the treatment switch time and efficacy test are optimally chosen. The proposed method assumes that the only and immediate effect of treatment switch is on the rate of cognitive change. Crucial design parameters for the clinical trials of disease-modifying agents on AD can be optimally chosen. Government and industry officials as well as academia researchers should consider the optimum use of the clinical trials design for disease-modifying agents on AD in their effort to search for the treatments with the potential to modify the underlying pathophysiology of AD.

On the Interpretation, Robustness, and Power of Varieties of Case-Only Tests of Gene-Environment Interaction

The author addresses issues related to interpretation of the parameters in the proposed case-only linear regression approach to testing for gene-environment interaction recently considered by Clarke and Morris (Am J Epidemiol. 2010;171(4):498-505). He also considers the robustness of their likelihood ratio test to violation of the assumption of Gaussian regression residuals under the null hypothesis of no interaction; shows how their approach can be extended to a more general class of regression models; and derives the optimal interaction test statistic for this class of regression models. Finally, the author briefly discusses case-only doubly robust methods recently proposed by Tchetgen Tchetgen and Robins (Biometrics. 2010;Mar 11).

Bayesian Data Fusion for Distributed Target Detection in Sensor Networks

In this correspondence, we study different approaches for Bayesian data fusion for distributed target detection in sensor networks. Due to communication and bandwidth constraints, we assume that each sensor can only transmit a local decision to the fusion center (FC), which is in charge to take the final decision about the presence of a target. The optimal Bayesian test statistic at the FC is derived in the case where both the number and locations of the sensors are known. On the other hand, if both the number and the locations of the sensors are unknown, the optimal Bayesian test statistic is computed based on the same observations that the Scan Statistic test utilizes. The performances of the different approaches are compared through simulation.

Cooperative Spectrum Sensing in Cognitive Radios With Incomplete Likelihood Functions

This paper investigates the problem of cooperative spectrum sensing in cognitive radios with unknown parameters in the likelihood function. We first derive the optimal likelihood ratio test (LRT) statistic based on the Neyman-Pearson (NP) criterion at the fusion center for hard (one-bit), soft (infinite precision) and quantized (multi-bit) local decisions. This NP-based LRT detector is feasible only if primary signal statistics and channel parameters are known. This assumption may not be realistic in cognitive radio systems. Thus, we propose a linear composite hypothesis testing approach which estimates the unknown parameters, and further simplify it so that it does not even require these estimates. Under the scenarios of: i) unknown primary signal and channel statistics; and ii) unknown primary signal statistics but known channel statistics, we apply the proposed test and also, for case ii), derive the locally most powerful (LMP) detector for weak signals. For performance analysis and threshold setting, we derive the distributions of the linear test and LMP statistics under the signal-absent hypothesis. Our simulation results show that the linear test performs very closely to the optimal LRT while not requiring the primary statistics. As a result, this method enhances robustness in cooperative spectrum sensing to uncertainties in channel gains and signal statistics.

Performance of MIMO Radar With Angular Diversity Under Swerling Scattering Models

The performance of statistical multiple-input multiple-output (MIMO) radar configurations that use distributed antennas is analyzed in this paper. Statistical MIMO radars exploit angular diversity to mitigate the impact of radar cross section (RCS) fluctuations. The fluctuations can be modeled with the Swerling scattering model consisting of four different cases with either fast or slow target RCS fluctuations. In this paper, the performance of different statistical MIMO radar configurations is compared in the different Swerling cases. Both target detection and direction of arrival estimation tasks are considered. We derive the optimal test statistics for target detection for non-orthogonal waveforms in all the Swerling cases in single-pulse as well as multi-pulse scenarios. We derive a closed-form density function for the test statistics under null and alternate hypotheses in the Swerling cases 1 and 2. For orthogonal waveforms in cases 3 and 4, the density function is given as a convolution involving a transcendental function. A suboptimal detector having a closed-form density function in cases 3 and 4 when the waveforms are orthogonal is introduced as well. In the direction finding task, confidence bounds of the squared estimation error of the different configurations are compared. The comparison is done in terms of the confidence bounds as the Cramer-Rao bounds are not defined for all the cases and configurations. The pros and cons of the angular diversity and each radar configuration are pointed out in different fluctuation scenarios.