Parameter Hypothesis Testing Research Articles

Utilities for quantifying separation in PCA/PLS-DA scores plots

Metabolic fingerprinting studies rely on interpretations drawn from low-dimensional representations of spectral data generated by methods of multivariate analysis such as principal components analysis and projection to latent structures discriminant analysis. The growth of metabolic fingerprinting and chemometric analyses involving these low-dimensional scores plots necessitates the use of quantitative statistical measures to describe significant differences between experimental groups. Our updated version of the PCAtoTree software provides methods to reliably visualize and quantify separations in scores plots through dendrograms employing both nonparametric and parametric hypothesis testing to assess node significance, as well as scores plots identifying 95% confidence ellipsoids for all experimental groups.

SECOND-ORDER REFINEMENT OF EMPIRICAL LIKELIHOOD FOR TESTING OVERIDENTIFYING RESTRICTIONS

This paper studies second-order properties of the empirical likelihood overidentifying restriction test to check the validity of moment condition models. We show that the empirical likelihood test is Bartlett correctable and suggest second-order refinement methods for the test based on the empirical Bartlett correction and adjusted empirical likelihood. Our second-order analysis supplements the one in Chen and Cui (2007, Journal of Econometrics141, 492–516) who considered parameter hypothesis testing for overidentified models. In simulation studies we find that the empirical Bartlett correction and adjusted empirical likelihood assisted by bootstrapping provide reasonable improvements for the properties of the null rejection probabilities.

Sensor network scheduling for identification of spatially distributed processes

Sensor network scheduling for identification of spatially distributed processesThe work treats the problem of fault detection for processes described by partial differential equations as that of maximizing the power of a parametric hypothesis test which checks whether or not system parameters have nominal values. A simple node activation strategy is discussed for the design of a sensor network deployed in a spatial domain that is supposed to be used while detecting changes in the underlying parameters which govern the process evolution. The setting considered relates to a situation where from among a finite set of potential sensor locations only a subset of them can be selected because of the cost constraints. As a suitable performance measure, theDs-optimality criterion defined on the Fisher information matrix for the estimated parameters is applied. The problem is then formulated as the determination of the density of gauged sites so as to maximize the adopted design criterion, subject to inequality constraints incorporating a maximum allowable sensor density in a given spatial domain. The search for the optimal solution is performed using a simplicial decomposition algorithm. The use of the proposed approach is illustrated by a numerical example involving sensor selection for a two-dimensional diffusion process.

Second-Order Refinement of Empirical Likelihood for Testing Overidentifying Restrictions

This paper studies second-order properties of the empirical likelihood overidentifying restriction test to check the validity of moment condition models. We show that the empirical likelihood test is Bartlett correctable and suggest second-order refinement methods for the test based on the empirical Bartlett correction and adjusted empirical likelihood. Our second-order analysis supplements the one in Chen and Cui (2007) who considered parameter hypothesis testing for overidentified models. In simulation studies we find that the empirical Bartlett correction and adjusted empirical likelihood assisted by bootstrapping provide reasonable improvements for the properties of the null rejection probabilities.

Parameter Estimation and Hypothesis Testing of Two Negative Binomial Distribution Population with Missing Data

Abstract Our purpose is to deal with the parameter estimation and hypothesis testing on the equality of two negative binomial distribution populations with missing data. The consistency and asymptotic normality of the estimations are proved. In addition statistic on testing equality of two negative distributions and its limiting distribution are obtained.

Determining the significance and relative importance of parameters of a simulated quenching algorithm using statistical tools

When search methods are being designed it is very important to know which parameters have the greatest influence on the behaviour and performance of the algorithm. To this end, algorithm parameters are commonly calibrated by means of either theoretic analysis or intensive experimentation. When undertaking a detailed statistical analysis of the influence of each parameter, the designer should pay attention mostly to the parameters that are statistically significant. In this paper the ANOVA (ANalysis Of the VAriance) method is used to carry out an exhaustive analysis of a simulated annealing based method and the different parameters it requires. Following this idea, the significance and relative importance of the parameters regarding the obtained results, as well as suitable values for each of these, were obtained using ANOVA and post-hoc Tukey HSD test, on four well known function optimization problems and the likelihood function that is used to estimate the parameters involved in the lognormal diffusion process. Through this statistical study we have verified the adequacy of parameter values available in the bibliography using parametric hypothesis tests.

Parametric methods outperformed non-parametric methods in comparisons of discrete numerical variables

BackgroundThe number of events per individual is a widely reported variable in medical research papers. Such variables are the most common representation of the general variable type called discrete numerical. There is currently no consensus on how to compare and present such variables, and recommendations are lacking. The objective of this paper is to present recommendations for analysis and presentation of results for discrete numerical variables.MethodsTwo simulation studies were used to investigate the performance of hypothesis tests and confidence interval methods for variables with outcomes {0, 1, 2}, {0, 1, 2, 3}, {0, 1, 2, 3, 4}, and {0, 1, 2, 3, 4, 5}, using the difference between the means as an effect measure.ResultsThe Welch U test (the T test with adjustment for unequal variances) and its associated confidence interval performed well for almost all situations considered. The Brunner-Munzel test also performed well, except for small sample sizes (10 in each group). The ordinary T test, the Wilcoxon-Mann-Whitney test, the percentile bootstrap interval, and the bootstrap-t interval did not perform satisfactorily.ConclusionsThe difference between the means is an appropriate effect measure for comparing two independent discrete numerical variables that has both lower and upper bounds. To analyze this problem, we encourage more frequent use of parametric hypothesis tests and confidence intervals.

Comparisons of Methods for Analysis of Repeated Binary Responses with Missing Data

It is important yet challenging to choose an appropriate analysis method for the analysis of repeated binary responses with missing data. The conventional method using the last observation carried forward (LOCF) approach can be biased in both parameter estimates and hypothesis tests. The generalized estimating equations (GEE) method is valid only when missing data are missing completely at random, which may not be satisfied in many clinical trials. Several random-effects models based on likelihood or pseudo-likelihood methods and multiple-imputation-based methods have been proposed in the literature. In this paper, we evaluate the random-effects models with full- or pseudo-likelihood methods, GEE, and several multiple-imputation approaches. Simulations are used to compare the results and performance among these methods under different simulation settings.

Non-parametric statistical fault localization

Abstract Fault localization is a major activity in program debugging. To automate this time-consuming task, many existing fault-localization techniques compare passed executions and failed executions, and suggest suspicious program elements, such as predicates or statements, to facilitate the identification of faults. To do that, these techniques propose statistical models and use hypothesis testing methods to test the similarity or dissimilarity of proposed program features between passed and failed executions. Furthermore, when applying their models, these techniques presume that the feature spectra come from populations with specific distributions. The accuracy of using a model to describe feature spectra is related to and may be affected by the underlying distribution of the feature spectra, and the use of a (sound) model on inapplicable circumstances to describe real-life feature spectra may lower the effectiveness of these fault-localization techniques. In this paper, we make use of hypothesis testing methods as the core concept in developing a predicate-based fault-localization framework. We report a controlled experiment to compare, within our framework, the efficacy, scalability, and efficiency of applying three categories of hypothesis testing methods, namely, standard non-parametric hypothesis testing methods, standard parametric hypothesis testing methods, and debugging-specific parametric testing methods. We also conduct a case study to compare the effectiveness of the winner of these three categories with the effectiveness of 33 existing statement-level fault-localization techniques. The experimental results show that the use of non-parametric hypothesis testing methods in our proposed predicate-based fault-localization model is the most promising.

Statistics for terrified biologists

Statistics for terrified biologists

Calculating radiation exposures during use of (14)C-labeled nutrients, food components, and biopharmaceuticals to quantify metabolic behavior in humans.

14C has long been used as a tracer for quantifying the in vivo human metabolism of food components, biopharmaceuticals, and nutrients. Minute amounts (≤1 × 10 −18 mol) of 14C can be measured with high-throughput 14C-accelerator mass spectrometry (HT 14C-AMS) in isolated chemical extracts of biological, biomedical, and environmental samples. Availability of in vivo human data sets using a 14C tracer would enable current concepts of the metabolic behavior of food components, biopharmaceuticals, or nutrients to be organized into models suitable for quantitative hypothesis testing and determination of metabolic parameters. In vivo models are important for specification of intake levels for food components, biopharmaceuticals, and nutrients. Accurate estimation of the radiation exposure from ingested 14C is an essential component of the experimental design. Therefore, this paper illustrates the calculation involved in determining the radiation exposure from a minute dose of orally administered 14C-β-carotene, 14C-α-tocopherol, 14C-lutein, and 14C-folic acid from four prior experiments. The administered doses ranged from 36 to 100 nCi, and radiation exposure ranged from 0.12 to 5.2 μSv to whole body and from 0.2 to 3.4 μSv to liver with consideration of tissue weighting factor and fractional nutrient. In comparison, radiation exposure experienced during a 4 h airline flight across the United States at 37000 ft was 20 μSv.

On Bahadur efficiency of empirical likelihood

This paper studies the Bahadur efficiency of empirical likelihood for testing moment condition models. It is shown that under mild regularity conditions, the empirical likelihood overidentifying restriction test is Bahadur efficient, i.e., its p -value attains the fastest convergence rate under each fixed alternative hypothesis. Analogous results are derived for parameter hypothesis testing and set inference problems.

Bias and conflict in phylogenetic inference of myco-heterotrophic plants: a case study in Thismiaceae.

Due to morphological reduction and absence of amplifiable plastid genes, the identification of photosynthetic relatives of heterotrophic plants is problematic. Although nuclear and mitochondrial gene sequences may offer a welcome alternative source of phylogenetic markers, the presence of rate heterogeneity in these genes may introduce bias/systematic error in phylogenetic analyses. We examine the phylogenetic position of Thismiaceae based on nuclear 18S rDNA and mitochondrial atpA DNA sequence data, as well as using parsimony, likelihood and Bayesian inference methods. Significant differences in evolutionary rates of these genes between closely related taxa lead to conflicting results: while parsimony analyses of 18S rDNA and combined data strongly support the monophyly of Thismiaceae, Bayesian inference, with and without a relaxed molecular clock, as well as the Swofford-Olsen-Waddell-Hillis (SOWH) test confidently reject this hypothesis. We show that rate heterogeneity in our data leads to long-branch attraction artifacts in parsimony analysis. However, using model-based inference methods the question of whether Thismiaceae are monophyletic remains elusive. On the one hand maximum likelihood nonparametric bootstrapping and parametric hypothesis tests fail to support a paraphyletic Thismiaceae, on the other hand Bayesian inference methods (both without and with a relaxed clock) significantly reject a monophyletic Thismiaceae. These results show that an adequate sampling, the use of rate homogeneous data, and the application of different inference methods are important factors for developing phylogenetic hypotheses of myco-heterotrophic plants. © The Willi Hennig Society 2009.

On the Distribution of the Usual Estimator of C pk and Some Applications in SPC

ABSTRACT This article presents a new and appealing derivation of the distribution of Ĉ pk when the quality characteristic is normally distributed. Our derivation is based on the folded normal distribution and the fact that sample mean and sample standard deviation are independent. The final result is a complete and self-contained formula that can be easily implemented in any modern math package. We illustrate the use of the pdf of Ĉ pk in joint hypothesis testing of process parameters and in process control and monitoring. The ARL performance of a proposed control chart based on Ĉ pk is compared against the performance of and R charts.

Configuring A Sensor Network for Fault Detection in Distributed Parameter Systems

Configuring A Sensor Network for Fault Detection in Distributed Parameter SystemsThe problem of fault detection in distributed parameter systems (DPSs) is formulated as that of maximizing the power of a parametric hypothesis test which checks whether or not system parameters have nominal values. A computational scheme is provided for the design of a network of observation locations in a spatial domain that are supposed to be used while detecting changes in the underlying parameters of a distributed parameter system. The setting considered relates to a situation where from among a finite set of potential sensor locations only a subset can be selected because of the cost constraints. As a suitable performance measure, theDs-optimality criterion defined on the Fisher information matrix for the estimated parameters is applied. Then, the solution of a resulting combinatorial problem is determined based on the branch-and-bound method. As its essential part, a relaxed problem is discussed in which the sensor locations are givena prioriand the aim is to determine the associated weights, which quantify the contributions of individual gauged sites. The concavity and differentiability properties of the criterion are established and a gradient projection algorithm is proposed to perform the search for the optimal solution. The delineated approach is illustrated by a numerical example on a sensor network design for a two-dimensional convective diffusion process.

Demonstration of statistical approaches to identify component's ageing by operational data analysis—A case study for the ageing PSA network

The paper presents some results of a case study on “Demonstration of statistical approaches to identify the component's ageing by operational data analysis”, which was done in the frame of the EC JRC Ageing PSA Network. Several techniques: visual evaluation, nonparametric and parametric hypothesis tests, were proposed and applied in order to demonstrate the capacity, advantages and limitations of statistical approaches to identify the component's ageing by operational data analysis. Engineering considerations are out of the scope of the present study.

Conditional empirical likelihood estimation and inference for quantile regression models

Abstract This paper considers two empirical likelihood-based estimation, inference, and specification testing methods for quantile regression models. First, we apply the method of conditional empirical likelihood (CEL) by Kitamura et al. [2004. Empirical likelihood-based inference in conditional moment restriction models. Econometrica 72, 1667–1714] and Zhang and Gijbels [2003. Sieve empirical likelihood and extensions of the generalized least squares. Scandinavian Journal of Statistics 30, 1–24] to quantile regression models. Second, to avoid practical problems of the CEL method induced by the discontinuity in parameters of CEL, we propose a smoothed counterpart of CEL, called smoothed conditional empirical likelihood (SCEL). We derive asymptotic properties of the CEL and SCEL estimators, parameter hypothesis tests, and model specification tests. Important features are (i) the CEL and SCEL estimators are asymptotically efficient and do not require preliminary weight estimation; (ii) by inverting the CEL and SCEL ratio parameter hypothesis tests, asymptotically valid confidence intervals can be obtained without estimating the asymptotic variances of the estimators; and (iii) in contrast to CEL, the SCEL method can be implemented by some standard Newton-type optimization. Simulation results demonstrate that the SCEL method in particular compares favorably with existing alternatives.

Hypothesis Testing of Parameters for Ordinary Linear Circular Regression

This paper presents the hypothesis testing of parameters for ordinary linear circular regression model assuming the circular random error distributed as von Misses distribution. The main interests are in testing of the intercept and slope parameter of the regression line. As an illustration, this hypothesis testing will be used in analyzing the wind and wave direction data recorded by two different techniques which are HF radar system and anchored wave buoy.

Inference on Reliability in Two-parameter Exponential Stress–strength Model

The problem of hypothesis testing and interval estimation of the reliability parameter in a stress–strength model involving two-parameter exponential distributions is considered. Test and interval estimation procedures based on the generalized variable approach are given. Statistical properties of the generalized variable approach and an asymptotic method are evaluated by Monte Carlo simulation. Simulation studies show that the proposed generalized variable approach is satisfactory for practical applications while the asymptotic approach is not satisfactory even for large samples. The results are illustrated using simulated data.

Testing for Spatial Clustering of Amino Acid Replacements Within Protein Tertiary Structure

Widely used models of protein evolution ignore protein structure. Therefore, these models do not predict spatial clustering of amino acid replacements with respect to tertiary structure. One formal and biologically implausible possibility is that there is no tendency for amino acid replacements to be spatially clustered during evolution. An alternative to this is that amino acid replacements are spatially clustered and this spatial clustering can be fully explained by a tendency for similar rates of amino acid replacement at sites that are nearby in protein tertiary structure. A third possibility is that the amount of clustering exceeds that which can be explained solely on the basis of independently evolving protein sites with spatially clustered replacement rates. We introduce two simple and not very parametric hypothesis tests that help distinguish these three possibilities. We then apply these tests to 273 homologous protein families. The null hypothesis of no spatial clustering is rejected for 102 of 273 families. The explanation of spatially clustered rates but independent change among sites is rejected for 43 families. These findings need to be reconciled with the common practice of basing evolutionary inferences on models that assume independent change among sites.