Wald Test Statistics Research Articles

On local power of likelihood-based tests in von Mises regressions

The von Mises distribution has played a central role as a distribution on the circle. Its associated circular regression model has been applied in a number of areas. In this paper, we consider the von Mises regression model and, under a sequence of Pitman alternatives, derive the nonnull asymptotic expansions of the cumulative distribution functions of the likelihood ratio, Wald, Rao score, and gradient test statistics for testing a subset of the von Mises regression parameters, as well as for testing the concentration parameter. We then compare analytically the local power of these likelihood-based tests on the basis of the asymptotic expansions and provide conditions where one test can be more locally powerful than the other one in this class of regression models. Consequently, on the basis of the general conditions established, the user can choose the most powerful test to make inferences on the model parameters. We also provide a numerical example to illustrate the usefulness and applicability of the general result.

Tricks with metrics: combining statistics for improved inference in regression analysis

. In maximum likelihood methods, the three classical tests statistics are often unreliable for inference in small samples, even under the correct model specification. In this article, I discuss how likelihood ratio and Wald test statistics can be combined to obtain highly improved parameter inference in regression models with small samples. I consider modifications obtained from both the Barndorff-Nielsen and the Lugannani and Rice likelihood approximations, and I show how they can produce highly accurate parameter inference in a general (possibly non linear) regression model with possibly non spherical disturbances. I discuss the underlying theory and provide Monte Carlo simulations demonstrating the superior accuracy of the proposed procedures over the first-order classical likelihood methods (i.e., the signed log-likelihood ratio test and the Wald test). An empirical application to a regression model of mobile money (“M-pesa”) adoption in Kenya is provided as an illustration of the usefulness of these methods in practice.

RNA-Seq Analysis of Blastocoel Fluid-Conditioned Media From Euploid Embryos Reveals Higher Expression of Specific Mitochondrial Genes in Media From Embryos Associated With Positive Implantation Outcomes [ID 2683525

INTRODUCTION: This retrospective study measured gene expression using RNA-seq of blastocoel fluid-conditioned media from euploid embryos with known implantation status to identify genes associated with implantation outcomes. METHODS: Blastocoel fluid-conditioned media was obtained after biopsy (ploidy status via NextGen sequencing) of intracytoplasmic sperm injection-generated day 5 blastocysts. Media used for RNA-seq were from 10 euploid blastocysts with known implantation outcomes. RNA was extracted, libraries were prepared, NextSeq500 sequencing was performed, and then sequences were aligned to the human genome. After quality control, the total gene count was 15,284. DESeq2 was used to test for differential gene expression. Raw read counts were normalized and variance stabilizing transformations were applied across samples. Log fold change shrinkage methods were used for gene visualization and rankings. Wald test statistic was used to compare implantation outcomes. Adjusted false-discovery rate P value of <.05 was considered statistically significant for differential expressed genes. RESULTS: Several genes were identified in this analysis revealing differential expression when comparing implantation outcomes. Of interest were two mitochondrial genes (DNAJC19 and MT-TK) and the NOA1 (required for mitochondrial function) with higher expression in media from embryos resulting in successful implantation. CONCLUSION: This study implicates mitochondrial function as a key player during preimplantation development that may affect implantation outcomes. DNAJC19 acts to bring proteins into the mitochondrial matrix, MT-TK encodes a mitochondrial tRNA, and NOA1 is a GTP binding protein residing in the mitochondria. The media samples in this study were collected from euploid blastocysts; therefore, gene expression differences detected represent potential molecular markers for predicting implantation success.

Piecewise Linear Multiple Change Point Modelling for Under-Five Child Mortality

Using a piecewise linear multiple change-point model instead of more traditional survival techniques is more beneficial when dealing with mortality data. Utilizing this technique, the hazard model is estimated and the number of cut-point locations is found. Using various covariates, such as sociodemographic, biological, and proximate co-factors, this piecewise hazard model is fitted to the Infant Mortality Data of Bangladesh Demographic and Health Survey 2014. Finding the change point and the impact of covariates on the hazard rate is done using the maximum likelihood estimation process. The parameter's significance is subsequently supported by the Wald test statistic. It turns out that the mother's educational status, religion, mother's age in years, the number of children they have ever had, currently breastfeeding, the size of the child, desire for more children, cesarean delivery, ANC visits, and birth orders are all significant factors. It is also discovered that the detected change point of the hazard rate is extremely important for the child until they reach the age of five. Through the various time cut points, it is found that a piecewise linear multiple change-point model is very important for under-five child mortality. Public health specialists, researchers, and clinicians can all benefit from this piecewise hazard model. One of the most crucial elements in lowering child mortality is time.

Asymptotics for the conditional self‐weighted M$$ M $$ estimator of GRCA(p$$ p $$) models and its statistical inference

SummaryUnder the ‐order generalised random coefficient autoregressive (GRCA()) model with random coefficients we propose a conditional self‐weighted estimator of . We investigate the asymptotic normality of this estimator with possibly heavy‐tailed random variables. Furthermore, a Wald test statistic is constructed for the linear restriction on the parameters. In addition, the simulation experiments are carried out to assess the finite sample performance of theoretical results. Finally, a real data analysis about the increase (%) in the number of construction projects this year over the same period of last year is provided.

Treatment Durability of Limited Fasciectomy versus Percutaneous Needle Fasciotomy for Dupuytren Disease.

Patients with Dupuytren disease (DD) are mostly surgically treated by percutaneous needle fasciotomy (PNF) or limited fasciectomy (LF), but data on time intervals to retreatment are lacking. The authors aimed to estimate the risk of retreatment within certain time periods after treatment with PNF and LF. The authors used data of participants of a cohort study on the course of DD who were treated only with PNF or LF. The primary outcome measure was time to retreatment of DD. The authors included sex, age at first treatment, and having a first-degree relative with DD as confounders in our analysis. A bivariate gamma frailty model was applied to estimate the risk of retreatment within 1, 3, 5, 10, and 20 years after treatment with PNF and LF. The time to retreatment was significantly shorter after treatment with PNF than after LF (Wald test statistic, 7.56; P < 0.001). The estimated 10-year risk of retreatment for men who underwent their first treatment at a younger age and with a first-degree relative with DD was 97% after PNF and 32% after LF. The estimated 10-year risk for women who underwent their first treatment at an older age without a first-degree relative with DD was 20% after PNF and 6% after LF. The results show that the patients treated with PNF have a higher risk of retreatment. The results of this study could contribute to individualized information on the treatment durability in the future, which would improve patient counseling about the expected retreatment needs. Therapeutic, III.

Comparison of paired ordinal data with mis-classification and covariates adjustment

Abstract In this paper, we develop an estimation and testing procedure for comparing matched-pair ordinal outcomes in studies with confounding factors. The classification method for the categories of ordinal outcomes that is accessible for all units may be prone to mis-classification, and thus another error-free classification method that can only be affordable for a fraction of the units are used, resulting in a dataset with partial validation. The distribution of categorical variables is modelled using correlated bivariate Gaussian latent variables, and the confounding factors are adjusted as covariates. The mis-classification of ordinal outcomes is addressed by estimating the mis-classification probabilities through the partial validation structure of the dataset. The mis-classification probabilities and the other parameters are estimated by a two-stage maximum likelihood estimator, and the difference between the matched-pair ordinal outcomes are assessed by a Wald test statistic. Simulation studies were conducted to investigate the accuracy of the estimates of the model parameters, and the type I error rates and power of the proposed testing procedure. The motivating dataset from the Garki Project was analysed to demonstrate the applicability of the proposed approach.

Complex Parameter Rao and Wald Tests for Assessing the Bandedness of a Complex-Valued Covariance Matrix

Banding the inverse of a covariance matrix has become a popular technique for estimating a covariance matrix from a limited number of samples. It is of interest to provide criteria to determine if a matrix is bandable, as well as to test the bandedness of a matrix. In this paper, we pose the bandedness testing problem as a hypothesis testing task in statistical signal processing. We then derive two detectors, namely the complex Rao test and the complex Wald test, to test the bandedness of a Cholesky-factor matrix of a covariance matrix’s inverse. Furthermore, in many signal processing fields, such as radar and communications, the covariance matrix and its parameters are often complex-valued; thus, it is of interest to focus on complex-valued cases. The first detector is based on the complex parameter Rao test theorem. It does not require the maximum likelihood estimates of unknown parameters under the alternative hypothesis. We also develop the complex parameter Wald test theorem for general cases and derive the complex Wald test statistic for the bandedness testing problem. Numerical examples and computer simulations are given to evaluate and compare the two detectors’ performance. In addition, we show that the two detectors and the generalized likelihood ratio test are equivalent for the important complex Gaussian linear models and provide an analysis of the root cause of the equivalence.

Power enhancement for testing multi-factor asset pricing models via Fisher’s method

Testing multi-factor asset pricing models is instrumental for asset pricing theory and practice. However, due to the accumulation of errors in estimating high-dimensional parameters, traditional quadratic-form tests such as the Wald test perform poorly against the sparse alternative hypothesis, i.e., a few mispriced assets. Fan et al. (2015b) introduced a powerful testing procedure by adding a power enhancement component to the Wald test statistic and proved power enhancement properties. To provide an alternative to their methodology, we first instantiate the power enhancement component by introducing a new maximum-form test statistic and then study the asymptotic joint distribution of the Wald test statistic and the maximum test statistic. We prove that these two test statistics are asymptotically independent. Given their asymptotic independence, we propose a new power-enhanced testing procedure to combine their respective power based on Fisher’s method (Fisher, 1925). Theoretically, we prove that the new power-enhanced test retains the desired nominal significance level and achieves asymptotically consistent power against more general alternatives. Furthermore, we demonstrate the finite-sample performance of our proposed power-enhanced test in both simulation studies and an empirical study of testing market efficiency using asset returns of the Russel-2000 portfolio.

LONG-RUN AND SHORT-RUN CAUSALITY BETWEEN STOCK PRICE INDICES AND MACROECONOMIC VARIABLES: EVIDENCE OF PANEL VECM ANALYSIS FROM BOSNIA AND HERZEGOVINA, CROATIA, NORTH MACEDONIA AND SERBIA

The purpose of this paper is to identify the long-run and short-run relationship between the values of the Macedonian Stock Exchange Index composed of 10 most liquid listed stocks (MBI10), the Zagreb Stock Exchange Index (CROBEX) composed of the most liquid listed stocks, the Sarajevo Stock Exchange Index (SASX-10) composed of 10 most liquid listed stocks and the Belgrade Stock Exchange Index composed of 15 most liquid listed stocks (BELEX 15) and the selected macroeconomic variables. In order to identify the macroeconomic variables that affect the values of the selected stock indices, the analytical-synthetic method and the statistical method are applied. The statistical method uses econometric models for data analysis and interpretation and includes the application of the following econometric tools: Panel unit root test, Fisher -Johansen cointegration test, application of the panel vector error correction model (PVECM) and the Wald test statistics. The results of PVECM between the values of the selected stock indices and independent variables such as industrial production index 2015=100, average monthly gross wages, shows existence of conditionality or causal relationship on the long-run, when independent variable Harmonized Index of Consumer Prices (HICP) according to the COICOP classification 2015=100 is exluded from the model. By applying PVECM, it can be concluded that there is a long run causality running from independent variable to dependent variable, meaning that between the values of the selected stock indices and industrial production and average gross wages there is speed of adjustment towards long run equilibrium.

Omnibus test for restricted mean survival time based on influence function.

The restricted mean survival time (RMST), which evaluates the expected survival time up to a pre-specified time point , has been widely used to summarize the survival distribution due to its robustness and straightforward interpretation. In comparative studies with time-to-event data, the RMST-based test has been utilized as an alternative to the classic log-rank test because the power of the log-rank test deteriorates when the proportional hazards assumption is violated. To overcome the challenge of selecting an appropriate time point , we develop an RMST-based omnibus Wald test to detect the survival difference between two groups throughout the study follow-up period. Treating a vector of RMSTs at multiple quantile-based time points as a statistical functional, we construct a Wald test statistic and derive its asymptotic distribution using the influence function. We further propose a new procedure based on the influence function to estimate the asymptotic covariance matrix in contrast to the usual bootstrap method. Simulations under different scenarios validate the size of our RMST-based omnibus test and demonstrate its advantage over the existing tests in power, especially when the true survival functions cross within the study follow-up period. For illustration, the proposed test is applied to two real datasets, which demonstrate its power and applicability in various situations.

Estimating Vertical Price Transmission in Pulse Markets of India

This study was conducted to analyze the vertical integration in selected chickpea and pigeon pea markets. The Johansen cointegration method was used to observe the relationship between wholesale prices and retail prices of pulses. Further, the Vector Error Correction Model (VECM) was used to show short-run dynamics. Wald test statistic was used to examine the influence of all the lagged variables on retail prices. It was observed from the results of vertical integration that wholesale and retail prices were cointegrated only for markets like Delhi, Mumbai and Bangalore, which were either central or terminal. No co-integration was found for producing markets like Indore and Jaipur. The wholesale and retail prices behaved independently in the short run. Lack of integration implied an imperfect market situation for pulses hindering the perfect flow of price transmission. So, government policies should be formulated in such a way that ensures greater market efficiency. Physical and institutional market infrastructure needs to improve price transmission, specifically in the producer market.

Which Performance Tests Best Define the Special Judo Fitness Test Classification in Elite Judo Athletes?

The normative values of the Special Judo Fitness Test (SJFT) are used to evaluate judo athletes, and the question arises of which performance tests from crucial motor abilities best define the SJFT classification in elite judo athletes. This study aimed to investigate the relationship between elite judo athletes' physical performance and the evaluation using SJFT index norms. Nineteen judo athletes (11 females) (22.8 ± 2.5 years old) from the senior judo national team voluntarily participated in this study. Body composition, reaction time, balance, flexibility, agility, hand grip strength, 20 m sprint, vertical jump, SJFT, and Wingate tests were performed by athletes on four separate days at one-day intervals. Athletes were classified as regular and above (≥regular) or poor and below (≤poor) according to their SJFT index scores. Simple logistic regression analysis was used to evaluate this classification's consistency with performance test results. Odds ratios (OR) and 95% confidence intervals related to each possible factor and Wald test statistics were calculated. The SJFT index classification was associated with Wingate peak and mean power, vertical jump, and sprint performance results (p &lt; 0.05), whereas it was not associated with body fat percentage, agility, reaction time, hand grip strength, flexibility, and balance performances (p &gt; 0.05). SJFT index classificatory norms are mainly related to athletes' anaerobic power. Higher anaerobic power increases athletes' possibility of being classified as ≥regular.

Tests for independence between categorical variables

I prove the numerical equivalence between Pearson’s independence test statistic for categorical variables and the Lagrange Multiplier and overidentifying restrictions test statistics in several popular linear and non-linear regression models. I also show that its asymptotically equivalent Likelihood Ratio test is numerically identical in the non-linear regression models, and that the heteroskedasticity-robust Wald test statistic in the multivariate linear probability model and the moment condition model coincide with the Wald test statistic in the conditional multinomial model. Finally, I show that all these equivalences also apply to serial independence tests in discrete Markov chains. • Pearson’s independence test is numerically equivalent to the LM in regression models. • LR test is numerically identical in the non-linear regression models. • Heteroskedastic Wald test in LPM and GMM coincide with Wald in multinomial model. • All these equivalences apply to serial independence tests in discrete Markov chains.

Pooled OLS and Fixed Effect Estimation of Wage Structure and Differential in Handloom Sector: Choosing the Better Method

This study analyzed the wage structures and differentials of weavers in the handloom sector taking pooled Ordinary Least Square (OLS) and fixed effect model. Within Assam, India, primary data was collected from Bodoland Territorial Area Districts (BTAD), both rural and urban areas in the years 2018 and 2021. The result estimated by using pooled OLS shows production, productivity, education, experience, training, and distance of weavers from weaving residence to have a positive impact on the wages of weavers. Age, distance of weaving, and location of weaving were found to have a negative impact on wages. However, the result estimated using panel least square (fixed effect) showed age and location of weaving to have a negative impact on wages. The study also chose the better method among pooled OLS and fixed effect model. Since the probability value the Wald test statistic is less than 0.05, the fixed-effect model is preferred to Pooled OLS.

Are children living with obesity more likely to consult their general practitioner for knee pain? Longitudinal analysis of linked primary care and National Child Measurement Programme (NCMP) records.

ObjectivesMore than one in four 11-year-old children in England are living with obesity. The implications for future musculoskeletal health remain unclear. We assessed whether general practitioner consultations for knee pain were more likely among children with obesity, and how this varied by sex, ethnic background, and area-level deprivation. ApproachOf 61,478 11-year-old NCMP participants (2013-19), we linked 60,723 (98.8%) to their primary care records. 58,761 children (50.9% male) had no recorded knee pain consultation (including arthralgia and Osgood-Schlatter’s disease) prior to the NCMP measurement date. We calculated the proportion with a consultation for knee pain by ethnic-adjusted weight status (underweight&lt;2nd; overweight≥91st; obese≥98th centile), sex, ethnic background and Index of Multiple Deprivation quintile. We studied time to first general practitioner consultation for knee pain after the NCMP date by fitting Cox proportional hazards models, estimating mutually-adjusted hazard ratios (aHRs) and 95% confidence intervals (CI) for boys and girls separately. ResultsWe identified 2503 (4.3%) children with at least one consultation for knee pain after the NCMP date. Boys were more likely to consult than girls (mean difference 1.5%; 95% CI: 1.2,1.9). Median time to first knee pain consultation was 1.88 years (IQR: 0.94,2.93). In adjusted analyses, boys with underweight (aHR 0.16; 95% CI: 0.05,0.51), from South Asian ethnic backgrounds (0.80; 0.69,0.92) and living in less deprived areas (Wald test statistic: 11.41; p-value=0.0223) were less likely, and those from Black ethnic backgrounds (1.31; 1.13,1.51) more likely, to consult with knee pain. Girls from South Asian ethnic backgrounds (0.70; 0.59,0.84) and those living in less deprived areas (15.44; p-value=0.0039) were less likely, and those with a BMI considered obese (1.30; 1.10,1.54) more likely to do so. ConclusionAdolescent girls, but not boys, living with obesity are more likely to consult their general practitioner with knee pain. Ethnic differences in knee pain consultations merit further study. Linkage of primary care and NCMP records enables greater understanding of health service utilisation by children by weight status and demographic characteristics.

The role of domestic and foreign economic uncertainties in determining the foreign exchange rates: an extended monetary approach

This study extends the monetary model of the exchange rate by incorporating news-based domestic and US economic policy uncertainties (EPUs). We consider 12 developed and developing economies and use monthly data covering 2000:M1 to 2017:M2. The extended monetary model is estimated by the panel quantile regression of Machado and Santos Silva (2019) and Pesaran (2006) common correlated effects within linear and nonlinear panel ARDL frameworks. The estimates illustrate the significant effects of EPUs on developed and developing economies. The ARDL models show that the impact of EPUs is mostly a long-run phenomenon. The Wald test statistics confirm asymmetric effects of EPUs at different quantiles. Moreover, the Wald statistics also support the asymmetric effects of increasing and decreasing EPUs. Overall, domestic, and foreign economic uncertainties significantly affect developed and developing economies’ exchange rates, at least in the long run. Therefore, economic uncertainty should be considered in determining the exchange rate. This extended model might be more appropriate in the post-Covid-19 era.

Moderation effects of perceived resilience on the relationship between screen time, unstructured socializing, and self-perceived overweight

Objective Research has shown that social factors like peer networks and screen time exposure have a critical role in personal perceptions of weight. This study examined the relationships between television, computer/video games exposure, unstructured socializing (UnS), perceived resilience (PR), self-perceived overweight (SPO), and misperceptions of overweight (MO) in early adulthood. Method Data were obtained from Add Health, a public use sample of 2033 men and 2336 women 18–26 years old (M = 21.81 years; SD = 1.80). Binary logistic regression was used for all data analyses. Hesmer-Lemeshow and Wald test statistics were reported to compare binary logit models. Nagelkerke pseudo-R2 was computed for effect sizes. Results The results showed that TV had a positive effect on SPO and MO. Gender-specific patterns were found in SPO and MO that women were more likely to overestimate their weight than men, and men were more likely to have MO compared to women. The results yielded that the effect of PR on SPO is significant at .001 level. The moderator effect of PR was statistically significant only for the relationship between computer/video games exposure and SPO. Conclusion Reducing TV exposure might be a protective factor to prevent weight misperceptions. Further studies are needed to examine the effects of low, moderate, and high levels of leisure-based ST and gender-specific resilience strength programs on weight misperceptions.

Joint comparison of the predictive values of multiple binary diagnostic tests: an extension of McNemar’s test

ABSTRACT Positive and negative predictive values are important measures of the clinical accuracy of a diagnostic test. Various test statistics have been proposed to compare positive predictive values or negative predictive values of two binary diagnostic tests separately. However, such separate comparisons do not present a complete picture of the relative accuracy of the two diagnostic tests. In this paper, we propose an extension of McNemar’s test for the joint comparison of predictive values of multiple diagnostic tests. The proposed extended McNemar’s test is intuitive and simple to compute, only involving cell counts of discordant pairs from multiple tables. Furthermore, we also propose a re-formulation of an existing Wald test statistic so that it can be implemented more easily than its original form. Simulations demonstrate that the proposed extended McNemar’s test statistic preserves type one error much better than the existing Wald test statistic. Thus, we believe that the proposed extended McNemar’s test statistic is the preferred statistic to simultaneously compare the predictive values of multiple binary diagnostic tests.

A weight Jackknife approach utilizing linear model based-estimators for clustered data

Small number of clusters combined with cluster level heterogeneity poses a great challenge for the data analysis. We have published a weighted Jackknife approach to address this issue applying weighted cluster means as the basic estimators. The current study proposes a new version of the weighted delete-one-cluster Jackknife analytic framework, which employs Ordinary Least Squares or Generalized Least Squares estimators as the fundamentals. Algorithms for computing estimated variances of the study estimators have also been derived. Wald test statistics can be further obtained, and the statistical comparison in the outcome means of two conditions is determined using the cluster permutation procedure. The simulation studies show that the proposed framework produces estimates with higher precision and improved power for statistical hypothesis testing compared to other methods.