Nonparametric regression is an approximation method in regression analysis that is not constrained by the assumption of knowing the regression curve. One of the functions to approximate the curve is a Fourier series function. The nonparametric regression model with approximation of a Fourier series function has been widely discussed by several researchers. However, discussions on statistical inference, particularly in partial hypothesis testing, has not been carried out previously. Therefore, the purpose of this research is to discuss the statistical inference on nonparametric regression model with approximation of a Fourier series function. The discussion includes parameter and model estimations, simultaneous and partial hypotheses testing. In the application, we use life expectancy data from East Java Province during 2022. Based on data analysis, we obtain a model estimation with an R-square value of 96.24 %. At a 5 % significance level, the parameters simultaneously have a significant influence on the model. Partially, four parameters are not significant. However, overall, the predictor variables significantly influence the life expectancy data.•The Fourier series function used is a Fourier series function introduced by Bilodeau (1992).•The model estimation is obtained by selecting the optimal number of oscillation parameters.•The statistical test is obtained using the LRT method.

Interval-censored data are ubiquitous in clinical studies where actual time-to-event is difficult to measure. A number of nonparametric tests have been proposed to conduct a two-sample test using interval-censored data, and these tests can be used for assessing and comparing treatment effects over the control group. Alternatively, as commonly perceived, parametric tests can also be used assuming data are generated from a parametric family of distributions. To provide some guidance on choosing an appropriate method, in this paper, the performance of parametric tests and a series of nonparametric tests are compared through extensive simulation studies that cover a wide range of scenarios with varying sample sizes, varying censoring mechanisms and varying alternative hypotheses. For the purpose of illustration, we also apply these procedures to analyse three real datasets.

Randomized clinical trials are the gold standard for clinical trials as they reduce bias and minimize variability between different arms of a study. One of the drawbacks of these designs is their lack of flexibility to incorporate participant\'s treatment choice, which may reduce recruitment rates and/or reduce participant\'s tolerance if they receive a non-preferred treatment. Designs incorporating choice allow a subset of participants to choose their preferred treatment. Most of the current methods to analyze these types of designs are based on an ANOVA approach that do not allow for inclusion of covariates in the model. In this paper, we propose an alternative approach based on likelihood methods that can be used with a broad class of distributions and allow for inclusion of covariates and multiple study arms in the model. Using simulations, we evaluate these methods for a variety of continuous and categorical outcomes. Finally, we illustrate these methods by analyzing change in six minute walking distance from a behavioral intervention study for women with heart disease.

Categorical data analysis of 2 × 2 contingency tables is extremely common, not least because they provide risk difference, risk ratio, odds ratio, and log odds statistics in medical research. A χ2 test analysis is most often used, although some researchers use likelihood ratio test (LRT) analysis. Does it matter which test is used? A review of the literature, examination of the theoretical foundations, and analyses of simulations and empirical data are used by this paper to argue that only the LRT should be used when we are interested in testing whether the binomial proportions are equal. This so-called test of independence is by far the most popular, meaning the χ2 test is widely misused. By contrast, the χ2 test should be reserved for where the data appear to match too closely a particular hypothesis (e.g., the null hypothesis), where the variance is of interest, and is less than expected. Low variance can be of interest in various scenarios, particularly in investigations of data integrity. Finally, it is argued that the evidential approach provides a consistent and coherent method that avoids the difficulties posed by significance testing. The approach facilitates the calculation of appropriate log likelihood ratios to suit our research aims, whether this is to test the proportions or to test the variance. The conclusions from this paper apply to larger contingency tables, including multi-way tables.

Likelihood-based inference under nonconvex constraints on model parameters has become increasingly common in biomedical research. In this paper, we establish large-sample properties of the maximum likelihood estimator when the true parameter value lies at the boundary of a nonconvex parameter space. We further derive the asymptotic distribution of the likelihood ratio test statistic under nonconvex constraints on model parameters. A general Monte Carlo procedure for generating the limiting distribution is provided. The theoretical results are demonstrated by five examples in Anderson\'s stereotype logistic regression model, genetic association studies, gene-environment interaction tests, cost-constrained linear regression and fairness-constrained linear regression.

This work defines a new correction for the likelihood ratio test for a two-sample problem within the multivariate normal context. This correction applies to decomposable graphical models, where testing equality of distributions can be decomposed into lower dimensional problems.

There is growing interest in understanding geographic patterns of medical device-related adverse events (AEs). A spatial scan method combined with the likelihood ratio test (LRT) for spatial-cluster signal detection over the geographical region is universally used. The spatial scan method used a moving window to scan the entire study region and collected some candidate sub-regions from which the spatial-cluster signal(s) will be found. However, it has some challenges, especially in computation. First, the computational cost increased when the number of sub-regions increased. Second, the computational cost may increase if a large spatial-cluster pattern is present and a flexible-shaped window is used. To reduce the computational cost, we propose a Bayesian nonparametric method that combines the ideas of Markov random field (MRF) to leverage geographical information to find potential signal clusters. Then, the LRT is applied for the detection of spatial cluster signals. The proposed method provides an ability to capture both locally spatially contiguous clusters and globally discontiguous clusters, and is manifested to be effective and tractable using hypothetical Left Ventricular Assist Device (LVAD) data as an illustration.

Use of nonlinear statistical methods and models are ubiquitous in scientific research. However, these methods may not be fully understood, and as demonstrated here, commonly-reported parameter p-values and confidence intervals may be inaccurate. The gentle introduction to nonlinear regression modelling and comprehensive illustrations given here provides applied researchers with the needed overview and tools to appreciate the nuances and breadth of these important methods. Since these methods build upon topics covered in first and second courses in applied statistics and predictive modelling, the target audience includes practitioners and students alike. To guide practitioners, we summarize, illustrate, develop, and extend nonlinear modelling methods, and underscore caveats of Wald statistics using basic illustrations and give key reasons for preferring likelihood methods. Parameter profiling in multiparameter models and exact or near-exact versus approximate likelihood methods are discussed and curvature measures are connected with the failure of the Wald approximations regularly used in statistical software. The discussion in the main paper has been kept at an introductory level and it can be covered on a first reading; additional details given in the Appendices can be worked through upon further study. The associated online Supplementary Information also provides the data and R computer code which can be easily adapted to aid researchers to fit nonlinear models to their data.

Estimating phenotype networks is a growing field in computational biology. It deepens the understanding of disease etiology and is useful in many applications. In this study, we present a method that constructs a phenotype network by assuming a Gaussian linear structure model embedding a directed acyclic graph (DAG). We utilize genetic variants as instrumental variables and show how our method only requires access to summary statistics from a genome-wide association study (GWAS) and a reference panel of genotype data. Besides estimation, a distinct feature of the method is its summary statistics-based likelihood ratio test on directed edges. We applied our method to estimate a causal network of 29 cardiovascular-related proteins and linked the estimated network to Alzheimer\'s disease (AD). A simulation study was conducted to demonstrate the effectiveness of this method. An R package sumdag implementing the proposed method, all relevant code, and a Shiny application are available.

The study was done to determine additive, maternal and common permanent environmental effects and best-suited model for some production traits using six univariate animal models that differed in the (co)variance components fitted to assess the importance of maternal effect using likelihood ratio test in Murrah buffaloes. Data from 614 Murrah buffaloes related to production traits were collected from history pedigree sheets maintained at the buffalo farm, Department of Livestock Production and Management (LPM), LUVAS, Hisar. The production traits under this study were 305 days milk yield (305DMY), peak yield (PY), lactation length (LL), dry period (DP), lactation milk yield (LMY) and wet average (WA). The heritability estimates were in the range of 0.33-0.44 for 305DMY, 0.25-0.51 for PY, 0.05-0.13 for LL, 0.03-0.23 for DP, 0.17-0.40 for LMY and 0.37-0.66 for WA. Model 1 was considered best for most of the traits, viz., 305DMY, PY, LL, LMY and WA followed by model 2 for DP. Covariance and correlated values within the traits caused inflation of heritability in model 3 and model 6. The maximum covariance between the additive and maternal effect was found in trait LMY, which was 14,183.90 in model 3 and the minimum value was also reported in the same trait for model 6, valued at -3522.37. Multivariate analysis showed that all production traits were moderate to high and positively correlated with each other except for DP, which was low and negative genetic and phenotypic correlated. Spearman\'s rank correlation coefficients of breeding value among all six models were high and significant, ranged from 0.78 to 1.00 for all the traits except DP, therefore any of the models could be taken into account depending upon the availability of data.