Critical Values For Tests Research Articles

The Impact of Public, Private, and Out-of-Pocket Health Expenditures on Under-Five Mortality in Malaysia.

Health financing in Malaysia is intensely subsidised by public funding and is increasingly sourced by household out-of-pocket financing, yet the under-five mortality rate has been gradually increasing in the last decade. In this context, this study aims to investigate the relationship between public, private, and out-of-pocket health expenditures and the under-five mortality rate in Malaysia using the autoregressive distributed lag (ARDL) estimation technique, whereby critical test values are recalculated using the response surface method for a time-series data of 22 years. The findings reveal that out-of-pocket health expenditure deteriorates the under-five mortality rate in Malaysia, while public and private health expenditures are statistically insignificant. Therefore, an effective health financing safety net may be an option to ensure an imperative child health outcome.

Bootstrap inference and diagnostics in state space models: With applications to dynamic macro models

AbstractThis paper investigates the potentials of the bootstrap as a tool for inference on the parameters of macroeconometric models which admit a state space representation. We consider a bootstrap estimator of the parameters of state space models and show that the bootstrap realizations of this estimator, usually employed to approximate asymptotic confidence intervals, p‐values, and critical values of tests, can be also constructively used to build a test for forms of misspecifications which invalidate asymptotic normality. The test evaluates how “close or distant” the estimated state space model is from the case where asymptotic inference based on the Gaussian distribution applies. We derive sufficient conditions on the number of bootstrap repetitions, B, relative to the number of sample observations, T, for the test statistic to have a well‐defined asymptotic distribution under the null. Throughout the paper, we focus on the state space form of small‐scale monetary dynamic stochastic general equilibrium (DSGE) models and investigate the usefulness of our approach through Monte Carlo experiments and empirical illustrations based on US quarterly data. Results show that (i) bootstrapping the state space form provides highly reliable inference and (ii) the suggested test detects weakly identified parameters reasonably well in finite samples.

Bootstrapping covariance operators of functional time series

For testing hypothesis on the covariance operator of functional time series, we suggest to use the full functional information and to avoid dimension reduction techniques. The limit distribution follows from the central limit theorem of the weak convergence of the partial sum process in general Hilbert space applied to the product space. In order to obtain critical values for tests, we generalise bootstrap results from the independent to the dependent case. This results can be applied to covariance operators, autocovariance operators and cross covariance operators. We discuss one sample and changepoint tests and give some simulation results.

Valid p-values and expectations of p-values revisited

We focus on valid definitions of p-values. A valid p-value (VpV) statistic can be used to make a prefixed level- $$ \alpha $$ decision. In this context, Kolmogorov–Smirnov goodness-of-fit tests and the normal two-sample problem are considered. We examine an issue regarding the goodness-of-fit testability based on a single observation. We exemplify constructions of new test procedures, advocating practical reasons to implement VpV mechanisms. The VpV framework induces an extension of the conventional expected p-value (EPV) tool for measuring the performance of a test. Associating the EPV concept with the receiver operating characteristic (ROC) curve methodology, a well-established biostatistical approach, we propose a Youden’s index-based optimality to derive critical values of tests. In these terms, the significance level $$ \alpha = 0.05 $$ is suggested. We introduce partial EPV’s to characterize properties of tests including their unbiasedness. We provide the intrinsic relationship between the Bayes Factor (BF) test statistic and the BF of test statistics.

Performance of Preliminary Test Estimators for Error Variance Based on W, LR and LM Tests

The performances of preliminary test estimators for error variance based on W, LR and LM tests in a normal linear model are considered in this paper. Firstly, the risks of the proposed estimators are derived and compared by theoretical analysis and numerical calculation, respectively. The results show that their risks are related to the equality constraint error and the critical value of test. Moreover, the minimum value of the risks can be achieved when the critical value of test equals to one. Secondly, the superiority conditions of the proposed estimators are discussed. Finally, the results are illustrated by a simulation example.

Measuring and testing for interval quantile dependence

In this article, we introduce the notion of interval quantile independence which generalizes the notions of statistical independence and quantile independence. We suggest an index to measure and test departure from interval quantile independence. The proposed index is invariant to monotone transformations, nonnegative and equals zero if and only if the interval quantile independence holds true. We suggest a moment estimate to implement the test. The resultant estimator is root-$n$-consistent if the index is positive and $n$-consistent otherwise, leading to a consistent test of interval quantile independence. The asymptotic distribution of the moment estimator is free of parent distribution, which facilitates to decide the critical values for tests of interval quantile independence. When our proposed index is used to perform feature screening for ultrahigh dimensional data, it has the desirable sure screening property.

Numerical distribution functions for seasonal unit root tests with OLS and GLS detrending

This paper implements the approach introduced by MacKinnon (J Bus Econ Stat 12:167–176, 1994, J Appl Econom 11:601–618, 1996) to estimate the response surface of the test statistics of seasonal unit root tests with OLS and GLS detrending for quarterly and monthly time series. The Gauss code that is available in the supplementary material of the paper produces p values for five test statistics depending on the sample size, deterministic terms and frequency of the data. A comparison with previous studies is undertaken, and an empirical example using airport passenger arrivals to a tourist destination is carried out. Quantile function coefficients are reported for simple computation of critical values for tests at 1, 5 and 10 % significance levels.

Estimating ARCH Models when the Coefficients are Allowed to be Equal to Zero

In order to be consistent with volatility processes, the autoregressive conditional heteroscedastic (ARCH) models are constrained to have nonnegative coefficients. The estimators incorporating these constraints possess non standard asymptotic distributions when the true parameter has zero coefficients. This situation, where the parameter is on the boundary of the parameter space, must be considered to derive the critical values of tests that one or several ARCH coefficients are equal to zero. In this paper we compare the asymptotic theoretical properties, as well as the finite sample behavior, of the main estimation methods in this framework.

Obtaining Critical Values for Test of Markov Regime Switching

For Markov regime-switching models, a nonstandard test statistic must be used to test for the possible presence of multiple regimes. Carter and Steigerwald (2013, Journal of Econometric Methods 2: 25–34) derive the analytic steps needed to implement the Markov regime-switching test proposed by Cho and White (2007, Econometrica 75: 1671–1720). We summarize the implementation steps and address the computational issues that arise. We then introduce a new command to compute regime-switching critical values, rscv, and present it in the context of empirical research.

Automated auditory response detection: Improvement of the statistical test strategy

Objective: Automated auditory response detection is always performed by applying an appropriate statistical test to a sample of stimulus-related epochs of the raw EEG. The often-used sequential test strategy saves time, but the multiple testing increases the probability of falsely detected responses. Therefore, the critical test value must guarantee the specified error probability for the maximum test step number. However, response detection at all lower test step numbers is disadvantaged. We propose calculating the critical test values for each test step number, which correspond exactly to the given error probability. Design: The critical test values for each test step were calculated by the method described by . A table with the test values was implemented with customized software of the Eclipse ASSR system® (Interacoustics, Denmark). Study sample: Table-related testing was performed on a sample of raw EEG data collected during the routine clinical measurement of frequency-specific auditory steady-state responses (ASSR) for hearing threshold assessment. Results: The new test strategy leads to a significantly increased detection rate and a significantly shorter detection time. Conclusions: The new test strategy can improve the performance of the objective hearing threshold assessment and of the newborn hearing screening.

Testing linear regression model with AR(1) errors against a first-order dynamic linear regression model with white noise errors: A point optimal testing approach

We know very little about the performance of point optimal (PO) and approximate point optimal (APO) tests in the presence of unavoidable nuisance parameters. Because marginal likelihood based tests are said to perform well in the presence of unavoidable nuisance parameters, this paper compares the performance of marginal likelihood based APO tests and classical tests using a testing problem which has been largely overlooked by econometric practitioners, namely testing for a static linear regression model with AR(1) errors against a dynamic linear regression model with white noise errors. It is well known that the classical tests are specifically designed for nested testing, they are applied to test for the significance of the dynamic coefficient of a dynamic linear regression model with AR(1) errors.A testing procedure is proposed, where the size and power comparisons used are based on near-exact non-similar critical values of tests obtained using the simulated annealing (SA) algorithm, as the near-exact non-similar critical values control the sizes of the tests well overall.Among marginal likelihood based classical tests, the likelihood ratio (LR) test and Lagrange multiplier (LM) test seem to perform well under the alternative hypothesis, particularly when the dynamic parameter is large and the sample size is reasonably big. The Wald (W) test is the worst performer overall. This concurs with previous observations that the W test performs poorly in small samples. Compared to the classical approach, APO tests appear to have good power properties, particularly in the neighborhood of the chosen parameter point under the alternative hypothesis. This finding may advance the use of PO and APO tests.

Bootstrap based model checks with missing binary response data

Dikta, Kvesic, and Schmidt proposed a model-based resampling scheme to approximate critical values of tests for model checking involving binary response data. Their approach is inapplicable when the binary response variable is not always observed, however. We propose a missingness adjusted marked empirical process under the framework that the missing binary responses are missing at random. We introduce a resampling scheme for the bootstrap and prove its asymptotic validity. We present some numerical comparisons and illustrate our methodology using a real data set.

Automated Extraction of Critical Test Values and Communications from Unstructured Radiology Reports: An Analysis of 9.3 Million Reports from 1990 to 2011

To determine the frequency of critical radiology results in 9.3 million radiology reports from our health system, to identify those containing documentation of communication by using automated text-classification algorithms, and to assess the impact of a policy requiring documentation of critical results communication. This HIPAA-compliant retrospective study received institutional review board approval. Text-mining algorithms that were previously validated to have mean accuracies of more than 90% for identifying certain critical results and documentation of communications were applied to a database of 9.3 million radiology reports. The frequency of critical results and documentation of communication were then determined from 1990 to 2011. There was an increase in documentation of communication for all critical results from 1990 to 2011. In 1990, 19.0% of reports with critical values had evidence of documentation of communication compared with 72.4% of reports in 2010. The linear trend for increasing documentation of communications began in 1997 and continued until 2011 (P < .001). From 1990 to 2011, documentation of communication was highest in acute scrotal torsion (70.6%) and ectopic pregnancy (65.4%) and lowest in unexplained free-intraperitoneal air (29.5%) and malpositioned tubes (30.4%). In 2010-2011, radiologists were least likely to document communication of results for malpositioned endotracheal and enteric tubes (2010, 58.56%; 2011, 57.50%) and unexplained free-intraperitoneal air (2010, 59.57%; 2011, 75.51%). They were most likely to document communication of results for ectopic pregnancy (2010, 94.12%; 2011, 93.48%) and acute appendicitis (2010, 86.87%; 2011, 84.31%). There was an increase in documentation of communication of critical results, which demonstrated a rising linear trend that began in 1997 and continued until 2011. The increasing trend began well before policy implementation, indicating that other factors such as heightened awareness among radiologists likely had a role.

Estimating critical values for testing the i.i.d. in standardized residuals from GARCH models in finite samples

Taking into account that the BDS test--which is used as a misspecification test applied to standardized residuals from the GARCH(1,1) model--is characterized by size distortion and departure from normality in finite samples, this paper obtains the critical values for the finite sample distribution of the BDS test. We focus on bootstrap simulation to avoid the sampling uncertainty of parameter estimation and make use of estimated response surface regressions (RSR) derived from the experimental results. We consider an extensive grid of models to obtain critical values with the results of the bootstrap experiments. The RSR used to estimate them is an artificial neural network (ANN) model, instead of the traditional linear regression models. Specifically, we estimate critical values by using a bootstrap aggregated neural network (BANN) and by employing functions of the sample size and parameters used in the experiment as the embedding dimension and proximity parameters in the BDS statistic, GARCH parameters and even the q-quantiles of the BDS distributions. The main results confirm that the sample size and BDS parameters play a role in size distortion. Finally, an empirical application to three price indexes is performed, to highlight the differences between decisions made using the asymptotic or our predicted critical values for the BDS test in finite samples.

A Bootstrap Test for the Equality of Nonparametric Regression Curves Under Dependence

A bootstrap procedure for testing the equality of several regression curves under dependence conditions is proposed. The errors are assumed to follow different ARMA structures. A test statistic based on the functional distances between nonparametric estimators of the regression functions is considered. The critical test values are obtained using a resampling method that takes into account the correlation structure. The consistency of the bootstrap procedure is established and its finite sample performance is investigated in a Monte Carlo study. Simulations show that our bootstrap-based test outperforms the asymptotic test. Applications are illustrated with a real data example.

A Comparison of Alternative Approaches to Supremum-Norm Goodness of Fit Tests with Estimated Parameters

Goodness of fit tests based on empirical processes have nonstandard limiting distributions when the null hypothesis is composite — that is, when parameters of the null model are estimated. Several solutions to this problem have been suggested, including the calculation of adjusted critical values for these nonstandard distributions and the transformation of the empirical process such that statistics based on the transformed process are asymptotically distribution-free. The approximation methods proposed by Durbin (1985) can be applied to compute appropriate critical values for tests based on supremum-norm statistics. The resulting tests have quite accurate size, a fact which has gone unrecognized in the econometrics literature. Some justification for this accuracy lies in the similar features that Durbin’s approximation methods share with the theory of extrema for Gaussian random fields and for Gauss-Markov processes. These adjustment techniques are also related to the transformation methodology proposed by Khmaladze (1981) through the score function of the parametric model. Simulation experiments suggest that these two testing strategies are roughly comparable to one another and more powerful than a simple bootstrap procedure.

Reality Checks and Comparisons of Nested Predictive Models

This article develops a simple bootstrap method for simulating asymptotic critical values for tests of equal forecast accuracy and encompassing among many nested models. Our method combines elements of fixed regressor and wild bootstraps. We first derive the asymptotic distributions of tests of equal forecast accuracy and encompassing applied to forecasts from multiple models that nest the benchmark model—that is, reality check tests. We then prove the validity of the bootstrap for these tests. Monte Carlo experiments indicate that our proposed bootstrap has better finite-sample size and power than other methods designed for comparison of nonnested models. Supplementary materials are available online.

Morphological differentiation of Primula veris L. pollen from natural and cultivated populations

Micromorphological characterisation and the comparative statistical analysis of the size of &lt;em&gt;Primula veris &lt;/em&gt;L. pollen grains collected in three natural and three cultivated populations were done. Observations were carried out with SEM. The obtained measurements were analysed with the use of one-way ANOVA, Kruskal-Wallis Test and the Student-&lt;em&gt;t&lt;/em&gt; Test. Pollen grains from long-styled ('pin') flower-morphs were mainly 6 colpate and from shortstyled ('thrum') flower-morphs 8 colpate. Colpi of some grains from 'thrum' flowers were 'sinuous' and 'circular', and they incised into the apocolpium zone. Ornamentation of 'pin' pollen grains was microreticulate, with lumina up to 0.8 μm wide, and for pollen grains from 'thrum' flowers was reticulate and eureticulate with lumina 1.1-1.7 μm wide. In lumina of mesocolpium area some free columellae were observed. Pollen grains from 'thrum' flower-morphs were more variable in size, both in natural and in cultivated populations, than grains from 'pin' flower-morphs. The differences in mean length (P) and breadth (E) of pollen grains from 'thrum' flowers collected in cultivated populations were statistically important (F&lt;sub&gt;P&lt;/sub&gt; = 3.154 for the critical F&lt;sub&gt;005&lt;/sub&gt; = 3.098; K-W&lt;sub&gt;e&lt;/sub&gt; = 7.469 for the critical Test value &lt;sub&gt;α=005&lt;/sub&gt; = 5.991). Pollen grains from 'thrum' flowers were bigger when coming from plants growing in natural populations (t&lt;sub&gt;E&lt;/sub&gt; = 2.784 for the critical Test value &lt;sub&gt;α=005&lt;/sub&gt; = 2.001).

On Critical Values of Tests against a Change in Persistence*

Kim, Belaire-Franch and Amador [Journal of Econometrics (2002) Vol. 109, pp. 389–392] and Busetti and Taylor [Journal of Econometrics (2004) Vol. 123, pp. 33–66] present different percentiles for the same mean score test statistic. We find that the difference by a factor 0.6 is due to systematically different sample analogues. Furthermore, we clarify which sample versions of the mean-exponential test statistic should be correctly used with which set of critical values. At the same time, we correct some of the limiting distributions found in the literature.

A Hypothesis Testing Procedure on Assessing Process Performance for Asymmetric Tolerances

The capability index Cpm takes into account the proximity of the process mean to the target and as well as the process variation. However, Cpm index has been shown to be inappropriate for measuring process performance with asymmetric tolerances. Several modifications of Cpm have been proposed to handle asymmetric tolerances, and has been shown to be superior to other existing generalizations. In this article, we implement the theory of hypothesis testing to develop a decision making procedure for assessing process performance based on index with critical values. The behavior of the critical values versus the unknown distribution parameter is also investigated to obtain reliable critical values for testing. To make the proposed procedure practical for in-plant applications, tables of critical values for various parameters are provided and an application example is demonstrated to evaluate the process performance for illustration.