Asymptotic Statistic Research Articles

Reduced‐rank space‐time adaptive processing algorithm based on multistage selections of angle‐Doppler filters

A new reduced-rank (RR) space-time adaptive processing (STAP) algorithm based on multistage selections of angle-Doppler filters is proposed in the form of a generalised sidelobe canceller. First, two types of the RR auxiliary angle-Doppler filters are designed based on the discrete Fourier basis functions. Then, a novel multistage method is implemented to select the angle-Doppler filters by using the cross-correlation observed at the current stage and the residual output observed at the previous stage. Finally, the asymptotic statistic performance of target detection is evaluated in terms of the conventional framework of STAP for the cases of both known and unknown covariance, which shows that the proposed algorithm is capable of providing the constant false alarm rate. Numerical examples are provided, and they demonstrate that the proposed algorithm is able to offer better performance than the existing sparsity-based and the conventional reduced-dimension algorithms under the intrinsic clutter motion and array gain and phase errors.

Multiple Group Comparisons of the Fixed and Random Effects From the Generalized Linear Mixed Model

In this article, we extend Liao’s test for across-group comparisons of the fixed effects from the generalized linear model to the fixed and random effects of the generalized linear mixed model (GLMM). Using as our basis the Wald statistic, we developed an asymptotic test statistic for across-group comparisons of these effects. The test can be applied when the fixed and random effects are multivariate normally distributed, and it works well for any link function and conditional distribution of the dependent variable of the GLMM. We also derived the asymptotic properties of this test, and because power information does not exist for either our new test statistic or Liao’s test, we implemented a power study to demonstrate the superiority of these tests over the alternatively proposed F test. Using an example, we show the application of the test and then discuss its possible restrictions with respect to the distribution of the random effects.

Effects of Electroconvulsive Therapy on Short-Term Suicide Mortality in a Risk-Matched Patient Population.

Although evidence has suggested that electroconvulsive therapy (ECT) is effective in reducing suicidal ideation, research establishing the effectiveness of ECT in reducing short-term risk of death by suicide is less conclusive. This study assessed whether receipt of ECT reduced suicide mortality among patients seeking healthcare in Veterans Health Administration hospitals. Annual cohorts of patients who received ECT between 2006 and 2015 were propensity score matched with mental health patients who did not receive ECT. After matching, population averaged adjusted odds were calculated to assess the risk of suicide in the year after receipt of ECT, compared with a control group. The study population consisted of 14,810 patients in the ECT cohort and 58,369 matched controls. Matching successfully reduced clinical and demographic differences between cohorts of patients who received ECT and those who did not (asymptotic Kolmogorov-Smirnov statistic = 0.02, P > 0.99). After matching and controlling for remaining between-group differences in an adjusted logistic regression, the odds of suicide in the year after receipt of ECT were not statistically different from those of matched patients who did not receive the procedure (odds ratio = 1.31, 95% confidence interval = 0.94-1.96, P = 0.095). Patients who received ECT were at a high risk for suicide. Electroconvulsive therapy did not seem to have a greater effect on decreasing short-term risk for suicide than other types of mental health treatment provided to patients with similar baseline risk.

Goodness of Fit Tests for Marshal-Olkin Extended Rayleigh Distribution

A class of goodness of fit tests for Marshal-Olkin Extended Rayleigh distribution with estimated parameters is proposed. The tests are based on the empirical distribution function. For determination of asymptotic percentage points, Kolomogorov-Sminrov, Cramer-von-Mises, Anderson-Darling,Watson, and Liao-Shimokawa test statistic are used. This article uses Monte Carlo simulations to obtain asymptotic percentage points for Marshal-Olkin extended Rayleigh distribution. Moreover, power of the goodness of fit test statistics is investigated for this lifetime model against several alternatives.

Asymptotic Maximum Order Statistic for SIR in ${\kappa} -{\mu}$ Shadowed Fading

Using tools from extreme value theory (EVT), it is proved that when the user signal and the interferer signals undergo independent and non-identically distributed (i.n.i.d.) $\kappa -\mu $ shadowed fading, the limiting distribution of the maximum of $L$ independent and identically distributed (i.i.d.) signal-to-interference ratio (SIR) random variables (RVs) is a Frechet distribution. It is observed that this limiting distribution is close to the true distribution of maximum for maximum SIR evaluated over moderate $L$ . Furthermore, moments of the maximum RV is shown to converge to the moments of the Frechet RV. In addition, the rate of convergence of the actual distribution of the maximum to the Frechet distribution is derived and analyzed for different $\kappa $ and $\mu $ parameters. Finally, results from the stochastic ordering are used to analyze the variation in the limiting distribution with respect to the variation in source fading parameters. These results are then used to derive upper bound for the rate in full array selection (FAS) schemes for the antenna selection and the asymptotic outage probability and the ergodic rate in maximum-sum-capacity (MSC) scheduling systems.

Single-trial Connectivity Estimation through the Least Absolute Shrinkage and Selection Operator.

Methods based on the use of multivariate autoregressive models (MVAR) have proved to be an accurate tool for the estimation of functional links between the activity originated in different brain regions. A well-established method for the parameters estimation is the Ordinary Least Square (OLS) approach, followed by an assessment procedure that can be performed by means of Asymptotic Statistic (AS). However, the performances of both procedures are strongly influenced by the number of data samples available, thus limiting the conditions in which brain connectivity can be estimated. The aim of this paper is to introduce and test a regression method based on Least Absolute Shrinkage and Selection Operator (LASSO) to broaden the estimation of brain connectivity to those conditions in which current methods fail due to the limited data points available. We tested the performances of the LASSO regression in a simulation study under different levels of data points available, in comparison with a classical approach based on OLS and AS. Then, the two methods were applied to real electroencephalographic (EEG) signals, recorded during a motor imagery task. The simulation study and the application to real EEG data both indicated that LASSO regression provides better performances than the currently used methodologies for the estimation of brain connectivity when few data points are available. This work paves the way to the estimation and assessment of connectivity patterns with limited data amount and in on-line settings.

Inference about the Ratio of the Coefficients of Variation of Two Independent Symmetric or Asymmetric Populations

Coefficient of variation (CV) is a simple but useful statistical tool to make comparisons about the independent populations in many research areas. In this study, firstly, we proposed the asymptotic distribution for the ratio of the CVs of two separate symmetric or asymmetric populations. Then, we derived the asymptotic confidence interval and test statistic for hypothesis testing about the ratio of the CVs of these populations. Finally, the performance of the introduced approach was studied through simulation study.

Generalized growth curve models for longitudinal data in application to a randomized controlled trial

Growth curve analysis is beneficial in longitudinal studies, where the pattern of response variables measured repeatedly over time is of interest, yet unknown. In this article, we propose generalized growth curve models under a polynomial regression framework and offer a complete process that identifies the parsimonious growth curves for different groups of interest, as well as compares the curves. A higher order of a polynomial degree generally provides more flexible regression, yet it may suffer from the complicated and overfitted model in practice. Therefore, we employ the model selection procedure that chooses the optimal degree of a polynomial consistently. Consideration of a quadratic inference function (Qu et al., 2000) for estimation on regression parameters is addressed and estimation efficiency is improved by incorporating the within-subject correlation commonly existing in longitudinal data. In biomedical studies, it is of particular interest to compare multiple treatments and provide an effective one. We further conduct the hypothesis test that assesses the equality of the growth curves through an asymptotic chi-square test statistic. The proposed methodology is employed on a randomized controlled longitudinal dataset on depression. The effectiveness of our procedure is also confirmed with simulation studies.

An Improved Hybrid Turbo Equalizer for Single Carrier Transmission with Impulsive Noise and ISI

In this paper, we propose an improved hybrid turbo equalizer (TEQ) for single-carrier transmission over multipath channels with symmetric alpha-stable noise. First, a nonlinear myriad filter is adopted for combating the effect of impulsive noise. The noise output of this nonlinear filter is analyzed by an asymptotic statistic method and shown to be asymptotically Gaussian. Then, a matched minimum mean square error based linear TEQ is proposed for further mitigating the effects of the residual impulsive noise and the intersymbol interference caused by multipath fading. In our proposed TEQ design procedure, the instantaneous estimation of the noise variance is exploited to obtain robust TEQ coefficients. Simulation results show that the proposed hybrid TEQ provides geometric signal-to-noise ratio improvements (of up to 4.5 dB) compared to conventional algorithms designed for Gaussian channels.

Median Tests for Censored Survival Data; a Contingency Table Approach

The median failure time is often utilized to summarize survival data because it has a more straightforward interpretation for investigators in practice than the popular hazard function. However, existing methods for comparing median failure times for censored survival data either require estimation of the probability density function or involve complicated formulas to calculate the variance of the estimates. In this article, we modify a K-sample median test for censored survival data (Brookmeyer and Crowley, 1982, Journal of the American Statistical Association 77, 433-440) through a simple contingency table approach where each cell counts the number of observations in each sample that are greater than the pooled median or vice versa. Under censoring, this approach would generate noninteger entries for the cells in the contingency table. We propose to construct a weighted asymptotic test statistic that aggregates dependent χ(2)-statistics formed at the nearest integer points to the original noninteger entries. We show that this statistic follows approximately a χ(2)-distribution with k-1 degrees of freedom. For a small sample case, we propose a test statistic based on combined p-values from Fisher's exact tests, which follows a χ(2)-distribution with 2 degrees of freedom. Simulation studies are performed to show that the proposed method provides reasonable type I error probabilities and powers. The proposed method is illustrated with two real datasets from phase III breast cancer clinical trials.

A Chi-Squared Statistic for Comparing the Independence of Out-of-Sample Factor Returns

We present a simple asymptotic statistic to evaluated the independence of factor return series when computed from orthogonal loadings used out-of-sample.

Regression on Quantile Residual Life

A time-specific log-linear regression method on quantile residual lifetime is proposed. Under the proposed regression model, any quantile of a time-to-event distribution among survivors beyond a certain time point is associated with selected covariates under right censoring. Consistency and asymptotic normality of the regression estimator are established. An asymptotic test statistic is proposed to evaluate the covariate effects on the quantile residual lifetimes at a specific time point. Evaluation of the test statistic does not require estimation of the variance-covariance matrix of the regression estimators, which involves the probability density function of the survival distribution with censoring. Simulation studies are performed to assess finite sample properties of the regression parameter estimator and test statistic. The new regression method is applied to a breast cancer data set with long-term follow-up to estimate the patients' median residual lifetimes, adjusting for important prognostic factors.

이변량 효능과 안전성 이항변수의 표본수 결정방법

두 군의 처리를 비교하는 임상시험에서 효능(efficacy)과 안전성(safety)이 동일하게 중요한 변수로 취급되는 경우에 이변량(bivariate) 반응변수로서 분석되고 연구계획의 단계에서도 이변량 표본수 결정방법이 사용되어야 한다. Thall과 Cheng (1999)은 효능과 안전성의 반응값이 이변량 이항(bivariate binary) 변수인 경우의 표본수 결정방법을 제시하였으며, 본 연구에서는 목표모수 설정과정은 기존의 연구와 같으나 월콕슨-만-휘트니(Wilcoxon-Mann-Whitney: WMW) 통계량에 근거한 검정법과 표본수 결정방법을 제시한다. Thall과 Cheng (1999)의 검정통계량은 변수 변환시킨 비율의 근사 정규성에 근거하는 반면에, WMW 통계량은 확률에 근거한 비모수적 방법으로 이변량 이항변수 뿐만 아니라 이변량 순위변수로 측정된 반응값에도 적용시킬 수 있다 Thall과 Cheng (1999)에 제시한 항암치료 임상연구의 두 예제에 위의 두 다른 방법으로 계산된 표본수를 비교한 결과, Thall과 Cheng (1999)의 첫째 예제에서는 이변량 WMW 방법에 의한 표본수가 더욱 작았으나 둘째 예제에서는 더욱 큰 것으로 나타났다. We consider sample-size determination problem motivated by comparative clinical trials where patient outcomes are characterized by a bivariate outcome of efficacy and safety. Thall and Cheng (1999) presented a sample size methodology for the case of bivariate binary outcomes. We propose a bivariate Wilcoxon-Mann-Whitney(WMW) statistics for sample-size determination for binary outcomes, and this nonparametric method can be equally used to determine sample sizes of ordinal outcomes. The two methods of sample size determination rely on the same testing strategy for the target parameters but differs in the test statistics, an asymptotic bivariate normal statistic of the transformed proportions in Thall and Cheng (1999) and nonparametric bivariate WMW statistic in the other method. Sample sizes are calculated for the two experimental oncology trials, described in Thall and Cheng (1999), and for the first trial example the sample sizes of a bivariate WMW statistic are smaller than those of Thall and Cheng (1999), while for the second trial example the reverse is true.

On the Existence of the Moments of the Asymptotic Trace Statistic

In this note we establish the existence of the flrst two moments of the asymptotic trace statistic, which appears as weak limit of the likelihood ratio statistic for testing the cointe- gration rank in a vector autoregressive model and whose moments may be used to develop panel cointegration tests. Moreover, we justify the common practice to approximate these moments by simulating a certain statistic, which converges weakly to the asymptotic trace statistic. To accomplish this we show that the moments of the mentioned statistic converge to those of the asymptotic trace statistic as the time dimension tends to inflnity.

Sample Size for Comparing Correlated Concordance Rates

We consider collecting the measurements of a gold standard and two methods with error from each site of subjects. We propose an asymptotic test statistic to compare the concordance rates of two methods with the gold standard and a closed-form sample size formula. Through simulations, we show that the test statistic accurately controls the type I error in small sample sizes, and the sample size formula accurately maintains the power in various settings. The proposed test statistic and the sample size formula can be easily modified for other indices for agreement such as sensitivity and specificity. A real eye study is taken as an example.

A note on calculating P values from 0.15–0.005 for the Anderson-Darling normality test using the F distribution

Exact P values in the range 0.15–0.005 for the Anderson-Darling statistic can be calculated using the F distribution by modifying the asymptotic statistic A* with a simple formula. The formula calculates F* and P is calculated using .

Selection of the best population: an information theoretic approach

This paper is devoted to the statistical problem of ranking and selection populations by using the subset selection formulation. The interest is focused (i) on the selection of the best population among k independent populations and (ii) on the selection of the best population, which is closest to an additional standard or control population. With respect to the first problem the populations are ranked in terms of entropies of their distributions and the population whose distribution has maximum entropy is selected. For the second problem the populations are ranked in terms of divergences between their distributions and the distribution of the standard or control population and the population with the minimum divergence is selected. In each case the populations are assumed to have general parametric densities satisfying the classical regularity conditions of asymptotic statistic. Large sample properties of the estimators of entropies and divergences of the populations will be studied and used in order to determine the probabilities of correct selection of the proposed asymptotic selection rules. Illustrative examples, including a numerical example using real medical data appeared in the literature, will be given for multivariate homoscedastic normal populations and populations described by the regular exponential family of distributions.

Simultaneous Non‐inferiority Test of Sensitivity and Specificity for Two Diagnostic Procedures in the Presence of a Gold Standard

AbstractSensitivity and specificity have traditionally been used to assess the performance of a diagnostic procedure. Diagnostic procedures with both high sensitivity and high specificity are desirable, but these procedures are frequently too expensive, hazardous, and/or difficult to operate. A less sophisticated procedure may be preferred, if the loss of the sensitivity or specificity is determined to be clinically acceptable. This paper addresses the problem of simultaneous testing of sensitivity and specificity for an alternative test procedure with a reference test procedure when a gold standard is present. The hypothesis is formulated as a compound hypothesis of two non‐inferiority (one‐sided equivalence) tests. We present an asymptotic test statistic based on the restricted maximum likelihood estimate in the framework of comparing two correlated proportions under the prospective and retrospective sampling designs. The sample size and power of an asymptotic test statistic are derived. The actual type I error and power are calculated by enumerating the exact probabilities in the rejection region. For applications that require high sensitivity as well as high specificity, a large number of positive subjects and a large number of negative subjects are needed. We also propose a weighted sum statistic as an alternative test by comparing a combined measure of sensitivity and specificity of the two procedures. The sample size determination is independent of the sampling plan for the two tests.

Comparison of Two Mesh Sizes for Collecting Larval Yellow Perch in Surface Trawls

Abstract We evaluated the differences in density estimates (larvae/100 m3), mean total lengths (TL; mm), and length frequency distributions of larval yellow perch Perca flavescens collected using 500- and 1,000-μm-mesh surface trawls in a small South Dakota lake. No significant difference in larval yellow perch density between mesh sizes was detected across sampling dates (F = 0.02, df = 1, P = 0.90). Significant differences in the length frequency distributions (Kolmogorov–Smirnov asymptotic test statistic = 1.532; df = 100, 106; P = 0.02) of larval yellow perch were detected on one early sampling date; however, when mean lengths exceeded 9 mm, total lengths and length frequency distributions were similar across mesh sizes. We collected smaller larval yellow perch (mean TL = 4.9 mm) earlier in the 500-μm-mesh net than in the 1,000-μm-mesh net. Peak larval yellow perch density was observed simultaneously and did not differ between mesh sizes. Estimates of precision associated with peak larval densities we...

TESTS OF COMMON STOCHASTIC TRENDS

This paper is concerned with tests in multivariate time series models made up of random walk (with drift) and stationary components. When the stationary component is white noise, a Lagrange multiplier test of the hypothesis that the covariance matrix of the disturbances driving the multivariate random walk is null is shown to be locally best invariant, something that does not automatically follow in the multivariate case. The asymptotic distribution of the test statistic is derived for the general model. The test is then extended to deal with a serially correlated stationary component. The main contribution of the paper is to propose a test of the validity of a specified value for the rank of the covariance matrix of the disturbances driving the multivariate random walk. This rank is equal to the number of common trends, or levels, in the series. The test is very simple insofar as it does not require any models to be estimated, even if serial correlation is present. Its use with real data is illustrated in the context of a stochastic volatility model, and the relationship with tests in the cointegration literature is discussed.