Chi-square Family Research Articles

Growth and biochemical markers of preterm newborns up to six months of corrected age

Introduction: Due to advances in recent decades in maternal-foetal and neonatal medicine, a greater survival of preterm infants with progressively smaller birth weight and gestational age is observed, increasing the risk of future morbidities on those infants. Among these morbidities, alterations in growth and metabolism are found. Objective: To analyze the evolution of the growth and the metabolic profile of preterm infants’ cohort from birth at six months of corrected age (CA).Methods: A descriptive and prospective study with a sample of 107 mothers and 115 preterm infants at birth and 72 preterm infants and 68 mothers at the end of follow-up. Growth (body weight, height, cephalic perimeter) was evaluated at six time points. Plasma concentrations of cholesterol, triglycerides, glucose and insulin of premature infants were assessed during three periods, from birth to 6 months of CA. Comparative analysis of the initial sample and the sample that finished the follow-up was used in chi-square family tests. To Evaluate the growth over the 6-month period by using repeated measurements.Results: Sociodemographic variables and maternal biochemical profile without statistical differences in the comparison of the mothers of the initial sample with those who completed the follow-up. Linear growth of preterm infants at six months of CA, however without recovery of growth. Plasma concentrations of triglycerides (birth = 48.1, 6 months = 151.1) and cholesterol (birth = 82.7, 6 months = 139.9) increased during the evaluations. Glycaemia remained stable (birth 80.4, 6 months = 83.3) and insulin decreased from 11.0 to 4.2.Conclusion: Growth of preterm infants, although linear, was lower than expected for age. Lipid profiles presented an ascending curve from birth onward. Therefore, this group is prone to delayed growth and to developing cardiovascular changes throughout life.

A note on the SG(m) test

Lopez et al. (Reg Sci Urban Econ 40(2–3):106–115, 2010) introduce a nonparametric test of spatial dependence, called SG(m). The test is claimed to be consistent and asymptotically Chi-square distributed. Elsinger (Reg Sci Urban Econ 43(5):838–840, 2013) raises doubts about the two properties. Using a particular counterexample, he shows that the asymptotic distribution of the SG(m) test may be far from the Chi-square family; the property of consistency is also questioned. In this note, the authors want to clarify the properties of the SG(m) test. We argue that the cause of the conflict is in the specification of the symbolization map. The discrepancies can be solved by adjusting some of the definitions made in the original paper. Moreover, we introduce a permutational bootstrapped version of the SG(m) test, which is powerful and robust to the underlying statistical assumptions. This bootstrapped version may be very useful in an applied context.

Steganalysis of JPEG steganography with complementary embedding strategy

Recently, a new high-performance JPEG steganography with a complementary embedding strategy (JPEG-CES) was presented. It can disable many specific steganalysers such as the Chi-square family and S family detectors, which have been used to attack J-Steg, JPHide, F5 and OutGuess successfully. In this work, a study on the security performance of JPEG-CES is reported. Our theoretical analysis demonstrates that in this algorithm, the number of the different quantised discrete cosine transform (qDCT) coefficients and the symmetry of the qDCT coefficient histogram both will be disturbed when the secret message is embedded. Moreover, the intrinsic sign and magnitude dependencies that existed in intra-block and inter-block qDCT coefficients will be disturbed too. Thus it may be detected by some modern universal steganalysers which can catch these disturbances. In this work, the authors have proposed two new steganalytic approaches. Through exploring the distortions that have been introduced into the qDCT coefficient histogram and the dependencies existed in the intra-block and inter-block sense, respectively, these two alternative steganalysers can detect JPEG-CES effectively. In addition, via merging the features of these two steganalysers, a more reliable classifier can be obtained.

Inferring the structure of latent class

Present optimization techniques in latent class analysis apply the expectation maximization algorithm or the Newton-Raphson algorithm for optimizing the parameter values of a prespecified model. These techniques can be used to find maximum likelihood estimates of the parameters, given the specified structure of the model, which is defined by the number of classes and, possibly, fixation and equality constraints. The model structure is usually chosen on theoretical grounds. A large variety of structurally different latent class models can be compared using goodness-of-fit indices of the chi-square family, Akaike's information criterion, the Bayesian information criterion, and various other statistics. However, finding the optimal structure for a given goodness-of-fit index often requires a lengthy search in which all kinds of model structures are tested. Moreover, solutions may depend on the choice of initial values for the parameters. This article presents a new method by which one can simultaneously infer the model structure from the data and optimize the parameter values. The method consists of a genetic algorithm in which any goodness-of-fit index can be used as a fitness criterion. In a number of test cases in which data sets from the literature were used, it is shown that this method provides models that fit equally well as or better than the models suggested in the original articles.

Postdetection integration analysis of the excision CFAR radar target detection technique in homogeneous and nonhomogeneous environments

The excision CFAR processor has been proposed for the detection of signals in an interference saturated environment, where such an environment is frequently encountered in radar applications (multiple target situations). The excision operation ensures that the calculation of the detection threshold is based on a set of samples which is purged of strong interferers and is therefore much more representative of the noise level. Since the frequency diversity between noncoherent pulse bursts is prevalent in radar detection systems, the performance evaluation of the excision CFAR detector with noncoherent integration is needed. Our goal in this paper is to analyze the performance of this type of CFAR radar target detection techniques when the radar receiver contains a noncoherent integrator amongst its basic elements. A chi-square family of fluctuating targets with an integer fluctuation parameter is employed as a model for the received signal. Our numerical results are focused on the important Swerling case II model because of the prevalence of frequency diversity between noncoherent pulse bursts. The processor performance is evaluated for the case where the background environment is assumed to be ideal (homogeneous) as well as in the presence of clutter power transitions and interfering targets amongst the contents of the reference window. It is found that the processor detectability loss, in homogeneous background, is very low and that the performance degradation, caused by interferers is quite small even if the number of the outlying targets is large. As the number of noncoherently integrated pulses increases, lower threshold values and consequently better detection performances are obtained, given that the excision threshold is held constant.

Beta Mixture of Transformed Chi-Square Family of Distributions

Beta Mixture of Transformed Chi-Square Family of Distributions

Analysis of adaptive radar systems processing M-sweeps in target multiplicity and clutter boundary environments

The problem of multipulse performance evaluation of radar detection systems in nonhomogeneous environments is addressed. The order-statistic (OS)-based algorithms, which set thresholds by processing magnitude-ordered observations within finite moving windows, give a marginal improvement compared with the cell-averaging (CA) procedure in false alarm rate performance in clutter power transitions and due to their immunity to the presence of spurious target returns among the reference cells. Three types of these CFAR detectors are analyzed in this paper. These systems are of the two-window type where they can be used to reduce the large processing time by half against the one-window scheme in ordering the contents of the estimation cells. The considered detectors are: the mean-level (ML) the maximum (MX) and the minimum (MN)-ordered statistics as well as the conventional OS scheme. The performance prediction of these systems employing noncoherent integration for chi-square family of fluctuating targets both in the absence and presence of clutter edges or interfering targets is calculated theoretically. Curves for the detectability loss required thresholds, false alarm rate performance in clutter boundaries and detection performance in multiple target situations are presented with special emphasis on the important Swerling II target fluctuation model. The results show that the ML-OS scheme has the best detection performance and the MX-OS scheme is the preferable one that behaves robust against clutter edges. While the MN-OS scheme does not appear to offer any advantage over others, except in the case where a cluster of radar targets exists among the contents of the reference windows.

A note on umvu estimation in the transformed chi-square family

The transformed chi-square family includes many common one-parameter continuous distributions. In that family, we give conditions under which a given function of the mean admits a minimum variance unbiased estimator and an orthogonal expansion for this estimator in terms of the generalized Laguerre polynomials. We show that such expansion is useful for obtaining bounds for the variance and for the study of the asymptotic properties of the unbiased estimators.

Radar probability of detection for some additional fluctuating target cases

The chi-square family of signal fluctuation distributions is defined. Rules are given for embedding the Swerling cases, and other cases of interest, in this family. Probability of detection curves are presented for the chi-square family of fluctuations, including cases whose probability of detection curves cannot be bracketed by the Swerling cases and the non-fluctuating case. The work of Weinstock has indicated such cases to be of practical interest; the fluctuation loss, for probability of detection exceeding 0.50, can be much larger than that for Swerling Case I. A discussion and partial analysis, accompanied by examples, is devoted to the question: when can the detection probability curves for signal fluctuations not belonging to the chi-square family be well approximated by curves resulting from chi-square fluctuations, and what methods can be used to choose adequately fitting chi-square fluctuation models when such a fit is possible?.

Umvu estimation for certain family of exponential distributions

In this paper we study certain properties of estimable and UMUV-estimable functions in a subfamily of the one-parameter exponential family of distributions for which there exists a sufficient and complete statistic following a Gamma distribution. These results are applied to the problem of estimation in the transformed chi-square family.

Performance off order-statistics CFAR detector with noncoherent integration in homogeneous situations

The order-statistics (OS) constant-false-alarm-rate (CFAR) detector has been known to have a small loss in detection performance relative to the cell-averaging (CA) CFAR detector in homogeneous situations. However, it results in much less performance degradation in nonhomogeneous situations, i.e. the OS CFAR detector has significant performance gain over the CA CFAR detector in nonhomogeneous environments. In general, as the frequency diversity between noncoherent pulse bursts is prevalent in radar detection systems, detection analysis of the OS CFAR detector with noncoherent integration is needed. In the paper, for the chi-square family of fluctuating targets with an integer fluctuation parameter, the detection performance of the OS CFAR detector with noncoherent integration in homogeneous situations, is discussed.

Detection performance in K-distributed and correlated Rayleigh clutters

Performance prediction for a detection system employing noncoherent integration is carried out for a chi-square family of fluctuating targets in K-distributed clutter plus noise. The detection performance for Swerling 11 targets in the K-distributed clutter plus noise is compared with that in exponentially correlated Rayleigh clutter. The results show that the performance prediction based on N pulses integrated in clutter plus noise using the K-distributed clutter model may be approximately equivalent to that using the exponentially correlated Rayleigh-distributed clutter model. >

Direct Evaluation of Radar Detection Probabilities

A simple and effective procedure for evaluating detectionperformances in radar and sonar detection problems is derived forboth fixed-threshold and adaptive-threshold detection. Using theprocedure, the cumulative probabilities of the test statistic can bedirectly evaluated from the moment generating functions bycalculating residues. The exact formulae for computing the detectionperformances for the chi-square family of fluctuating targets withan integer fluctuation parameter are given in a finite sum formwithout any special functions for both fixed threshold and cellaverageconstant false-alarm rate detection by using the methoddeveloped here.

Adaptive Detection Probabilities for Fluctuating Target Models in Nonhomogeneous Gaussian Noise

Under the assumption that the average noise power may vary from cell to cell, new, more easily computed expressions are given for the probability of detecting a fluctuating target by means of a cell-averaging CFAR test. The generalized chi-square family of fluctuating targets is considered with the Swerling I and III models given as special cases.

Probability of Detecting Aircraft Targets

The statistics of aircraft radar cross section (RCS) are estimated by fitting members of the chi-square family of distributions to empirical distributions obtained from blocks of RCS data, each block of data corresponding to a particular aircraft azimuth aspect. The parameters of the fitted distributions vary with azimuth aspect angle, type of aircraft, and radar frequency. Detection probabilities based on the estimated statistics are calculated and compared with detection probabilities based on Rayleigh statistics. This comparison indicates that the average value of radar cross section has much more effect on probability of detection than the normalized variance of RCS, and in the usual situation tends to mask the effect of the normalized variance on probability of detection.

Recursive Methods for Computing Detection Probabilities

Recursive methods are drived for computing detection probabilities for general fluctuating targets in Gaussian noise. For the generalized chi-square family of fluctuating targets, very simple and convenient recursive algrithms result. The methods are also extended to cell-averaging CFAR. Although the detection probability is expressed iw: terms of an infinite series, a convenient expression is derived for the resulting error when the series is truncated. Cell-averaging CFAR results are computed for nonfluctuating, Swering case I, and Swerling case II fluctuating targets.

How to Use Ridit Analysis

In many scientific studies in the biological and behavioral sciencesprobably in a majority of such studies-the scientist has to work with a response variable which falls in the borderland between dichotomous classifications (e.g. lived-died, yes-no) and refined measurement systems (i.e. measurements which are highly reproducable at different times or at different places). Sometimes the response variable is a subjective scale (i.e. a well ordered series of categories such as minor, moderate, severe). At other times the response variable takes numerical values but the measurement system is heavily dependent on the quality of experimental material, details of protocol, or the technical skill of the scientist. These borderland response variables may not be adequately analysed by the chi-square family of statistical methods and at the same time the t-test family of techniques may not be appropriate. In this situation ridit analysis may serve as a missing link between the two traditional families of statistical methods. This paper is addressed to scientists who are working with borderland response variables. It will contain no mathematical derivations (these will appear in a subsequent paper [1]). Its purpose is to explain and illustrate how to use ridit analysis in a scientific study. For this purpose a ridit analysis of data from the Cornell Automotive Crash Injury Research Program (ACIR) will be presented. This material will serve to illustrate the various problems that come up in actual studies, problems ranging from difficulties due to peculiarities and imperfections of the basic data to questions of presentation and interpretation of the results. The ACIR analysis will also show the role of ridit analysis in achieving the objectives of a scientific study. In this particular case the analysis throws light on a major public health problem-the carnage due to auto accidents. Nowadays the catalogue of statistical methods is so very extensive that a working scientist is somewhat less than overjoyed at the prospect