A changepoint statistic with uniform type I error probabilities

Graphs are commonly used in various applications such as online social networks (OSNs), E-commerce systems and social recommender systems. Random walk sampling is often used to conduct statistical estimation over such graphs. This paper develops an algorithmic framework to reduce the mean square error of such statistical estimation. Our algorithmic framework is inspired by that the mean square error can be decomposed into a sum of the bias and variance of the estimator. More specifically, we apply the bootstrapping technique to design a bias reduction algorithm. A new feature of this bias reduction algorithm is that it allows the variance to increase whenever the bias can be further reduced. The increased variance may lead to a large mean square error of the estimator. We use multiple parallel random walks to reduce this variance such that it can be reduced to arbitrarily small by deploying a sufficient number of random walks. Our algorithmic framework enables one to attain different trade-offs between the sample complexity (i.e., number of parallel random walks) and the mean square error of the statistical estimation. Also, the proposed bias reduction algorithm is generic and can be applied to optimize a large class of random walk sampling algorithms. To demonstrate the versatility of the framework, we apply it to optimize the Metropolis random walk and simple random walk sampling. Extensive experiments confirm the effectiveness and efficiency of our proposed algorithmic framework.

We discuss the effect of imperfect knowledge of the transmission channel on the performance of multicarrier-OFDM and DMT -systems. The limited accuracy in the identification of the transmission channel is caused either by errors in the estimate of the channel or by variations in the channel due to motion of the transmitter, the receiver, and/or the reflectors. We develop a model to analyze the impact of these errors and derive analytic expressions for the signal-to-interference ratio (SIR) and the probability of error as a function of the initial SNR and the mean square error in channel estimation. We compare these results to those obtained assuming Gaussian errors and show that in both cases, the performance of multicarrier systems degrades when the normalized mean square error in channel estimation is greater than 10/sup -3/ (-30 dB). Finally, we extend these concepts to errors due to variations in the transmission channel.

Co-efficient of variation is a unitless measure of dispersion and is very frequently used in scientific investigations. This has motivated several researchers to propose estimators and tests concerning the co-efficient of variation of normal distribution(s). While proposing a class of estimators for the co-efficient of variation of a finite population, Tripathi et al., (2002) suggested that the estimator of co-efficient of variation of a finite population can also be used as an estimator of C.V for any distribution when the sampling design is SRSWR. This has motivated us to propose 28 estimators of finite population co-efficient of variation as estimators of co-efficient of variation of one component of a bivariate normal distribution when prior information is available regarding the second component. Cramer Rao type lower bound is derived to the mean square error of these estimators. Extensive simulation is carried out to compare these estimators. The results indicate that out of these 28 estimators, eight estimators have larger relative efficiency compared to the sample co-efficient of variation. The asymptotic mean square errors of the best estimators are derived to the order of  for the benefit of users of co-efficient of variation.

The extensive use of maximum likelihood estimates underscores the importance of the problem of statistical estimation of their errors. These estimates are of utmost importance in cases where the family of normal distributions and the families related to the normal distributions are considered [1, 2, 4]. The mean square errors of the maximum likelihood estimates of the normal density were investigated in the author's paper [3]. The mean square errors of statistical estimates of some families of densities related to the normal distributions were considered in the papers [4–6]. In the present paper, we obtain an asymptotic expansion of the mean square error of the maximum likelihood estimates of the densities of the joint distribution of sufficient statistics of the family of multivariate normal distributions. The results obtained allow us to construct the mean square errors of the maximum likelihood estimates for the chi-square density and Wishart's density.

Many species on Earth can carry up to two different versions of a given gene, with each of these ‘alleles’ having only a 50/50 chance of being transmitted to the next generation via sexual reproduction. Certain ‘selfish’ sequences, however, can hijack this process and increase their probability of being passed on to an offspring. Known as transmission distortion, this phenomenon may result in alleles spreading through the population even if they are detrimental to fertility. Transmission distortion has been detected in many species such as flies, mice and some plants. It can take place at various stages during reproduction; for example, the selfish alleles may become overrepresented among eggs or sperm. However, scientists need to study a large number of offspring or reproductive cells to be able to detect whether an allele is inherited more often than expected. This has made it difficult to determine whether transmission distortion also happens in humans, and research so far has resulted in conflicting conclusions. A recently published dataset of human sperm from 25 donors offered Carioscia, Weaver et al. the opportunity to examine this question. Every volunteer had produced between 969 and 3377 sperm cells, each with about 1% of their genome sequenced. Carioscia, Weaver et al. developed a computational method, which they named rhapsodi, that allowed them to ‘fill in the gaps’ and infer missing regions of the genome for each cell. To do so, they relied on the fact that sperm cells from a given individual are highly related to one another. With this more complete data at hand, it became possible to look for evidence of transmission distortion by searching for alleles that were overrepresented in sperm from a given donor. No selfish sequence could be detected in any of the 25 individuals, suggesting that human sperm may not be subject to pervasive transmission distortion. Signatures of selfish alleles detected in previous human studies may have therefore not resulted from this mechanism taking place at the sperm level. Instead, transmission distortion in humans could primarily target eggs or happen at later stages (for instance, if embryos carrying the selfish allele have better chances of survival). The ‘rhapsodi’ method developed by Carioscia, Weaver et al. should allow other scientists to work with datasets for which large portions of the genetic information is missing. It may therefore become easier for researchers to track selfish alleles which are difficult to detect, and to examine bigger, more diverse samples which also include individuals with known fertility challenges.

In deriving the bias and mean square error of the ratio estimator , it is generally assumed that for all possible samples. This assumption is, however, unlikely to be satisfied except in special situations. This article presents a justification for the use of the usual approximations to the bias and mean square error of . Bounds for the deviations of the approximations from the true values are also given.

The prediction of human motion is essential for safe human-robot collaboration (HRC). For existing prediction methods based on adaptive neural network (NN) models, estimation errors (EEs) of model parameters are directly coupled with prior EEs of trajectories. This results in poor assessment of the mean square estimation error (MSEE) of model parameters, which is a potential danger to the safety HRC. In this paper, a novel “look-backward-and-forward” method is proposed to assess the EEs of model parameters. This method firstly computes EEs of model parameters in the past few time instants based on the actual error of trajectory predicted in the past. Subsequently, the EEs of model parameters are recursively updated till the current time instant. In this way, the trajectory of a single particle and its MSEE are accurately accessed. The direct coupling between the MSEE of the trajectory and that of model parameters is cut off and the mean estimation errors (MEEs) of parameters are only affected by the EEs of the past trajectory at the recent several time instants, rather than accumulating as the time propagates. This method is further extended to estimate the pose trajectory of a rigid body based on fitting of an ellipsoid’s parameters. The experimental results of predicting 3-D trajectories of human motions show the effectiveness of the proposed method.

This paper provides a fortran algorithm that can be used to compute the cdf of the product of two normal distribution random variables. We also give references that provide mathematical properties, tables, and applications of this distribution

Introduction: Quantile regression is a valuable alternative for survival data analysis, enabling flexible evaluations of covariate effects on survival outcomes with intuitive interpretations. It offers practical computation and reliability. However, challenges arise when applying quantile regression to censored data, particularly for upper quantiles. The minimum distance approach, utilizing dual-kernel estimation and the inverse cumulative distribution function, shows promise in addressing these challenges, especially with higher-dimensional covariates. Methods: This study contrasts two methods within the realm of quantile linear regression for survival analysis: check-based modeling and the minimum distance approach. Effectiveness is assessed across various scenarios through comprehensive simulation. Results: The simulation results showed that using the quantile regression model with the minimum distance approach reduces the percentage of root mean square error in parameter estimation compared to the quantile regression models based on the check loss function. Additionally, a larger sample size and reduced censoring percentage led to decreased root mean square error in parameter estimation. Conclusion: The research highlights the benefits of using the minimum distance approach for quantile regression. It reduces errors, improves model predictions, captures patterns, and optimizes parameters even with complete data. However, this approach has limitations. The accuracy of estimated quantiles can be influenced by the choice of distance metric and weighting scheme. The assumption of independence between censoring mechanism and survival time may not hold in real-world scenarios. Additionally, dealing with large datasets can be computationally complex.

Change-point analysis of time-series data plays a vital role in various fields of earth sciences under changing environments. Most of the analysis approaches were usually designed to detect the change-point in the level of time-series mean. In this study, we aimed to propose a non-parametric approach to detect the change-point of different parameters of time-series data. In this approach, the Boot- strap method, coupling with Kernel density estimation, was first used to estimate the probability distribution function (pdf) of a parameter before and after any potential change-points. Second, the Ar-index based on the uncross area of the two pdfs was designed to quantify the difference of the parameter before and after each potential change-point. Finally, the potential change-point owning the largest Ar-index value was determined as the locations of the change-point of the parameter. The hydrological extreme series from four stations in the Hanjiang basin were used to demonstrate this approach. The Pettitt test method commonly used in hydrology was employed as a comparison to indirectly analyze the reliability of the proposed approach. The results show that change-point detected by the proposed approach in the four stations are identified with those detected by the Pettitt approach in the level of time-series mean. But in comparison with the Pettitt test, the proposed approach can provide more detection information for other parameters, such as coefficient of variation (Cv) and coefficient of skewness (Cs) of the series. The results also show that the degree of change in the series mean is greater than its Cv and Cs, while the degree of change in series Cv is greater than its Cs.

Using the Land Use and Coverage Frame Survey (LUCAS) database of European soil surface layer properties, statistical and machine learning predictive models for several key soil characteristics (clay content, pH in CaCl2, concentration of organic carbon, calcium carbonates and nitrogen and exchange cations capacity) were compared on the basis of processing their spectral responses in the visible (Vis) and near‑infrared (NIR) parts. Standard methods of relationship modeling were used: stepwise regression, partial least squares regression and linear regression with input data obtained from principal components analysis. Using the inputs extracted by statistical algorithms various machine learning algorithms were used in the modeling. The usefulness of the models was analyzed by comparison with the values of the determination coefficients, the root mean square error and the distribution of residual values. The mean square error of estimation in the cross‑validation procedure for the stack model using the multilayer perceptron and the distributed random forest were as follows: for clay content – ca. 4.5%; for pH – ca. 0.35; for SOC – ca. 7.5 g/kg (0.75% by weight); for CaCO3 content – ca. 19 g/kg; for N content – ca. 0.50 g/kg; and for CEC – ca. 3.5 cmol(+)/kg.

PurposeThe purpose of this paper is to develop FT‐NIR technique for determination of moisture content in bael pulp.Design/methodology/approachCalibration and validation sets were designed for the conception and evaluation of the method adequacy in the range of moisture content 70 to 95 per cent (wb). The prediction models based on partial least squares (PLS) regression, were developed in the near‐infrared region (4,000‐2,500cm‐1). Conventional criteria such as the R2, the root mean square errors of cross validation (RMSECV), root mean square errors of estimation (RMSEE) as well as the number of PLS factors were considered for the selection of three pre‐processing (vector normalization, minimum‐maximum normalization and multiplicative scatter correction) methods.FindingsThe best calibration model was developed with min‐max normalization (MMN) spectral pre‐processing (R2=99.3). The MMN pre‐processing method was found most suitable and the maximum coefficient of determination (R2) value of 0.993 was obtained for the calibration model developed. The developed results indicated that FTNIR spectroscopy could be used for rapid detection of moisture content in bael pulp samples without any sample destruction.Originality/valueThe research in this paper is useful for the quick detection of moisture content of bael fruit pulp during processing.

Quality assessment of liquorice combined with quantum fingerprint profiles and electrochemical activity

The threshold de-noising method based on the wavelet transform is an effective approach to reduce the white noise of the digit signal. Considering the different characters of signal and white noise in the wavelet domain, a novel algorithm to determine the adaptive wavelet threshold is proposed with the use of False Discovery Rate (FDR) step-up-down procedure. Since the wavelet de-noising transform process can be regarded as a multiple hypothesis process and both the step-up and step-down procedures can control the FDR independently, the new method FDR step-up-down procedure combining the above-mentioned procedures determines the wavelet threshold. An attractive advantage of this method is it can obtain the desired result by adjusting the FDR level flexibly. Numerical results show that this procedure works as effective as Hearsure procedure and gives better Signal Noise Ratio (SNR) gains and Mean Square Error (MSE) performance than both the traditional BH FDR and Sqtwolog procedure. In addition, this proposed algorithm has a substantially better power and higher resolution speed.

In this article, we propose two methods for selection of meta parameter (C) in support vector regression. The proposed methods are robust because these are based on the robust statistical measures. The performance of the proposed parameter selection methods is evaluated in case of normal and non-normal distributed error variables. It is evaluated in the sense of prediction risk and mean square error of estimates of regression parameters for clean and outlier data.