Finite Mean Research Articles

Identifying causes of errors between two wave-related data using performance metrics

Recently, numerous prediction methods of time-series data of wave-related phenomena have been developed. Quantitative evaluation of an error of a predicted result against a reference result is important to improve prediction accuracy. Many performance metrics are engaged to evaluate their accuracy. However, it is difficult for them to identify the error causes because all errors, no matter what the cause, are combined together. This paper presents new representations of performance metrics to separate errors by causes. Performances are evaluated in a frequency domain instead of a time domain. A frequency domain’s amplitude and phase are respectively evaluated using performance metrics. In addition, to detect errors due to instantaneous phenomena and changes in an error trend over time, mean errors are defined by three-time intervals. The original metric uses all time-series data. On the other hand, a finite interval mean error at the present time is calculated by the mean of the preceding data. In addition, cumulative mean error at the present time is calculated by the mean of the data up to the present time. These new representations of performance metrics could help to identify error causes. Benchmark tests are carried out to demonstrate the validity of the proposed representations.

Indirect Questioning Technique Related to Sensitive Quantitative Variables with Options for Direct, Randomized and Item Count Responses

Randomized Response (RR) Technique (RRT) pioneered by Warner (1965) is a useful tool to elicit responses on sensitive characteristics, such as induced abortions, drug abuse, drunken driving, total amount of counterfeit notes of a particular denomination held by individuals in the population, etc. There exists a huge literature on Randomized Response (RR) devices for estimation of finite population mean of quantitative variables, sensitive in nature mostly based on Eichhorn and Hayre (1983). Device-I and Device-II vide Chaudhuri and Christofides (2013) allow estimation of population mean of sensitive quantitative variables using sample chosen by a general sampling design. On the other hand, Item Count Technique (ICT), described elaborately in Chaudhuri and Christofides (2013), is an alternative to RRT for respondents who do not choose to provide RRs. While some respondents may find a variable as sensitive, others may find it innocuous enough to provide a direct response (DR) about his/her true value. In such a case, Optional Randomized Response (ORR) Technique (ORRT) with options for DR and RR was introduced by Chaudhuri and Mukherjee (1985). Pal (2007) proposed an ORR device which offers choices for RR and ICT to the respondents for giving their answers. A new ORRT with options for DR, RR and ICT was provided by Shaw and Pal (2021) for eliciting indirect responses on sensitive characteristics. As this device relates to estimation of population proportion of sensitive characteristics, an attempt has been made to extend it for sensitive quantitative variables. Further, to take care of individuals’ varying choices for DR, RR and ICT and to protect the privacy of the respondents’ choices, this paper develops an ORR device allowing the respondents chosen by a general sampling design, to choose any one of the three options according to their choices.   International Journal of Statistical Sciences, Vol.24(1), March, 2024, pp 155-170

Weighted Strategy for Estimation of Finite Population Mean in Presence of Auxiliary Information

ABSTRACT In sample designs, it is commonly recognized that using auxiliary information significantly increases an estimator’s precision. This manuscript introduces an weighted strategy for computing the finite population mean using auxiliary information in sample surveys. The equations for the mean squared error (MSE) of the proposed estimator are derived under large sampling approximation. A graphical representation of efficiency comparison is provided to show the ranges where the proposed estimator performs more efficiently. Additionally, a numerical analysis is conducted to evaluate the performance of the suggested estimator using actual datasets.

Almost Unbiased Optimum Ratio-type Estimator for Estimating Population Mean in Stratified Sampling in Presence of Non-response

In this paper we have proposed classes of ratio-type estimators for finite population mean in presence of non-response in stratified sampling. The properties of the estimators have been discussed. We have also derived optimum choices of scalar constant to reduce the bias in the estimators which make suggested classes of estimators almost unbiased. The expressions of mean square error (MSE) have been derived up to the first order of approximation. We have compared our proposed classes of estimators with natural ratio estimators and with estimator under complete response. Results are also supported by empirical study.

Calibration estimator for a sensitive variable using dual auxiliary information under measurement errors

In survey research, it is commonly assumed that all the observations are measured accurately. However, in practice, this assumption is not achieved due to many reasons, so it causes measurement errors to be inevitably present in the sample estimation. This article addresses the problem of estimation of finite population mean under stratified random sampling in the presence of measurement errors. A calibration estimator is proposed for the sensitive variable by utilizing suitable calibration techniques, which can be applied to obtain the optimal strata weight. The calibration estimator not only incorporates the auxiliary information but also the ranks of the auxiliary variable. Expressions for bias and mean square error are derived up to first order of approximation. Simulation studies and real-life datasets are used to assess the performances of the proposed estimator by comparing them with the contemporary estimators in the presence and absence of measurement errors. The theoretical and empirical studies demonstrate that the proposed calibration estimator consistently outperforms classical mean, usual ratio, conventional difference, Khail randomized response estimators.

Coupling Drug Dissolution with BCS

PurposeThe purpose of this study is to develop a Temporal Biopharmaceutic Classification System (T-BCS), linking Finite Dissolution Time (F.D.T.) and Mean Dissolution Time (M.D.T.) for Class I/III drugs and Mean Dissolution Time for saturation (M.D.T.s.) for Class II/IV drugs.MethodsThese parameters are estimated graphically or by fitting dissolution models to experimental data and coupled with the dose-to-solubility ratio (q) for each drug normalized in terms of the actual volume of dissolution medium (900 mL).ResultsClass I/III drugs consistently exhibited q values less than 1, aligning with expectations based on their solubility, while some Class II/IV drugs presented a deviation from anticipated q values, with observations of q < 1. This irregularity was rendered to the dissolution volume of 250 mL used for biopharmaceutical classification purposes instead of 900 mL applied as well as the dual classification of some sparingly soluble drugs. Biowaivers were also analyzed in terms of M.D.T., F.D.T. estimates and the regulatory dissolution time limits for rapidly and very-rapidly dissolved drugs.ConclusionsThe T-BCS is useful for establishing correlations and assessing the magnitude of M.D.T., F.D.T., or M.D.T.s. for inter- and intra-class comparisons of different drugs and provide relationships between these parameters across all the models that were utilized.Graphical

Incorporating the neutrosophic framework into kernel regression for predictive mean estimation

In traditional statistics, all research endeavors revolve around utilizing precise, crisp data for the predictive estimation of population mean in survey sampling, when the supplementary information is accessible. However, these types of estimates often suffer from bias. The major aim is to uncover the most accurate estimates for the unknown value of the population mean while minimizing the mean square error (MSE). We have employed the neutrosophic approach, which is the extension of classical statistics that deals with the uncertain, vague, and indeterminate information, and proposed a neutrosophic predictive estimator of finite population mean using the kernel regression. The proposed estimator does not yield a single numerical value but instead provides an interval range within which the population parameter is likely to exist. This approach enhances the efficiency of the estimators by offering an estimated interval that encompasses the unknown value of the population mean with the least possible mean squared error (MSE). The simulation-based efficiency of the proposed estimator is discussed using the Sine, Bump and real-time temperature data set of Islamabad by using symmetric (Gaussian) kernel. The proposed non-parametric neutrosophic estimator has shown more effective results under the various bandwidth selectors than the adapted neutrosophic estimators.

Prediction and estimation of random variables with infinite mean or variance

. In this article, we propose an optimal predictor of a random variable that has either an infinite mean or an infinite variance. The method consists of transforming the random variable such that the transformed variable has a finite mean and finite variance. The proposed predictor is a generalized arithmetic mean which is similar to the notion of certainty price in utility theory. Typically, the transformation consists of a parametric family of bijections, in which case the parameter might be chosen to minimize the prediction error in the transformed coordinates. The statistical properties of the estimator of the proposed predictor are studied, and confidence intervals are provided. The performance of the procedure is illustrated using simulated and real data.

Forecasting environmental water availability of lakes using temporal fusion transformer: case studies of China's two largest freshwater lakes.

Preserving lacustrine ecosystems is vital for sustainable watershed development, and forecasting the environmental water availability of lakes would support policymakers in developing sound management strategies. This study proposed a methodology that merges the lake water level prediction and environmental water availability evaluation. The temporal fusion transformer (TFT) model forecasted the lake water levels for the next 7 days by inputting the streamflow and lake water level data for the past 30 days. The environmental water availability was assessed by comparing the forecasted lake water levels with the environmental water requirements, resulting in adequate, regular, scarce, and severely scarce environmental water availability. The methodology was tested in two case studies: Poyang Lake and Dongting Lake, the two largest freshwater lakes in the Yangtze River Basin, China. The TFT model performed well in forecasting the lake water levels, as shown by the high coefficient of determination and finite root mean square error. The coefficients of determination exceeded 0.98 during the model training, validation, and test for both Poyang Lake and Dongting Lake, and the root mean square errors ranged from 0.06 to 0.46 m. The accurate prediction of lake water level promoted the precise forecasting of the environmental water availability with the high Kappa coefficient exceeding 0.90. Results indicated the rationality and effectiveness of integrating the lake water level prediction and environmental water availability evaluation. Future research includes the applicability of the TFT model to other lakes worldwide to test the proposed approach and investigate strategies to cope with environmental water scarcity.

On correlation functions in models related to the Temperley-Lieb algebra

We deal with quantum spin chains whose Hamiltonian arises from a representation of the Temperley-Lieb algebra, and we consider the mean values of those local operators which are generated by the Temperley-Lieb algebra. We present two key conjectures which relate these mean values to existing literature about factorized correlation functions in the XXZ spin chain. The first conjecture states that the finite volume mean values of the current and generalized current operators are given by the same simple formulas as in the case of the XXZ chain. The second conjecture states that the mean values of products of Temperley-Lieb generators can be factorized: they can expressed as sums of products of current mean values, such that the coefficients in the factorization depend neither on the eigenstate in question, nor on the selected representation of the algebra. The coefficients can be extracted from existing work on factorized correlation functions in the XXZ model. The conjectures should hold for all eigenstates that are non-degenerate with respect to the local charges of the models. We consider concrete representations, where we check the conjectures: the so-called golden chain, the QQ-state Potts model, and the trace representation. We also explain how to derive the generalized current operators from concrete expressions for the local charges.

Q-voter model with independence on signed random graphs: Homogeneous approximations.

The q-voter model with independence is generalized to signed random graphs and studied by means of Monte Carlo simulations and theoretically using the mean-field approximation and different forms of the pair approximation. In the signed network with quenched disorder, positive and negative signs associated randomly with the links correspond to reinforcing and antagonistic interactions, promoting, respectively, the same or opposite orientations of two-state spins representing agents' opinions; otherwise, the opinions are called mismatched. With probability 1-p, the agents change their opinions if the opinions of all members of a randomly selected q neighborhood are mismatched, and with probability p, they choose an opinion randomly. The model on networks with finite mean degree 〈k〉 and fixed fraction of the antagonistic interactions r exhibits ferromagnetic transition with varying the independence parameter p, which can be first or second order, depending on q and r, and disappears for large r. Besides, numerical evidence is provided for the occurrence of the spin-glass-like transition for large r. The order and critical lines for the ferromagnetic transition on the p vs r phase diagram obtained in Monte Carlo simulations are reproduced qualitatively by the mean-field approximation. Within the range of applicability of the pair approximation, for the model with 〈k〉 finite but 〈k〉≫q, predictions of the homogeneous pair approximation concerning the ferromagnetic transition show much better quantitative agreement with numerical results for small r but fail for larger r. A more advanced signed homogeneous pair approximation is formulated which distinguishes between classes of active links with a given sign connecting nodes occupied by agents with mismatched opinions; for the model with 〈k〉≫q its predictions agree quantitatively with numerical results in a whole range of r where the ferromagnetic transition occurs.

Lévy-walk-like Langevin dynamics with random parameters.

Anomalous diffusion phenomena have been widely found in systems within an inhomogeneous complex environment. For Lévy walk in an inhomogeneous complex environment, we characterize the particle's trajectory through an underdamped Langevin system coupled with a subordinator. The influence of the inhomogeneous environment on the particle's motion is parameterized by the random system parameters, relaxation timescale τ, and velocity diffusivity σ. We find that the two random parameters make different effects on the original superdiffusion behavior of the Lévy walk. The random σ contributes to a trivial result after an ensemble average, which is independent of the specific distribution of σ. By contrast, we find that a specific distribution of τ, a modified Lévy distribution with a finite mean, slows down the decaying rate of the velocity correlation function with respect to the lag time. However, the random τ does not promote the diffusion behavior in a direct way, but plays a competition role to the superdiffusion of the original Lévy walk. In addition, the effect of the random τ is also related to the specific subordinator in the coupled Langevin model, which corresponds to the distribution of the flight time of the Lévy walk. The random system parameters are capable of leading to novel dynamics, which needs detailed analyses, rather than an intuitive judgment, especially in complex systems.

Geographically weighted ridge regression estimator of finite population mean to tackle multicollinearity in survey sampling

Geographically weighted ridge regression estimator of finite population mean to tackle multicollinearity in survey sampling

Estimating A Finite Population Mean Under Two-Phase Sampling Using Exponential Ratio Estimator

Estimation of population parameters such as population mean, and population total has been a major concern in Sample Survey Theory. In sampling theory, researchers employ auxiliary information to improve precision and validity of estimators. This study applies two-phase sampling in estimation of a finite population mean using modified exponential ratio estimator. Two-phase sampling was used since it leverages on the information collected in the first phase, along with auxiliary variables, to guide the selection of a more targeted and efficient second-phase sample, resulting in increased precision for the estimates of interest. Study results showed that the proposed modified exponential ratio estimator produced a smaller Bias and MSE than Shabbir and Gupta (2007), and Singh and Solanki (2013). Further, the proposed estimator produced a higher relative efficiency as compared to Shabbir and Gupta (2007), and Singh and Solanki (2013).

A NEW LOGARITHMIC RATIO TYPE ESTIMATOR OF POPULATION MEAN FOR SIMPLE RANDOM SAMPLING: A SIMULATION STUDY

This paper provides a logarithmic ratio type estimator of a finite population mean using an auxiliary variable in simple random sampling. The expression for the mean square error (MSE) of the proposed estimator and some selected estimators are calculated along with the theoretical conditions. Further the numerical comparisons and simulation study based on different probability distributions supports the claim that the proposed estimator performs better as compared to the ones used in this study.

Improved exponential type ratio estimator in double sampling for stratification

The objective of this research is to create a chain-ratio-type exponential estimator in order to estimate the finite population mean in double sampling for stratification. An estimator for population mean has been constructed based on the concept of chain-ratio estimators. The constructed estimator is compared to the standard unbiased estimator, as well as the other relevant existing estimators and conditions are shown to yield better results in terms of efficiency. To support the theoretical results the study has been done on both natural as well as simulated populations.

Power ratio cum median-based ratio estimator of finite population mean with known population median

The search for an efficient estimator of the finite population mean has been a critical problem to the sample survey research community. This study is motivated by the fact that the conducted literature review showed that no research has developed such an average ratio estimator of the population mean that would utilize both the population and the sample medians of study variable, as well as the Srivastava (1967) estimator at a time. In this paper we proposed the power ratio cum median-based ratio estimator of the finite population mean, which is a function of two ratio estimators in the form of an average. The estimator assumes the population to be homogeneous and skewed. The properties (i.e. the Bias and the Mean Squared Error – MSE) of the proposed estimator were derived alongside its asymptotically optimum MSE. We demonstrated the efficiency of the proposed estimator jointly with its efficiency conditions by comparing it to selected estimators described in the literature. Empirically, a real-life dataset from the literature and a simulation study from two skewed distributions (Gamma and Weibull) were used to examine the efficiency gain. The empirical analysis and simulation study demonstrated that the efficiency gain is significant. Hence, the practical application of the proposed estimator is recommended, especially in socio-economic surveys.

Tail behavior of ACD models and consequences for likelihood-based estimation

We establish new results for estimation and inference in financial durations models, where events are observed over a given time span, such as a trading day, or a week. For the classical autoregressive conditional duration (ACD) models by Engle and Russell (1998), we show that the large sample behavior of likelihood estimators is highly sensitive to the tail behavior of the financial durations. In particular, even under stationarity, asymptotic normality breaks down for tail indices smaller than one or, equivalently, when the clustering behavior of the observed events is such that the unconditional distribution of the durations has no finite mean. Instead, we find that estimators are mixed Gaussian and have non-standard rates of convergence. The results are based on exploiting the crucial fact that for duration data the number of observations within any given time span is random. Our results apply to general econometric models where the number of observed events is random.

Nonparametric augmented probability weighting with sparsity

Nonresponse frequently arises in practice, and simply ignoring it may lead to erroneous inference. Besides, the number of collected covariates may increase as the sample size in modern statistics, so parametric imputation or propensity score weighting usually leads to estimation inefficiency and introduces a large variability without consideration of sparsity. In this paper, we propose a nonparametric imputation method with sparsity to estimate the finite population mean, where an efficient kernel-based method in the reproducing kernel Hilbet space is employed for estimation and sparse learning. Moreover, an augmented inverse probability weighting framework is adopted to achieve a central limit theorem for the proposed estimator under regularity conditions. The performance of the proposed method is also supported by several simulated examples and one real-life analysis.

Fast-slow wave transitions induced by a random mean flow.

Motivated by recent asymptotic results in atmosphere-ocean fluid dynamics, we present an idealized numerical and theoretical study of two-dimensional dispersive waves propagating through a small-amplitude random mean flow. The objective is to delineate clearly the conditions under which the cumulative Doppler shifting and refraction by the mean flow can change the group velocity of the waves not only in direction, but also in magnitude. The latter effect enables a possible transition from fast to slow waves, which behave very differently. Within our model we find the conditions on the dispersion relation and the mean flow amplitude that allow or rule out such fast-slow transitions. For steady mean flows we determine a finite mean flow amplitude threshold below which such transitions can be ruled out indefinitely. For unsteady mean flows a sufficiently rapid rate of change means that this threshold goes to zero, i.e., in this scenario all waves eventually undergo a fast-slow transition regardless of mean flow amplitude, with corresponding implications for the long-term fate of these waves.