A nonparametric test for stop‐loss order


 
 
 
 We considered the Bayesian analysis of a shape parameter of the Weibull-Exponential distribution in this paper. We assumed a class of non-informative priors in deriving the corresponding posterior distributions. In particular, the Bayes estimators and associated risks were calculated under three different loss functions. The performance of the Bayes estimators was evaluated and compared to the method of maximum likelihood under a comprehensive simulation study. It was discovered that for the said parameters to be estimated, the quadratic loss function under both uniform and Jeffrey’s priors should be used for decreasing parameter values while the use of precautionary loss function can be preferred for increasing parameter values irrespective of the variations in sample size.
 
 
 
 

Reinsurance is an effective way for an insurance company to control its risk. How to design an optimal reinsurance contract is not only a key topic in actuarial science, but also an interesting research question in mathematics and statistics. Optimal reinsurance design problems can be proposed from different perspectives. Risk measures as tools of quantitative risk management have been extensively used in insurance and finance. Optimal reinsurance designs based on risk measures have been widely studied in the literature of insurance and become an active research topic. Different research approaches have been developed and many interesting results have been obtained in this area. These approaches and results have potential applications in future research. In this article, we review the recent advances in optimal reinsurance designs based on risk measures in static models and discuss some interesting problems on this topic for future research.

In order to improve the monitoring efficiency of the multivariable autocorrelation process and reduce the cost of process control, an economic design method of residual Multivariate Exponentially Weighted Moving Average (MEWMA) control charts with variable sample size and sampling intervals (VSSIs) was proposed. First, residual MEWMA control charts with VSSI were designed for monitoring multivariable autocorrelation processes. Second, the economic model of the VSSI residual MEWMA control chart was established, and a data example was given. The optimal design parameters of the control chart were obtained by using a genetic algorithm to minimize the expected cost per unit time. Third, using orthogonal experimental design and regression analysis, a sensitivity analysis of the economic model was carried out to get the relationship between the model parameters and the design parameters of the control chart. Finally, through the optimality analysis, it was verified that the proposed economic model was superior to the models established by the variable sampling intervals strategy and the variable sample size strategy and had less expected cost per unit time.

The Pareto distribution has been widely used to model data in numerous areas including actuarial science, climatology, economics, finance, and reliability. The exponential weighted moving average (EWMA) chart with variable sample size and sampling interval (VSSI) is quicker than EWMA chart, EWMA chart with variable sample size (VSS), and EWMA chart with variable sampling interval (VSI) in detecting the mean shifts of a normal process. In this study, we present an EWMA‐VSSI chart to monitor the Pareto data with estimated parameters. The average time to signal (ATS) is computed by using the Markov chain approach. The results indicate that the proposed chart performs better than the other EWMA charts with fixed sample size, VSS, and VSI in terms of ATS. The design parameters of the proposed control charts are given in order to expedite the use of the chart by practitioners. Two examples are used to illustrate the application of the proposed control charts.

Traditional control charts for process monitoring are based on taking samples of fixed size from the process using a fixed sampling interval. Variable sample size (VSS) and variable sampling interval (VSI) control charts vary the sampling rate from the process as a function of the data from the process. By sampling at a higher rate when there is an indication of a change in the process, VSS and VSI control charts can detect process changes faster than traditional control charts. Previous research has considered the properties of CUSUM charts which use the VSI feature. This paper considers CUSUM charts with the VSS feature and with both the VSS and VSI features. Two ways of developing the control statistic of these charts are considered. It is shown that using either the VSS or VSI feature in a CUSUM control chart will improve the ability to detect all but very large process shifts. The VSI feature usually gives more improvement in detection ability than the VSS feature, but using both features together will give more improvement than either one separately. Guidelines are given for choosing the possible sample sizes and the possible sampling intervals for these charts. Methods for setting up these charts for practical applications are also given.

Establishing reference databases generally requires a large sample size to achieve reliable results. Our study revealed that the varying sample size from hundreds to thousands of individuals has no decisive effect on the bone mineral density (BMD) reference curve, peak BMD, and diagnosing osteoporosis. It provides a reference point for determining the sample size while establishing local BMD reference databases. This study attempts to determine a suitable sample size for establishing bone mineral density (BMD) reference databases in a local laboratory. The total reference population consisted of 3,662 Chinese females aged 6-85 years. BMDs were measured with a dual-energy X-ray absorptiometry densitometer. The subjects were randomly divided into four different sample groups, that is, total number (Tn) = 3,662, 1/2n = 1,831, 1/4n = 916, and 1/8n = 458. We used the best regression model to determine BMD reference curve and peak BMD. There was no significant difference in the full curves between the four sample groups at each skeletal site, although some discrepancy at the end of the curves was observed at the spine. Peak BMDs were very similar in the four sample groups. According to the Chinese diagnostic criteria (BMD >25% below the peak BMD as osteoporosis), no difference was observed in the osteoporosis detection rate using the reference values determined by the four different sample groups. Varying the sample size from hundreds to thousands has no decisive effect on establishing BMD reference curve and determining peak BMD. It should be practical for determining the reference population while establishing local BMD databases.

BackgroundA typical antipsychotics for neuropsychiatric symptoms in dementia have been tested in much larger trials than the older conventional drugs. The advantage of larger sample sizes is that negative findings become less likely and the effect estimates more precise. However, as sample sizes increase, the trials also get more expensive and time consuming while exposing more patients to drugs with unknown safety profiles. Moreover, a large sample size might yield a statistically significant effect that is not necessarily clinically relevant.ObjectiveTo assess (1) the variation in sample size and sample size calculations of antipsychotic trials in dementia, (2) the size of reported treatment effects and related statistical significance, and (3) general study characteristics that might be related to sample size.Study Design and SettingWe performed a meta-epidemiological study of randomized trials that tested antipsychotics for neuropsychiatric symptoms in dementia. The trials compared conventional or atypical antipsychotics with placebo or another antipsychotic. Two reviewers independently extracted sample size, sample size calculations, reported treatment effects with p-values, and general study characteristics (drug type, trial duration, type of funding). We calculated a reference sample size of 83 and 433 per study group for the placebo-controlled and head-to-head trials respectively.ResultsWe identified 33 placebo-controlled trials, and 18 head-to-head trials. Only 14 (42%) and 2 (11%), respectively, reported a sample size calculation. The average sample size per arm was 34 (range 6–179) in placebo-controlled trials testing conventional drugs, 107 (8–237) in such trials testing atypical drugs, and 104 (95–115) in such trials testing both drug types; it was 31 (10–88) in head-to-head trials. Thirteen out of 18 trials with sample sizes larger than required (72%) reported a statistically significant treatment effect, of which two (15%) were clinically relevant. None of the head-to-head trials reported a statistically significant treatment effect, even though some suggested non-inferiority. In placebo-controlled trials of atypical drugs, longer trial duration (>6 weeks) and commercial funding were associated with higher sample size.ConclusionSample size calculations were poorly reported in antipsychotic trials for dementia. Placebo-controlled trials of atypical antipsychotics showed large sample size fallacy while head-to-head trials were massively underpowered.

Despite the recent evidence of population-level handedness in nonhuman primates, continued debate persists over the analysis and interpretation of findings on handedness, particularly in great apes (Hopkins, 1999; McGrew and Marchant, 1997). Palmer (2002) recently questioned the analysis and interpretation of findings on hand preference in nonhuman primates, and in particular, results suggesting population-level right-handedness in chimpanzees. Specifically, Palmer (2002) reanalyzed hand-preference data for bimanual feeding in chimpanzees reported by Hopkins (1994) and argued, based on his analysis using funnel-graphs, that there were unusual patterns in the data that raised questions on the validity of the results for these data. With respect to the findings reported by Hopkins (1994), Palmer (2002) argued that a fundamental problem with the data was in the relationship between the number of individual data points collected for each subject and the distribution of hand preferences in the sample. Palmer (2002) quartiled the sample (N = 140) on the basis of the total number of observations used to derive the individual handedness scores (see his Table 1), and showed that as the number of observation increased, the number of ambiguously handed subjects increased. According to Palmer, this pattern of results should not have been evident under basic statistical assumptions of increasing effects with increasing sample size. In short, the data regressed toward a mean of zero, or no hand preference, with increasing sample size. Palmer (2002) also created funnel graphs of individual variation in percent right-hand use as a function of sample size, and argued that the patterns did not conform to patterns that would normally reflect nonsampling error in the data of Hopkins (1994). Lastly, Palmer (2002) applied funnel-graph analysis to 14 selective studies on hand preference in chimpanzees, and argued that most studies found no evidence of population-level handedness. TABLE 1 Distribution of hand preference as a function of sex and rearing history With respect to the data of Hopkins (1994), Palmer (2002) fairly and representatively indicated the inherent problems with the variation in percent right-hand use as a function of sample size. Our main response to this criticism is that the bulk of the youngest subjects make up the group comprising the largest N and most ambiguously handed subjects. In other words, sample size is confounded by subject age, and it is clearly legitimate to assume that there may be age differences in the expression and magnitude of hand preference in chimpanzees. If the youngest subjects are removed from the analysis, one-sample t-tests still reveal population-level right-handedness for bimanual feeding. The effect is not terribly robust, and this is largely due to the fact that there are so many ambiguously handed subjects. The fact that there were so many ambiguously handed subjects was clearly noted as a limitation of this measure in Hopkins (1994). Further, in Hopkins (1994), it is emphasized that measures involving coordinated actions of the hands may better elicit population-level hand preferences in chimpanzees than the bimanual feeding measure employed in that study. Although we recognize the limitations of the findings by Hopkins (1994), we do not believe that all studies of chimpanzee handedness are subject to the same criticism, and in this paper we report on evidence that contradicts the conclusions of Palmer (2002). Specifically, we developed a measure of hand preference for coordinated bimanual actions, referred to as the TUBE task (Hopkins, 1995; Hopkins et al., 2001). This measure of hand use also elicits a population-level hand preference in captive chimpanzees, but unlike the feeding task used by Hopkins (1994), the majority (90%) of chimpanzees show a significant hand preference (either left or right). Palmer (2002, personal communication) has been equally critical of these data, in terms of the application of funnel plots to the distribution of hand preference in relation to sample size. To address this issue of whether individual differences in sample size influence the distribution of hand preference in chimpanzees, we conducted an experiment in which we assessed hand preference for the TUBE task. This experiment differed from previous studies in that the exact same number of observations was collected in each subject. If the degree of hand preference found in chimpanzees is determined by sampling biases associated with N, then no population-level hand preferences should be found for this measure when sample sizes are identical for all subjects. In contrast, if the reported effects of population-level right handedness are consistent and not influenced by sample size, then population-level right-handedness should be found for this measure of hand use in this sample of chimpanzees.

This paper improves the sensitivity of the existing run sum chart for shifts in the coefficient of variation by proposing two types of adaptive schemes, i.e. the variable sample size and sampling interval (VSSI) and variable parameter (VP) schemes. The VSSI run sum chart varies the sample size and sampling interval , while the VP run sum chart varies not only n and h but also the size of each region of the run sum chart. The operations, as well as formulae and algorithms to optimize the charts’ performance, are developed. Subsequently, tables of optimal charting parameters are obtained. The VP run sum chart is shown to outperform the VSSI run sum chart. The proposed charts are also shown to outperform the variable sampling interval (VSI) run sum, variable sample size (VSS) run sum, and the VSSI, VSS and VSI charts, as well as the VSS and VSI EWMA charts for moderate and large shift sizes. Implementation on an actual industrial example shows the sensitivity of the proposed charts towards small shifts.

The objective of this study is to evaluate and compare the performance of different machine learning (ML) algorithms, viz., multi-layer perceptron (MLP), random forest (RF), extra trees regressor (ETR), CatBoost, and gradient boost (GB), considering the impact of variation in sample sizes for theprediction of soil nutrients. In this context, this study evaluates the impact of sample size on the prediction performance of five ML algorithms for mapping 14 soil properties, including key soil physico-chemical properties (soil organic carbon, pH, and electrical conductivity), and multiple macro (available nitrogen, phosphorus, potassium, calcium, magnesium, and sulfur) and micronutrients (available iron, manganese, copper, zinc, and boron) at a geographical extent of 8303 km2 located in eastern India. A total of 1024 surface soil samples were collected, of which 800 were used for model training, while the remaining 224 were reserved for independent validation (IV) of the resultant maps. The original training data set (800 samples) was reduced by random selection into six different sample sizes, i.e., 800, 400, 200, 100, 50, and 25. An exhaustive set of 574 environmental variables, derived from digital terrain derivatives and Sentinel-2 satellite imagery, was used as predictors. Popular statistical indicators, such as Lin's concordance correlation coefficient (CCC) and root mean squared error (RMSE) were employed to evaluate the predictive capability of the algorithms under different sample size scenarios. The results showed that prediction accuracy and reliability of prediction performance across multiple target variables improved with sample size. However, beyond a certain point, improvement in predictive performance became substantially negligible compared to the efforts in additional sampling. All the ML algorithms performed well (mean IV-CCC varied between 0.26 and 0.64 for different soil properties) to increase insample size, except MLP, which exhibited a poorer prediction performance(mean IV-CCC varied between 0.14 and 0.29 for different soil properties). Micronutrients in general responded well to the increase in sample sizes. The uncertainty analysis revealed that increasing sample size generally reduced prediction uncertainty, though the extent varied by soil property and ML algorithm. Concisely, the results presented herein showed an effective manner of selecting an appropriate sample size and a suitable ML algorithm to predict multiple soil nutrients accurately, which would be recommended to achieve optimal accuracy for a project.

Cognitive diagnostic models (CDMs) are increasingly being used in various assessment contexts to identify cognitive processes and provide tailored feedback. However, the most commonly used estimation method for CDMs, marginal maximum likelihood estimation with Expectation–Maximization (MMLE-EM), can present difficulties when sample sizes are small. This study compares the results of different estimation methods for CDMs under varying sample sizes using simulated and empirical data. The methods compared include MMLE-EM, Bayes modal, Markov chain Monte Carlo, a non-parametric method, and a parsimonious parametric model such as Restricted DINA. We varied the sample size, and assessed the bias in the estimation of item parameters, the precision in attribute classification, the bias in the reliability estimate, and computational cost. The findings suggest that alternative estimation methods are preferred over MMLE-EM under low sample-size conditions, whereas comparable results are obtained under large sample-size conditions. Practitioners should consider using alternative estimation methods when working with small samples to obtain more accurate estimates of CDM parameters. This study aims to maximize the potential of CDMs by providing guidance on the estimation of the parameters.

Various studies have examined generalized additive models (GAMs), comparing thin plate splines (tp), P‐splines (ps), cubic regression splines (cr), and Gaussian processes (gp) for discrete choice data, function approximation, and in the presence of multicollinearity and outliers. Some studies have applied ps to models with correlated and heteroscedastic errors, while others have reviewed multiple smoothing term packages for modeling GAMs. This study seeks to examine the performance of semiparametric models in the presence of different noise and outliers within the framework of GAMs through simulation. The study adopted four GAMs, cr, ps, tp, and gp, for simulated data with different noise and outliers with varying sample sizes. According to our investigation, the cr model performs well in terms of deviance for the majority of sample sizes and all types of noise. With higher sample sizes, the ps model frequently performs well, particularly in terms of AIC and GCV under noise that is heteroscedastic and Gaussian. The gp model excels with the smallest sample size under Gaussian and lognormal noise in terms of GCV, and the tp model frequently performs best under exponential and lognormal noise for larger samples in terms of AIC and GCV. For data containing outliers, the cr and tp models are effective with smaller sample sizes, while the gp model excels with larger sample sizes based on AIC and GCV. Regarding deviance, the cr model consistently performs best across all sample sizes. Our results show that the sample size and kind of noise in the data have a significant impact on the smoothing model’s performance. No single model consistently outperforms the others for all noise types and sample sizes, suggesting that the choice of model should be based on the specific goal of a study.

Incident duration models are often developed to assist incident management and traveler information dissemination. With recent advances in data collection and management, enormous achieved incident data are now available for incident model development. However, a large volume of data may present challenges to practitioners, such as data processing and computation. Besides, data that span multiple years may have inconsistency issues because of the data collection environments and procedures. A practical question may arise in the incident modeling community—Is that much data really necessary (“all-in”) to build models? If not, then how many data are necessary? To answer these questions, this study aims to investigate the relationship between the data sample sizes and the reliability of incident duration analysis models. This study proposed and demonstrated a sample size determination framework through a case study using data of over 47,000 incidents. This study estimated handfuls of hazard-based duration models with varying sample sizes. The relationships between sample size and model performance, along with estimate outcomes (i.e., coefficients and significance levels), were examined and visualized. The results showed that the variation of estimated coefficients decreases as the sample size increases, and becomes stabilized when the sample size reaches a critical threshold value. This critical threshold value may be the recommended sample size. The case study suggested a sample size of 6,500 to be enough for a reliable incident duration model. The critical value may vary significantly with different data and model specifications. More implications are discussed in the paper.

ABSTRACTThis study addresses equating issues with varying sample sizes using the Rasch model by examining how sample size affects the stability of item calibrations and person ability estimates. A resampling design was used to create 9 sample size conditions (200, 100, 50, 45, 40, 35, 30, 25, and 20), each replicated 10 times. Items were recalibrated using each of these 90 samples. The deviation of these calibrations from the full sample (N = 9,678) calibrations were then computed. The ability estimates for all 9,678 examinees were then recomputed 90 times using the item calibrations from each of the 90 different samples. The deviation of 90 sets of ability estimates from the original set of ability estimates was computed. This study found that less precision and item calibration instability occur with smaller sample sizes; however, the decreasing sample size has minimal effect on the person ability estimates.

The control charts are graphical tools and proven techniques to improve the performance of a process. Usually, the processes are not naturally controlled, so the use of control charts will help to reduce the variability and increase the stability of the process. In the traditional approach, control charts with fix sample size and constant sampling intervals were used to identify the changes in the process. While, control charts can be examined from different statistical and economical directions using different sampling schemes for achieving a better result. In past studies, it has been shown that np control charts show better results in detecting shifts by using variable sampling schemes but it is also important to consider how the cost of using variable sampling schemes will be, since the cost of a process depends on the parameters of the control chart. In this paper, the economic-statistical design of np control chart with variable sample size and sampling interval (VSSI) is formulated and then we compare and analyze the resulted obtained with other schemes. Results show significant improvement in terms of economic and statistical performance.