scholarly journals Revisiting the critical values of the Lilliefors test: towards the correct agrometeorological use of the Kolmogorov-Smirnov framework

Bragantia ◽  
2014 ◽  
Vol 73 (2) ◽  
pp. 192-202 ◽  
Author(s):  
Gabriel Constantino Blain
Keyword(s):  
Monte Carlo ◽  
Critical Values ◽  
Type I ◽  
Significance Level ◽  
Normal Distributions ◽  
Monte Carlo Experiments ◽  
Distribution Parameters ◽  
Lilliefors Test ◽  
Kolmogorov Smirnov ◽  
Type Ii Errors

Several studies have applied the Kolmogorov-Smirnov test (KS) to verify if a particular parametric distribution can be used to assess the probability of occurrence of a given agrometeorological variable. However, when this test is applied to the same data sample from which the distribution parameters have been estimated, it leads to a high probability of failure to reject a false null hypothesis. Although the Lilliefors test had been proposed to remedy this drawback, several studies still use the KS test even when the requirement of independence between the data and the estimated parameters is not met. Aiming at stimulating the use of the Lilliefors test, we revisited the critical values of the Lilliefors test for both gamma (gam) and normal distributions, provided easy-to-use procedures capable of calculating the Lilliefors test and evaluated the performance of these two tests in correctly accepting a hypothesized distribution. The Lilliefors test was calculated by using critical values previously presented in the scientific literature (KSLcrit) and those obtained from the procedures proposed in this study (NKSLcrit). Through Monte Carlo simulations we demonstrated that the frequency of occurrence of Type I (II) errors associated with the KSLcrit may be unacceptably low (high). By using the NKSLcrit we were able to meet the significance level in all Monte Carlo experiments. The NKSLcrit also led to the lowest rate of Type II errors. Finally, we also provided polynomial equations that eliminate the need to perform statistical simulations to calculate the Lilliefors test for both gam and normal distributions.

scholarly journals Testing for Cointegration in the Presence of Moving Average Errors

2012 ◽  
Vol 4 (2) ◽  
Author(s):  
Mindy Mallory ◽  
Sergio H. Lence
Keyword(s):  
Monte Carlo ◽  
Sample Size ◽  
Moving Average ◽  
Commodity Prices ◽  
Asymptotic Distributions ◽  
Critical Values ◽  
Monte Carlo Experiments ◽  
Cointegration Tests ◽  
Johansen Cointegration ◽  
Actual Test

AbstractThis study explores performance of the Johansen cointegration statistics on data containing negative moving average (NMA) errors. Monte Carlo experiments demonstrate that the asymptotic distributions of the statistics are sensitive to NMA parameters, and that using the standard 5% asymptotic critical values results in severe underestimation of the actual test sizes. We demonstrate that problems associated with NMA errors do not decrease as sample size increases; instead, they become more severe. Further we examine evidence that many U.S. commodity prices are characterized by NMA errors. Pretesting data is recommended before using standard asymptotic critical values for Johansen’s cointegration tests.

scholarly journals Statistical Tests for Cross-Validation of Kriging Models

2021 ◽  
Author(s):  
Jack P. C. Kleijnen ◽  
Wim C. M. van Beers
Keyword(s):  
Monte Carlo ◽  
Cross Validation ◽  
Statistical Tests ◽  
Computer Experiments ◽  
Simulation Models ◽  
Statistical Test ◽  
Type I ◽  
Monte Carlo Experiments ◽  
Leave One Out ◽  
Kriging Predictor

Kriging or Gaussian process models are popular metamodels (surrogate models or emulators) of simulation models; these metamodels give predictors for input combinations that are not simulated. To validate these metamodels for computationally expensive simulation models, the analysts often apply computationally efficient cross-validation. In this paper, we derive new statistical tests for so-called leave-one-out cross-validation. Graphically, we present these tests as scatterplots augmented with confidence intervals that use the estimated variances of the Kriging predictors. To estimate the true variances of these predictors, we might use bootstrapping. Like other statistical tests, our tests—with or without bootstrapping—have type I and type II error probabilities; to estimate these probabilities, we use Monte Carlo experiments. We also use such experiments to investigate statistical convergence. To illustrate the application of our tests, we use (i) an example with two inputs and (ii) the popular borehole example with eight inputs. Summary of Contribution: Simulation models are very popular in operations research (OR) and are also known as computer simulations or computer experiments. A popular topic is design and analysis of computer experiments. This paper focuses on Kriging methods and cross-validation methods applied to simulation models; these methods and models are often applied in OR. More specifically, the paper provides the following; (1) the basic variant of a new statistical test for leave-one–out cross-validation; (2) a bootstrap method for the estimation of the true variance of the Kriging predictor; and (3) Monte Carlo experiments for the evaluation of the consistency of the Kriging predictor, the convergence of the Studentized prediction error to the standard normal variable, and the convergence of the expected experimentwise type I error rate to the prespecified nominal value. The new statistical test is illustrated through examples, including the popular borehole model.

scholarly journals The probabilities of type I and II error of null of cointegration tests: A Monte Carlo comparison

PLoS ONE ◽  
2022 ◽  
Vol 17 (1) ◽  
pp. e0259994
Author(s):  
Ahmet Faruk Aysan ◽  
Ibrahim Guney ◽  
Nicoleta Isac ◽  
Asad ul Islam Khan
Keyword(s):  
Monte Carlo ◽  
Time Trend ◽  
Type I Error ◽  
Linear Time ◽  
Critical Values ◽  
Type I ◽  
Sample Sizes ◽  
Linear Time Trend ◽  
Lm Test ◽  
Cointegration Tests

This paper evaluates the performance of eight tests with null hypothesis of cointegration on basis of probabilities of type I and II errors using Monte Carlo simulations. This study uses a variety of 132 different data generations covering three cases of deterministic part and four sample sizes. The three cases of deterministic part considered are: absence of both intercept and linear time trend, presence of only the intercept and presence of both the intercept and linear time trend. It is found that all of tests have either larger or smaller probabilities of type I error and concluded that tests face either problems of over rejection or under rejection, when asymptotic critical values are used. It is also concluded that use of simulated critical values leads to controlled probability of type I error. So, the use of asymptotic critical values may be avoided, and the use of simulated critical values is highly recommended. It is found and concluded that the simple LM test based on KPSS statistic performs better than rest for all specifications of deterministic part and sample sizes.

An old friend is better than two new ones? Approaches to market research in the context of digital transformation for the antitrust laws enforcement

2020 ◽  
pp. 37-55 ◽  
Author(s):  
A. E. Shastitko ◽  
O. A. Markova
Keyword(s):  
Business Models ◽  
Rapid Development ◽  
Digital Transformation ◽  
Market Definition ◽  
Type I ◽  
Type Ii ◽  
Digital Platforms ◽  
Advantages And Disadvantages ◽  
Pass Through ◽  
Type Ii Errors

Digital transformation has led to changes in business models of traditional players in the existing markets. What is more, new entrants and new markets appeared, in particular platforms and multisided markets. The emergence and rapid development of platforms are caused primarily by the existence of so called indirect network externalities. Regarding to this, a question arises of whether the existing instruments of competition law enforcement and market analysis are still relevant when analyzing markets with digital platforms? This paper aims at discussing advantages and disadvantages of using various tools to define markets with platforms. In particular, we define the features of the SSNIP test when being applyed to markets with platforms. Furthermore, we analyze adjustment in tests for platform market definition in terms of possible type I and type II errors. All in all, it turns out that to reduce the likelihood of type I and type II errors while applying market definition technique to markets with platforms one should consider the type of platform analyzed: transaction platforms without pass-through and non-transaction matching platforms should be tackled as players in a multisided market, whereas non-transaction platforms should be analyzed as players in several interrelated markets. However, if the platform is allowed to adjust prices, there emerges additional challenge that the regulator and companies may manipulate the results of SSNIP test by applying different models of competition.

The Potential of Tax Surprises to Affect Measures of Tax Avoidance and Researchers' Inferences

2018 ◽  
Vol 41 (1) ◽  
pp. 1-30 ◽  
Author(s):  
Chelsea Rae Austin
Keyword(s):  
Stock Options ◽  
Tax Avoidance ◽  
Type I ◽  
Type Ii ◽  
Effective Tax Rate ◽  
Tax Rate ◽  
Tax Savings ◽  
Type Ii Errors

ABSTRACT While not explicitly stated, many tax avoidance studies seek to investigate tax avoidance that is the result of firms' deliberate actions. However, measures of firms' tax avoidance can also be affected by factors outside the firms' control—tax surprises. This study examines potential complications caused by tax surprises when measuring tax avoidance by focusing on one specific type of surprise tax savings—the unanticipated tax benefit from employees' exercise of stock options. Because the cash effective tax rate (ETR) includes the benefits of this tax surprise, the cash ETR mismeasures firms' deliberate tax avoidance. The analyses conducted show this mismeasurement is material and can lead to both Type I and Type II errors in studies of deliberate tax avoidance. Suggestions to aid researchers in mitigating these concerns are also provided.

The Effect of Stage of Development and Financial Health on Auditor Decision Behavior in the Going-Concern Task

1999 ◽  
Vol 18 (1) ◽  
pp. 37-54 ◽  
Author(s):  
Andrew J. Rosman ◽  
Inshik Seol ◽  
Stanley F. Biggs
Keyword(s):  
Information Acquisition ◽  
Type I ◽  
Type Ii ◽  
Financial Health ◽  
Inference Problem ◽  
Going Concern ◽  
Start Up ◽  
Mitigating Factors ◽  
Type Ii Errors ◽  
Problem Representations

The effect of different task settings within an industry on auditor behavior is examined for the going-concern task. Using an interactive computer process-tracing method, experienced auditors from four Big 6 accounting firms examined cases based on real data that differed on two dimensions of task settings: stage of organizational development (start-up and mature) and financial health (bankrupt and nonbankrupt). Auditors made judgments about each entity's ability to continue as a going concern and, if they had substantial doubt about continued existence, they listed evidence they would seek as mitigating factors. There are seven principal results. First, information acquisition and, by inference, problem representations were sensitive to differences in task settings. Second, financial mitigating factors dominated nonfinancial mitigating factors in both start-up and mature settings. Third, auditors' behavior reflected configural processing. Fourth, categorizing information into financial and nonfinancial dimensions was critical to understanding how auditors' information acquisition and, by inference, problem representations differed across settings. Fifth, Type I errors (determining that a healthy company is a going-concern problem) differed from correct judgments in terms of information acquisition, although Type II errors (determining that a problem company is viable) did not. This may indicate that Type II errors are primarily due to deficiencies in other stages of processing, such as evaluation. Sixth, auditors who were more accurate tended to follow flexible strategies for financial information acquisition. Finally, accurate performance in the going-concern task was found to be related to acquiring (1) fewer information cues, (2) proportionately more liquidity information and (3) nonfinancial information earlier in the process.

scholarly journals Detecting Heterogeneity of Substitution Along DNA and Protein Sequences

Genetics ◽  
1996 ◽  
Vol 143 (1) ◽  
pp. 589-602 ◽  
Author(s):  
Peter J E Goss ◽  
R C Lewontin
Keyword(s):  
Null Hypothesis ◽  
Nonuniform Distribution ◽  
Critical Values ◽  
Third Order ◽  
Variance Test ◽  
Data Set ◽  
Significance Level ◽  
Uniformly Most Powerful Test ◽  
Interval Lengths ◽  
Uniformly Most Powerful

Abstract Regions of differing constraint, mutation rate or recombination along a sequence of DNA or amino acids lead to a nonuniform distribution of polymorphism within species or fixed differences between species. The power of five tests to reject the null hypothesis of a uniform distribution is studied for four classes of alternate hypothesis. The tests explored are the variance of interval lengths; a modified variance test, which includes covariance between neighboring intervals; the length of the longest interval; the length of the shortest third-order interval; and a composite test. Although there is no uniformly most powerful test over the range of alternate hypotheses tested, the variance and modified variance tests usually have the highest power. Therefore, we recommend that one of these two tests be used to test departure from uniformity in all circumstances. Tables of critical values for the variance and modified variance tests are given. The critical values depend both on the number of events and the number of positions in the sequence. A computer program is available on request that calculates both the critical values for a specified number of events and number of positions as well as the significance level of a given data set.

scholarly journals A novel algorithm to detect non-wear time from raw accelerometer data using deep convolutional neural networks

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Shaheen Syed ◽  
Bente Morseth ◽  
Laila A. Hopstock ◽  
Alexander Horsch
Keyword(s):  
Threshold Value ◽  
Detection Algorithm ◽  
Classification Model ◽  
Type I ◽  
Accelerometer Data ◽  
Deep Convolutional Neural Networks ◽  
Major Drawback ◽  
Wear Time ◽  
Detection Algorithms ◽  
Type Ii Errors

AbstractTo date, non-wear detection algorithms commonly employ a 30, 60, or even 90 mins interval or window in which acceleration values need to be below a threshold value. A major drawback of such intervals is that they need to be long enough to prevent false positives (type I errors), while short enough to prevent false negatives (type II errors), which limits detecting both short and longer episodes of non-wear time. In this paper, we propose a novel non-wear detection algorithm that eliminates the need for an interval. Rather than inspecting acceleration within intervals, we explore acceleration right before and right after an episode of non-wear time. We trained a deep convolutional neural network that was able to infer non-wear time by detecting when the accelerometer was removed and when it was placed back on again. We evaluate our algorithm against several baseline and existing non-wear algorithms, and our algorithm achieves a perfect precision, a recall of 0.9962, and an F1 score of 0.9981, outperforming all evaluated algorithms. Although our algorithm was developed using patterns learned from a hip-worn accelerometer, we propose algorithmic steps that can easily be applied to a wrist-worn accelerometer and a retrained classification model.

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