The Estimation of Location and Scale Parameters from Grouped Data

Biometrika ◽  
1954 ◽  
Vol 41 (3/4) ◽  
pp. 296 ◽  
Author(s):  
J. M. Hammersley ◽  
K. W. Morton
Keyword(s):  
Grouped Data ◽  
Scale Parameters

THE ESTIMATION OF LOCATION AND SCALE PARAMETERS FROM GROUPED DATA

Biometrika ◽  
1954 ◽  
Vol 41 (3-4) ◽  
pp. 296-301 ◽  
Author(s):  
J. M. HAMMERSLEY ◽  
K. W. MORTON
Keyword(s):  
Grouped Data ◽  
Scale Parameters

Ukuran Gejala Pusat Data Belum Dikelompokan(Kebakaran di Provinsi-Provinsi Tertentu di Indonesia Tahun 2015-2016)

2020 ◽  
Author(s):  
Riska Nurhapsari Santoso ◽  
Yudis Satrio Utomo ◽  
Yuliani Luturmasse
Keyword(s):  
Statistical Analysis ◽  
Frequency Distribution ◽  
Data Center ◽  
Grouped Data ◽  
Sample Data ◽  
Calculated Average

Abstract - Statistics is a framework of theories and methods that have been developed to collect, analyze, and write sample data in order to obtain useful conclusions. Statistics is the science of ways of collecting, classifying, analyzing, and searching for information related to the collection of data that investigations and conclusions based on evidence in the form of figures.Based on the results of the study can be concluded as follows: the size of the symptoms of the data center has not been grouped is the data compiled into the frequency distribution so that it does not have class intervals and midpoints of the class. Symptom Size Un-Grouped Data Center The size of the data center included in the statistical analysis is the calculated average (mean), median, mode, and fractil (quartile, decile, percentile)

Box-Cox Transformations

2017 ◽  
Author(s):  
Russell Cheng
Keyword(s):  
Maximum Likelihood ◽  
Normal Form ◽  
Maximum Likelihood Estimate ◽  
Likelihood Estimate ◽  
Grouped Data ◽  
Numerical Example ◽  
Alternative Method ◽  
Modified Likelihood

This chapter examines the well-known Box-Cox method, which transforms a sample of non-normal observations into approximately normal form. Two non-standard aspects are highlighted. First, the likelihood of the transformed sample has an unbounded maximum, so that the maximum likelihood estimate is not consistent. The usually suggested remedy is to assume grouped data so that the sample becomes multinomial. An alternative method is described that uses a modified likelihood similar to the spacings function. This eliminates the infinite likelihood problem. The second problem is that the power transform used in the Box-Cox method is left-bounded so that the transformed observations cannot be exactly normal. This biases estimates of observational probabilities in an uncertain way. Moreover, the distributions fitted to the observations are not necessarily unimodal. A simple remedy is to assume the transformed observations have a left-bounded distribution, like the exponential; this is discussed in detail, and a numerical example given.

scholarly journals Understanding, Choosing, and Unifying Multilevel and Fixed Effect Approaches

2020 ◽  
pp. 1-20
Author(s):  
Chad Hazlett ◽  
Leonard Wainstein
Keyword(s):  
Random Effects ◽  
Fixed Effects ◽  
Multilevel Models ◽  
Standard Errors ◽  
Point Estimate ◽  
Fe Model ◽  
Grouped Data ◽  
Coefficient Estimates ◽  
Political Science Education ◽  
Robust Standard Errors

Abstract When working with grouped data, investigators may choose between “fixed effects” models (FE) with specialized (e.g., cluster-robust) standard errors, or “multilevel models” (MLMs) employing “random effects.” We review the claims given in published works regarding this choice, then clarify how these approaches work and compare by showing that: (i) random effects employed in MLMs are simply “regularized” fixed effects; (ii) unmodified MLMs are consequently susceptible to bias—but there is a longstanding remedy; and (iii) the “default” MLM standard errors rely on narrow assumptions that can lead to undercoverage in many settings. Our review of over 100 papers using MLM in political science, education, and sociology show that these “known” concerns have been widely ignored in practice. We describe how to debias MLM’s coefficient estimates, and provide an option to more flexibly estimate their standard errors. Most illuminating, once MLMs are adjusted in these two ways the point estimate and standard error for the target coefficient are exactly equal to those of the analogous FE model with cluster-robust standard errors. For investigators working with observational data and who are interested only in inference on the target coefficient, either approach is equally appropriate and preferable to uncorrected MLM.

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