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We estimate historical stock returns for Swedish listed companies in a newly constructed data set of daily stock prices that spans more than 100 years. Stock returns exhibit all the familiar characteristics. The growth of the public sector depressed the stock market, and the process of globalization revitalized it. Banks played an important role in the early development of the stock market. There was little trading in the past, and we examine the effects on return measurement from missing data. Stock selection and the replacement of missing transaction prices through search back procedures or limit orders make little difference to a value-weighted stock price index, while ignoring the price effects of capital operations makes a big difference.
Standard portions or substitution of missing portion sizes with medians may generate bias when quantifying the dietary intake from FFQ. The present study compared four different methods to include portion sizes in FFQ.
Design
We evaluated three stochastic methods for imputation of portion sizes based on information about anthropometry, sex, physical activity and age. Energy intakes computed with standard portion sizes, defined as sex-specific medians (median), or with portion sizes estimated with multinomial logistic regression (MLR), ‘comparable categories’ (Coca) or k-nearest neighbours (KNN) were compared with a reference based on self-reported portion sizes (quantified by a photographic food atlas embedded in the FFQ).
Setting
The Danish Health Examination Survey 2007–2008.
Subjects
The study included 3728 adults with complete portion size data.
Results
Compared with the reference, the root-mean-square errors of the mean daily total energy intake (in kJ) computed with portion sizes estimated by the four methods were (men; women): median (1118; 1061), MLR (1060; 1051), Coca (1230; 1146), KNN (1281; 1181). The equivalent biases (mean error) were (in kJ): median (579; 469), MLR (248; 178), Coca (234; 188), KNN (−340; 218).
Conclusions
The methods MLR and Coca provided the best agreement with the reference. The stochastic methods allowed for estimation of meaningful portion sizes by conditioning on information about physiology and they were suitable for multiple imputation. We propose to use MLR or Coca to substitute missing portion size values or when portion sizes needs to be included in FFQ without portion size data.
This work deals with prediction of IBNR reserve under a different data ordering of the non-cumulative runoff triangle. The rows of the triangle are stacked, resulting in a univariate time series with several missing values. Under this ordering, two approaches entirely based on state space models and the Kalman filter are developed, implemented with two real data sets, and compared with two well-established IBNR estimation methods — the chain ladder and an overdispersed Poisson regression model. The remarks from the empirical results are: (i) computational feasibility and efficiency; (ii) accuracy improvement for IBNR prediction; and (iii) flexibility regarding IBNR modeling possibilities.
To investigate item non-response in a postal food-frequency questionnaire (FFQ), and to assess the effect of substituting/imputing missing values on dietary intake levels in the Norwegian Women and Cancer study (NOWAC). We have adapted and probably for the first time applied k nearest neighbours (KNN) imputation to FFQ data.
Design
Data from a recent reproducibility study were used. The FFQ was mailed twice (test–retest) about 3 months apart to the same subjects. Missing responses in the test FFQ were imputed using the null value (frequencies = null, amount = smallest), the sample mode, the sample median, KNN, and retest values.
Setting
A methodological substudy of NOWAC, a national population-based cohort.
Subjects
A random sample of 2000 women aged 46–75 years was drawn from the cohort in 2002 (response 75%). The imputation methods were compared for 1430 women who completed at least 50% of the test FFQ.
Results
We imputed 16% missing values in the overall test data matrix. Compared to null value imputation, the largest differences in estimated dietary intake were seen for KNN, and for food items with a high proportion of missing. Imputation with retest values increased total energy intake, indicating that not all missing values are caused by respondents failing to specify no consumption, and that null value imputation may lead to underestimation and misclassification.
Conclusion
Missing values in FFQs present a methodological challenge. We encourage the application and evaluation of newer imputation methods, including KNN, which may reduce imputation errors and give more accurate intake estimates.
By using the alternating projection theorem of J. von Neumann, we obtain explicit formulae for the best linear interpolator and interpolation error of missing values of a stationary process. These are expressed in terms of multistep predictors and autoregressive parameters of the process. The key idea is to approximate the future by a finite-dimensional space.
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