Table 1 MSE of conventional estimators for chosen values of \(\rho _{xy}\), n, r, and \(\kappa\).

From: Optimal class of memory type imputation methods for time-based surveys using EWMA statistics

Strategies

\(\rho _{xy}\)

n

r

Estimators

Strategy 1

\(t_{r_1}\)

\(t_i,~i=1,4\)

\(t_{s_1}\)

\(t_{s_4}\)

 

0.1

15

12

325641.90

24.72

19.51

20.02

14

18671.68

21.17

17.39

17.60

150

120

4.45

2.36

2.33

2.32

140

4.04

1.98

1.95

1.95

300

240

1.84

1.02

1.02

1.02

280

1.65

0.86

0.83

0.83

0.5

15

12

33788.55

19.67

16.27

15.47

14

2960.04

16.18

13.89

11.95

150

120

2.76

1.89

1.86

1.86

140

2.37

1.54

1.50

1.50

300

240

1.16

0.83

0.82

0.82

280

0.98

0.76

0.64

0.64

0.9

15

12

1546.08

6.96

6.43

6.01

14

1432.05

5.25

4.94

4.98

150

120

0.99

0.94

0.87

0.87

140

0.61

0.53

0.50

0.50

300

240

0.45

0.43

0.41

0.41

280

0.30

0.25

0.22

0.22

Strategy 2

   

\(t_{r_2}\)

\(t_i,~i=2,5\)

\(t_{s_2}\)

\(t_{s_5}\)

 

0.1

15

12

408285.30

24.21

19.15

19.88

14

20024.02

21.04

17.30

17.49

150

120

5.05

2.36

2.32

2.32

140

4.21

1.98

1.95

1.95

300

240

2.14

1.03

1.02

1.02

280

1.73

0.84

0.81

0.81

0.5

15

12

42357.76

18.10

15.10

13.86

14

3173.08

15.75

13.55

12.69

150

120

2.89

1.76

1.75

1.74

140

2.41

1.48

1.45

1.46

300

240

1.23

0.77

0.76

0.76

280

0.99

0.72

0.62

0.62

0.9

15

12

1783.81

4.30

4.06

3.63

14

1534.28

4.02

3.82

3.87

150

120

0.59

0.55

0.45

0.45

140

0.50

0.43

0.38

0.38

300

240

0.26

0.23

0.20

0.19

280

0.24

0.19

0.16

0.16

Strategy 3

   

\(t_{r_3}\)

\(t_i,~i=3,6\)

\(t_{s_3}\)

\(t_{s_6}\)

 

0.1

15

12

82670.21

26.25

20.55

20.83

14

1375.27

22.80

18.56

18.61

150

120

2.99

2.38

2.34

2.34

140

2.17

2.00

1.97

1.97

300

240

1.32

1.03

1.02

1.02

280

0.92

0.85

0.83

0.83

0.5

15

12

8595.05

24.27

19.47

19.22

14

235.20

21.72

17.86

17.87

150

120

2.44

2.18

2.14

2.15

140

1.97

1.90

1.86

1.87

300

240

1.06

0.96

0.93

0.93

280

0.82

0.87

0.79

0.79

0.9

15

12

261.71

21.32

17.61

17.52

14

124.51

21.05

17.48

17.46

150

120

1.93

1.89

1.87

1.87

140

1.83

1.82

1.80

1.80

300

240

0.84

0.81

0.79

0.78

280

0.79

0.77

0.75

0.75

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