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1 NLAS 7 2 Excel Excel Excel i

2 ii

3 Excel PC 1 Excel Excel 2 x y x y iii

4 yuhikaku-nibu.txt-nifty.com/blog/2008/10/post-1d7f.html Cook book iv

5 Ph.D., R The discontinuous Trend Unit Root Test When the Break Point is Misspecified, Mathematics and Computers in Simulation, 48 (4), Elsevier, 1999; Power Comparisons of Discontinuous Trend Unit Root v

6 Tests, in C. Hsiao, K. Morimune, and J. L. Powell (eds.), Nonlinear Statistical Modeling: Essays in Honor of Takeshi Amemiya, Cambridge University Press, 2001; Discontinuous Trend Unit Root Test with a Break Interval, The Kyoto Economic Review, 73 (1), COLUMN A Random Walk Stochastic Volatility Model for Income Inequality, Japan and the World Economy, 36, 2015; Bayesian Estimation of Persistent Income Inequality Using the Lognormal Stochastic Volatility Model, Journal of Income Distribution, 21 (1), 2012; Grouped Data Estimation and Testing of Gini Coefficient Using Lognormal Distributions, Sankhya, Ser. B, 73(2), COLUMN Asymptotic Properties of the Efficient Estimators for Cointegrating Regression Models with Serially Dependent Errors, Journal of Econometrics, 149 (2), 2009; Model Selection Criteria in Multivariate Models with Multiple Structural Changes, Journal of Econometrics, 164 (2), 2011; Model Selection Criteria for the Leads-and-Lags Cointegrating Regression, Journal of Econometrics, 169 (2), 2012; Testing for Multiple Structural Changes with Non-Homogeneous Regressors, Journal of Time Series Econometrics, 7 (1), 2015; 2016 vi

7 i ii v xiv xv 1 1 Σ GDP vii

8 Excel viii

9 Excel Excel 2 3 Excel ix

10 4 2 e MSE 4 x

11 10 1 P 2 1σ 2 2σ 2 3σ 2 4σ 2 p σx 2 = σy 2 3 σx 2 σ2 y AIC σ 2 3 P 4 R 2 xi

12 5 6 t P BLUE AR PAC PAC 4 AC 5 MA AR 6 ARIMA GDP Z xii

13 n =5, 10, 15 n =20, χ 2 6 t 7 F COLUMN CPI JIS AIC ARCH 13 1 xiii

14 AVERAGE,, BINOMDIST,,,, CHIDIST, CHIINV CHISQ.DIST, CORREL F.INV FDIST FINV GEOMEAN, KURT MAX MEDIAN MIN MODE NORMDIST,,, NORMINV NORMSDIST, NORMSINV POISSON,, QUARTILE RANDBETWEEN RANK.AVG, SKEW STDEV, STDEVP SUMPRODUCT TDIST T.INV TINV TRIMMEAN VAR, VARP,, AC AIC AR ARCH ARIMA auto-regressive integrated moving average process ARMA BLUE Box Jenkins Box Pierce CFA CI CPI DI EFA ESS F F GARCH GDPgross domestic product GDP GMM i.i.d. IIP Ljung Box MA MSE 2 PAC PPI PPP P P-value, RSS TOPIX TSS t t statisitic t Akaike information criterionaic,, Z outliner,

15 consistent estimator, consistency, generalized method of momentsgmm moving average moving averagema innovation factor score factor loading factor analysis weight Epanechnikov,,,, explained sum of squaresess class, factorial 2 Gauss Markov theorem,,,, probability density function weighted average, hypothesis testing one-sided test trimmed mean sample size geometric mean reject rejection region standardization expectation null hypothesis common factor, communality covariance, interval estimation combination cluster analysis Cramer Rao s inequality duration model coefficient of determination power power function power curve confirmatory factor

16 analysiscfa test statisitic indices of industrial productioniip updating,, structural change purchasing power parity PPP efficiency,, producer price index PPI GDP Cauchy Schwarz s inequality,,, CI maximum likelihood estimation,, best linear unbiased estimatorblue, residual sum of squaresrss, scatter plot,, experiment auto-regressive moving averagearma auto-regressionar posterior probability auto-correlation auto-correlation coefficient AC, posterior distribution event prior probability natural conjugate distribution prior distribution AIC least squares estimate 2 least squares estimator 2 least squares method Gini coefficient,, quartile inter quartile range, simulation accept

17 , degrees of freedom 12 marginal probability marginal probability function,, marginal density function permutation conditional probability, conditional variance, conditional mean, conditional density function law of small numbers consumer price index CPI, shock diagnostic test estimator Starjes formula Stirling s formula, Spearman s rank correlation coefficient,,, moment moment generating function, kurtosis, total sum of squarestss correlation coefficient,, relative frequency type error, 3 law of large numbers,,,, type error alternative hypothesis multi-colinearity

18 , exploratory factor analysisefa simple alternative hypothesis elasticity Chebyshev s inequality,, central limit theorem,, DI goodness of fit point estimation, statistically significant statistic joint probability joint probability function,, TOPIX specific factor independent events, (independent and identically distributedi. i. d. frequency frequency distribution table, 2 binomial expansion, binomial distribution 2 noise, percentile parameter, Pareto coefficient Pareto distribution range, discriminant analysis histogram, normalization,, standard normal distribution, standard deviation, sample, AC AC sample covariance sample space,

19 sample autocorrelation coefficient, sample correlation coefficient,,,, sample variance, Sampling distribution sample mean, partial auto-correlation PAC frequentist, Fisher information heteroscedasticity, composite alternative hypothesis unbiasedness,, subset unbiased estimator Black-Scholes formula,,, quantile contingency table variance,, distribution function, mean, 2 mean squared errormse,, Bayesian method Bernoulli experiments,, partial correlation coefficient Poisson probability function, interpolation complement population,,,, volatility,, density function random sample

20 median, mode method of moments, significant,, significance level, P, likelihood likelihood function, likelihood ratio likelihood ratio test,, random number random seed discrete random variable two-sided test critical value cumulative probability distribution function, cumulative relative frequency, cumulative frequency continuous random variable, Lorenz curve, skewness,

21 Statistics: Data Science for Social Studies, 2nd ed http:// c 2015, Kimio Morimune, Nobuhiko Terui, Mitsuru Nakagawa, Haruhisa Nishino, Eiji Kurozumi. Printed in Japan ISBN

最小2乗法

最小2乗法 2 2012 4 ( ) 2 2012 4 1 / 42 X Y Y = f (X ; Z) linear regression model X Y slope X 1 Y (X, Y ) 1 (X, Y ) ( ) 2 2012 4 2 / 42 1 β = β = β (4.2) = β 0 + β (4.3) ( ) 2 2012 4 3 / 42 = β 0 + β + (4.4) ( )