Analytic clustered SEs

[grantmcdermott]

As discussed offline, I just added these to dbreg. See here for the implementation and some examples (validated against fixest). Should be a relatively low lift to adapt to Python. grantmcdermott/dbreg#29

(You want to look at the main dbreg.R file. Apologies; it's gotten long and unwieldy. I plan to modularize soon.)

I haven't benchmarked against the current bootstrap approach of duckreg, but I'm pretty pleased with the example I highlight in the PR (and updated README). Clustered SEs on a 180m row NYC taxi data in < 3 seconds :-)

dbreg(
   tip_amount ~ fare_amount + passenger_count | month + vendor_name,
   path     = "read_parquet('nyc-taxi/**/*.parquet')",
   vcov     = ~month,    # clustered SEs
   strategy = "compress" # skip auto strategy overhead
)
#> [dbreg] Using strategy: compress
#> [dbreg] Executing compress strategy SQL
#>
#> Compressed OLS estimation, Dep. Var.: tip_amount 
#> Observations.: 178,544,324 (original) | 70,782 (compressed)
#> Standard Errors: Clustered (12 clusters)
#>                  Estimate Std. Error  t value   Pr(>|t|)    
#> fare_amount      0.106744   0.000657 162.4934  < 2.2e-16 ***
#> passenger_count -0.029086   0.001030 -28.2278 1.2923e-11 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> RMSE: 1.7                 Adj. R2: 0.243549